thesis subm
Heidelberg, September 2011
-Star Formation in the COSMOS Field-
A radio view on the build-up of
stellar mass over 12 billion years
CO(5-4)
Dust Continuum
Radio Continuum
A
B
2"
ACS-F814W
13 kpc
Alexander Karim
Dissertation
submitted to the
Combined Faculties of the Natural Sciences and Mathematics
of the Ruperto-Carola-University of Heidelberg, Germany
for the degree of
Doctor of Natural Sciences
Put forward by
Dipl. Phys. Alexander Karim
born in: Mönchengladbach, Germany
Oral examination: 23rd of November, 2011.
–Star Formation in the COSMOS Field–
A radio view on the build-up of
stellar mass over 12 billion years
Referees:
Prof. Dr. Hans-Walter Rix (MPIA Heidelberg)
Prof. Dr. Ralf Klessen (ITA Heidelberg)
Stellares Massenwachstum über 12 Milliarden Jahre aus Radiosicht
In der vorliegenden Arbeit wird die Evolution von Galaxien im Hinblick auf ihre Fähigkeit
Sterne zu bilden untersucht, wobei die vorhandenen umfangreichen Multi-Wellenlängen
Datensätze im 2 Quadratgrad grossen COSMOS Feld genutzt werden. Tiefe Beobachtungen
im Radiokontinuum mit dem Very Large Array bei einer Frequenz von 1.4 GHz (entprechend
einer Wellenlänge von 20 cm) bilden das Fundament einer Analyse der kosmischen Sternentstehungsgeschichte, die nicht durch Staub verfälscht wird. Ein neu entwickelter Bildstapelalgorithmus ermöglicht einen einmalig repräsentativen Einblick in die Evolution der
mittleren Sternentstehungsrate bis hin zu Galaxien von geringem (stellaren) Massengehalt seit einer Rotverschiebung von z ∼ 3 (ca. 2 Milliarden Jahre nach dem Urknall). Die
Ergebnisse stimmen gut mit denen anderer Sternentstehungsdiagnostiken überein, welche
oftmals von grossen Staubkorrekturen und signifikant schlechterer Statistik geprägt sind.
Ein Hauptergebnis dieser Dissertation ist die Identifikation einer konstanten charakteristischen Masse sternbildender Galaxien. Es legt nahe, dass Galaxien von ähnlicher Masse
wie unsere Milchstrasse stets die Hauptschauplätze von Sternbildung waren. Oft diskutierte Szenarien, in denen diese charakteristische Masse im Laufe der kosmischen Zeit abnehmen sollte, werden damit widerlegt. In dieser Arbeit wurde zudem erfolgreich nach den
extremsten sternbildenden Umgebungen im frühen Universum (. 1.5 Milliarden Jahre nach
seiner Entstehung) gesucht. Jene stellen wichtige Objekte zur Eingrenzung der kosmischen
Strukturbildung und der durch Staub verdeckten Sternentstehung zu frühesten Zeiten dar.
Eine detaillierte Fallstudie enthüllt grosse Mengen an molekularem Gas aber auch einen
versteckten aktiven Galaxienkern in einem solchen extrem sternbildenden Objekt. Dieses
Ergebnis demonstriert die Vielfalt dieser kosmologisch wichtigen Galaxienpopulation.
A radio view on the build-up of stellar mass over 12 billion years
In this thesis I study the evolution of galaxies with a special focus on their star forming
ability by using the extensive multi-wavelength data sets available for the 2 square degree
COSMOS deep field. The deep radio continuum data from Very Large Array observations at
a frequency of 1.4 GHz (a wavelength of 20 cm) form the basis of my analysis of the cosmic
star formation history unaffected by dust obscuration. A newly developed stacking algorithm enabled an unprecedentedly representative view on the evolution of the average star
formation rate within galaxies down to low limiting (stellar) masses since a redshift of z ∼ 3
(i.e. ∼ 2 billion years after the Big Bang). My findings are in good agreement with results
from different star formation diagnostics that often suffer from large dust corrections or
significantly worse statistics. A main result of this thesis is the identification of a constant
characteristic mass for star forming galaxies. It implies that galaxies with masses similar
to our Milky Way have always been the main sites of star formation. Therefore the often
debated ’downsizing scenario’ where the characteristic mass decreases with cosmic time is
ruled out. In the young universe (. 1.5 billion years of cosmic age) I successfully searched
for the most extreme star forming environments. These provide critical constraints on cosmic structure formation and dust enshrouded star formation at early times. A detailed case
study not only reveals large amounts of molecular gas but also a powerful hidden active
galactic nucleus in one such massive starburst. This finding demonstrates the diversity of
this cosmologically important galaxy population.
Die Straße nämlich,
die Hauptstraße des Dorfes,
führte nicht zum Schloßberg,
sie führte nur nahe heran,
dann aber, wie absichtlich,
bog sie ab,
und wenn sie sich auch vom Schloss nicht entfernte,
so kam sie ihm doch auch nicht näher.
Franz Kafka, D as Schloß
x
Contents
Contents
xi
List of Figures
xv
List of Tables
xvii
1. Introduction
1.1. Panchromatic galaxy evolution in a dark universe . . . . . . . . .
1.2. Tools to study cosmic evolution: Simulations and surveys . . . . .
1.2.1. Redshift surveys and deep fields . . . . . . . . . . . . . . . .
1.3. The global population of galaxies over time . . . . . . . . . . . . .
1.3.1. The growth of stellar mass through star formation . . . . .
1.3.2. The role of starbursts in galaxy evolution and observational
1.4. Essentials: Star formation and its measurement . . . . . . . . . .
1.4.1. Star formation rates in galaxies from (far-IR) emission . . .
1.4.2. The (far-)IR/radio correlation in star forming galaxies . . .
1.5. Observatories and instruments . . . . . . . . . . . . . . . . . . . .
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cosmology
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2. Overview
3. Seeing through the noise: Pushing observational limits via
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. Image stacking techniques . . . . . . . . . . . . . . . . . . . .
3.3. Full implementation of an image stacking algorithm . . . . .
3.3.1. Workflow and performance . . . . . . . . . . . . . . . .
3.3.2. Flux measurement and error estimation . . . . . . . .
3.3.3. Additional software features and prospects . . . . . .
3.3.4. Applications of the image stacking routine . . . . . . .
3.4. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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image stacking
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4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2. The pan-chromatic COSMOS data used . . . . . . . . . . . . .
4.2.1. VLA-COSMOS radio data . . . . . . . . . . . . . . . . . .
4.2.2. A 3.6 µm selected sample of COSMOS galaxies . . . . .
4.2.3. Estimation of stellar masses . . . . . . . . . . . . . . . .
4.2.4. Spectral classification . . . . . . . . . . . . . . . . . . . .
4.2.5. AGN contamination . . . . . . . . . . . . . . . . . . . . .
4.2.6. Completeness considerations . . . . . . . . . . . . . . .
4.3. Image stacking at radio continuum wavelengths . . . . . . . .
COSMOS
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CONTENTS
4.3.1. Median stacking and error estimates . . . . . . . . . . . . . . . . . . . . . 48
4.3.2. Radio stacking derived star formation rates . . . . . . . . . . . . . . . . . 49
4.4. The evolution of the specific SFR . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.4.1. The relation between SSFR and stellar mass . . . . . . . . . . . . . . . . . 56
4.4.2. A potential upper limit to the average SSFR . . . . . . . . . . . . . . . . . 57
4.4.3. The mass-dependent SSFR-evolution . . . . . . . . . . . . . . . . . . . . . 59
4.4.4. Comparison to other studies . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.5. The selection of star forming galaxies . . . . . . . . . . . . . . . . . . . . . . . . 64
4.5.1. Highly active star forming galaxies . . . . . . . . . . . . . . . . . . . . . . 64
4.5.2. (s)BzK galaxies at z ∼ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.6. Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5. A constant characteristic mass for star forming galaxies
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5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2. The mass distribution function of the SFRD at fixed redshift
. . . . . . . . . . . 70
5.3. The evolution of the SFRD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.4. Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6. Extreme star formation within 1.5 Gyr after the Big Bang: a case study
85
6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.2. Target selection and observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2.1. Panchromatic COSMOS data and selection criteria . . . . . . . . . . . . . 89
6.2.2. Keck/DEIMOS observations
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6.2.3. Millimeter continuum and CO-line observations . . . . . . . . . . . . . . . 91
6.3. Source properties of Vd-17871 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.3.1. The molecular gas reservoir . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.3.2. Panchromatic morphology and ultraviolet to mid-IR photometry
. . . . . 92
6.3.3. The thermal dust to radio continuum emission properties and indications
for nuclear activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.4. The diversity of extreme starbursts at high redshift
7. Summary and outlook
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7.1. A newly developed image stacking routine . . . . . . . . . . . . . . . . . . . . . . 107
7.2. The mass-uniform evolution of the average star formation rate . . . . . . . . . . 108
7.2.1. Results presented in this thesis . . . . . . . . . . . . . . . . . . . . . . . . 108
7.2.2. Prospects for ongoing and future research . . . . . . . . . . . . . . . . . . 110
7.3. The mass-resolved cosmic star formation history . . . . . . . . . . . . . . . . . . 113
7.3.1. Results presented in this thesis . . . . . . . . . . . . . . . . . . . . . . . . 113
7.3.2. Prospects for ongoing and future research . . . . . . . . . . . . . . . . . . 114
7.4. Extreme starbursts < 1.5 Gyr after the Big Bang . . . . . . . . . . . . . . . . . . 115
7.4.1. Results presented in this thesis . . . . . . . . . . . . . . . . . . . . . . . . 116
7.4.2. Prospects for ongoing and future research . . . . . . . . . . . . . . . . . . 116
Appendix
xii
123
CONTENTS
A. Statistical background
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A.1. Noise weighted estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
A.2. Bootstrapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
A.3. Estimating the stellar mass representativeness of a flux-limited sample . . . . . 127
B. Calculus and formulae
B.1. Measures of cosmological distances . . . . . . . . . . . . . . . . . . . . . .
B.2. K-corrections at radio and mm wavelengths . . . . . . . . . . . . . . . . . .
B.3. Visualizing luminosity and mass functions in the Schechter representation
B.4. 12 CO line emission tracing molecular gas . . . . . . . . . . . . . . . . . . .
B.5. Dust emission properties and derivation of dust mass . . . . . . . . . . . .
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C. Fundamental constants, units and definitions
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Acknowledgments
146
References
148
xiii
CONTENTS
xiv
List of Figures
1.1.
1.2.
1.3.
1.4.
1.5.
1.6.
1.7.
1.8.
The artist’s view on cosmic history . . . . . . . . . . . . . .
Hubble Space Telescope survey of the COSMOS field . . .
Cosmological simulation of a 2 deg2 field . . . . . . . . . .
Cosmic star formation history . . . . . . . . . . . . . . . . .
The COSMOS AzTEC-3 galaxy proto-cluster at z = 5.3 . . .
The star formation law for normal galaxies and starbursts
The relation between far-infrared and radio emission . . .
The IRAM 30 m telescope . . . . . . . . . . . . . . . . . . .
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Illustration of a stacking experiment . . . . . . . . . . . . . . . . . . . . .
Cutout images affected by noise distortions . . . . . . . . . . . . . . . . .
Evolution of the radio luminosity function for massive quiescent galaxies
Comoving volume averaged heating rate (’radio-mode feedback’) . . . .
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4.6.
4.7.
4.8.
4.9.
Observed 3.6 µm flux versus stellar mass from SED fits . . . . . .
Binning scheme in stellar mass and photometric redshift . . . . .
Examples of 1.4 GHz postage stamp images obtained via stacking
Ratio of integrated to peak flux density in stacks at 1.4 GHz . . .
SSFR as a function of stellar mass at 0.2 < z < 3.0 . . . . . . . . .
Redshift evolution of the SSFRs for mass-selected galaxies . . . .
Comparison of the mass-depent SSFR evolution to other studies .
SSFR(M∗ ,z) for galaxies with high star formation activity . . . . .
BzK diagrams of our sample . . . . . . . . . . . . . . . . . . . . . .
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5.2.
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5.4.
The
The
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6.4.
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6.6.
6.7.
Keck/DEIMOS spectrum for the z = 4.622 starburst Vd-17871 . . .
Redshifted 12 CO(5-4) spectrum from IRAM/PdBI observations . . .
Rest-frame UV-to-near-IR SEDs of both emission components . . . .
Redshift probability distribution functions . . . . . . . . . . . . . . .
Rest-frame near-to-far-IR SED of Vd-17871 . . . . . . . . . . . . . .
Distribution of z ≫ 1 sources in the L′CO /LIR plane . . . . . . . . . .
Postage stamps for the Vd-17871 system as seen in different bands
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distribution of the SFR density with respect to stellar mass
Schechter-function description of the SFRD . . . . . . . . .
redshift dependence of the Schechter parameter Φ∗SFG . . .
cosmic star formation history out to z = 3 . . . . . . . . . .
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7.1. Panchromatic sensitivities of the COSMOS survey . . . . . . . . . . . . . . . . . 110
7.2. Confirmed z > 4 massive starburst and candidates in COSMOS . . . . . . . . . 119
7.3. Current and future (sub-)mm surveys in the COSMOS field . . . . . . . . . . . . 121
xv
LIST OF FIGURES
A.1. Analytic evaluation of the statistical 95 % statistical completeness . . . . . . . . 128
xvi
List of Tables
4.1.
4.2.
4.3.
4.4.
4.5.
Stellar mass limits for all/SF galaxies . . . . . . . . . . . .
Radio stacking results for the entire mass-selected sample
Radio stacking results for star forming systems . . . . . .
Two parameter fits to the mass dependence of the SSFR .
Two parameter fits to the redshift evolution of the SSFR .
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5.1. Schechter parameters for the stellar mass function of star forming galaxies . . 72
5.2. The total SFR density as a function of redshift (cosmic star formation history) . 79
6.1. Mid-IR-to-millimeter flux densities and derived quantities of Vd-17871
. . . . . 104
C.1. Fundamental physical constants . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
C.2. Astronomical and SI-derived units . . . . . . . . . . . . . . . . . . . . . . . . . . 145
xvii
LIST OF TABLES
xviii
1. Introduction
Understanding the evolution of the universe on large scales is a major challenge in astrophysics. Observationally, the analysis is mostly restricted to luminous matter and hence
visible structures. Galaxies therefore constitute the key-element in observational cosmology. Understanding their formation but also revealing their evolution over long timescales
is an essential prerequisite to insights into cosmic evolution as a whole. Clearly, even the
properties of a single galaxy and the physical processes by which its baryonic constituents
interact are of vast complexity. Galaxy evolution therefore is a broad research field with a
large number of very different foci.
The light emitted by stars is a longstanding key diagnostic in celestial observations and
in studying entire galaxies. The process of star formation within galaxies is therefore of
fundamental importance. It is the aim of this thesis to investigate the process of how stars
formed in galaxies over cosmic time. We will thereby build on previous work that found
the essential calibrations needed to measure the rate of star formation in galaxies and
concentrate on the evolution of this quantity with respect to other global galaxy properties.
Large samples of galaxies are needed hereby to obtain a representative view of the entire
galaxy population over a substantial range in cosmic time.
At the earliest cosmic epochs the study of individual objects with exceptionally high star
formation rates is vital to understand how cosmic structures form and how the first massive
galaxies assemble. This thesis therefore deals with both, large data sets of galaxies as well
as those of individual sources that reside at the earliest times and are of special interest
in their own right. While we will make use of the emission of galaxies over a wide range
of the electromagnetic spectrum a clear focus of this thesis is at radio wavelengths from
the sub-millimeter to centimeter regime (i.e. several hundreds of gigahertz down to a few).
This Chapter is meant to give the reader an overview of the essential scientific context,
the state of this research field and the most important tools needed for galaxy evolution
studies. The reader might wish to obtain deeper methodological and physical insights into
the topics covered in the scientific Chapters of this thesis: Fundamental laws and their
derivation based on the important assumptions that are used in this thesis are therefore
presented in Appendix B.
1.1. Panchromatic galaxy evolution in a dark universe
The universe as we find it today is a dark place. A (hypothetic) present day space-traveller
would encounter a single particle of baryonic matter1 – on average – only every fourth
cubic meter along his way. Dark matter, on the other hand is claimed to be about five times
more abundant but its origin and nature remains elusive. The by far dominant content of
the present universe is supposed to be of dark origin in the same sense: While being of
1
I.e. the kind of matter he is used to from daily life experience.
1
1. Introduction
exceptional importance as the driver for the (nowadays even accelerated) expansion2 of
the universe this so-called dark energy – possibly related to vacuum energy – is not directly
observable.
Perhaps humans tend to focus on what is obvious, what they already know and, particularly, what they know to handle. Celestial observations therefore have a longstanding
tradition in focussing on electromagnetic waves, in particular visible light. Other parts of
the electromagnetic spectrum, however, are of vast and partially growing importance for
modern observational astrophysics. Despite their advantages (see below), electromagnetic
wave observations are inevitably restricted to phenomena that involve the electromagnetic
force. To our knowledge this excludes the possibility to study all sorts of dark phenomena
by direct observations of electrodynamically driven emission and it explains why those phenomena are actually referred to as being dark. In other words, only the baryonic world
is accessible to direct observations with instruments that are sensitive to electromagnetic
emission.
Photons, the carriers of electromagnetic emission, have the advantage that they are comparatively easy to detect because they interact with matter but not as rapidly as massive
particles. Hence, they can travel substantial distances without significant disturbance before being caught in any adequately designed man-made device. Photons are abundant in
the cosmos. Other particles like neutrinos which are barely massive, might also be abundant but they hardly interact with matter. Moreover, it is the panchromatic view that makes
photons exceptional. Over all wavelengths they carry an ubiquitous variety of information,
involving high energy processes (often taking place at the smallest scales), emission and
absorption features due to the presence of individual atomic or molecular species to all
sorts of thermal and non-thermal phenomena. The variety of physical processes that produce photons thereby explains their abundance. Finally, the finite but constant speed of
light enables a view into the cosmic past when observing distant objects.3 Thus, it is the
electromagnetic (baryonic) universe that literally sets a colorful contrast against the energetically dominant dark side of the cosmos. Both worlds are solely connected through
gravity and the details on how and why constitute perhaps the toughest remaining mystery
in our understanding of the cosmos.
Galaxies as well as groups and clusters of galaxies are unique structures to reflect this
dichotomy in the most vital way. Any individual galaxy consists of (luminous) baryonic
material4 but is hosted by a halo of dark matter (White and Rees 1978) and it is the grav2
Cosmic expansion can be measured using a variety of diagnostics with the same underlying requirement of
measuring cosmological distances to highest possible accuracy. The calibration of observable distance indicators on different distance scales against each other (the so-called distance ladder) therefore is a critical
prerequisite. For an excellent summary on recent (combined) results and on the different methods starting
from Cepheid stars, type Ia supernovae (acting as ’standard candles’ out to substantial distances due to
their known luminosity) to global galaxy scaling relations the reader is referred to Freedman et al. (2001).
3
Strictly speaking, not the full cosmic past can be explored based on photonic observations. The universe
was practically opaque at the earliest times when radiation and matter plasma were in thermal equilibrium.
After the cosmologically short phase of recombination the universe was predominantly neutral. The mean
free path of energetic photons emerging from the relatively rare first population stars as well as quasars
was hence short. This resulted in a high opacity at short wavelengths. It is common practice and in the
spirit of this introduction to refer to this epoch as the ’dark ages’. As a result, our full panchromatic view is
thought to reach out to a few hundred millions of years after the Big Bang (i.e. a redshift of z ≪ 10).
4
Note that it is the author’s opinion that a galaxy is an object that needs to contain baryonic material. An
absolutely clear definition of what a galaxy is does not exist at the time of writing this thesis. For an
2
1.1. Panchromatic galaxy evolution in a dark universe
itational potential of this dark halo that enables the funneling of baryonic material to the
central parts of the galaxy. On adequately large scales dark as well as baryonic matter are
distributed homogeneously and isotropically5 in the present day universe while on smaller
scales the baryonic matter follows the filamentary structure of the dark matter distribution
(the so-called cosmic web).
This homogeneity and isotropy is the
reason why in our modern view of the
universe no observer (in particular no
observer located on earth or any other
point of our solar system) is exceptional or preferred.6 Asides small initial density fluctuations, meant to be
the seeds of the gravitationally driven
hierarchical assembly of the cosmic
web (White and Rees 1978) and imprinted in the cosmic microwave background as observed today (e.g. Smoot
et al. 1992; Spergel et al. 2003, 2007;
Komatsu et al. 2009), the universe is
also thought to have been homogeneous at earliest times after the Big
Bang.
It is of marginal importance for
this thesis how these initial inhomogeneities are thought to have been
produced, in an early cosmic epoch
cosmologists refer to as inflation. Figure 1.1. – The artist’s view on cosmic history with
The puzzling quest for an observer
a non-linear time axis. While this sketch has a certain focus on the epoch of reionization it summarather is how the comparatively simrizes the essential phases in cosmic evolution that reple structural agglomerations of lumisult from the observationally supported dark energy
nous matter (manifesting themselves
dominated universe and that are mentioned in this
in a well classifiable zoo of local galaxSection. Image courtesy of the NASA/WMAP
ies) emerged from a vastly homogeScience Team.
neous and dense mix of neutral primordial hydrogen gas and dark matter residing in an initially hot environment. The processes that shape the morphologies of galaxies can – in principle – be understood within well established modern standard physical
overview on possible definitions we refer the critical reader to Forbes and Kroupa (2011).
Cosmic isotropy on large scales is an observable since the present day cosmic microwave background, observationally discovered by Penzias and Wilson (1965), is found to be globally isotropic (e.g. Spergel et al.
2003, or the results from any other space-based measurements of the cosmic microwave background).
6
On cosmic scales gravity clearly is the dominant force so that cosmic evolution and structure formation is
described in a purely gravitational framework assuming large scale homogeneity and isotropy. This framework is given by Einstein’s theory of general relativity. For a thorough introduction starting from the general
relativistic field equations prominent textbooks (e.g. Padmanabhan 1993) should be consulted. The geometrical consequences that are most important for this thesis are presented in Appendix B.1 along with our
observationally supported assumptions.
5
3
1. Introduction
paradigms. Moreover, these processes can be observed in the way described above. As the
luminous matter, essentially in form of galaxies, follows the global dark matter distribution,
it is the observational study of galaxies over time that is the key diagnostic to understand
cosmic evolution regardless if the latter is predominantly driven by dark phenomena. Finally, the study of the intrinsic evolution of the galaxy population enables us to identify
cosmic turning points and key epochs in the gravitational interplay of baryonic and dark
matter.
A question of fundamental importance for galaxy (and hence cosmic) evolution research
is how hydrogen gas is converted into the fundamental building blocks of the luminous universe, namely stars. Stars are of critical important because of various reasons: It is stellar
emission that tells us about a galaxy’s age and most other galaxy properties of interest.
The composition of stellar populations within a galaxy shed light on its history and its past
ability to form stars. It is the (young) stars that predominantly illuminate and thereby heat
their surrounding medium, producing to a large extent the global cosmic infrared emission
observed (see Hauser and Dwek 2001, for a review on the cosmic infrared background).
Studying star formation over time and revealing its globally most important drivers will
therefore yield key insights into the evolution of luminous matter on galaxy scales and set
tight constraints on the interplay of baryonic and dark matter and the growth of cosmic
structure. It is the aim of this thesis to investigate galaxies with respect to their star
formation over a broad baseline in cosmic time and, in particular, to connect their star
formation activity to their intrinsic global properties. Due to the exceptional role gravity
plays in connecting dark and baryonic matter a particular focus of this thesis will be on
how star formation activity in galaxies is related to their observationally accessible (i.e.
stellar) mass content. The observational results presented in this thesis, based on a multiwavelength view on an unprecedentedly rich galaxy sample, are the basis for constraining
theoretical models of matter and structure formation in the universe. Those models, in
turn, constitute the fundament of our current state of knowledge on cosmic evolution in
this dark universe.
1.2. Tools to study cosmic evolution: From simulations to
multi-wavelength deep field surveys
Surprisingly few parameters are needed to describe – in principle – the cosmos and its
evolution and they are constrained by observations of the cosmic microwave background
combined with established distance indicators (e.g. Spergel et al. 2003, 2007; Komatsu
et al. 2009). These measurements favor a set of parameter values that describes a cold dark
matter model with cosmological constant, the so-called concordance or ΛCDM cosmology
(see also Appendix B.1). As mentioned above, the total matter budget is clearly dominated
by dark matter which is used to theoretically predict structure formation and evolution
based on (N -body) computer simulations (e.g. Springel et al. 2005). Those simulations
form the basis of our understanding of matter agglomeration and evolution in the universe.
They reveal the important physical scales in terms of matter density as a function of cosmic
time (see, e.g., Springel et al. 2006, for comprehensive insights into the cosmic large scale
structure found in simulations compared to observational results). They also quantify the
hierarchical merging of individual dark matter halos, a prerequisite for predicting merger
4
1.2. Tools to study cosmic evolution: Simulations and surveys
Figure 1.2. – The full COSMOS Hubble Space Telescope (HST) survey, the largest contiguous
HST deep field survey ever undertaken. The celestial area covered by the Advanced Camera
for Surveys (ACS; Ford et al. 2003) observations corresponds to slightly less than 2 deg2 , the
angular area achieved or even exceeded by most other space- and ground-based observing
efforts in the COSMOS field. For size comparison other prominent HST deep field surveys
(see explanations in the text) are indicated as well as the full moon to scale with respect
to the survey fields. Image courtesy of NASA, ESA and Z. Levay (Space Telescope
Science Institute).
rates of galaxies.
Two diagnostics are essential to observationally probe the simulated structures. First,
the technique of (weak) gravitational lensing can be used to reveal the total matter distribution (see, e.g., Bartelmann and Schneider 2001, for an introduction and review). Second,
directly observed galaxies trace the density field of luminous matter which is supposed to
follow the walls of the dark cosmic web (e.g. Kovač et al. 2010, for recent results). Both
diagnostics require similar observational efforts, namely deep imaging of a (preferably)
contiguous and sufficiently large patch of the sky, a so-called deep-field survey.
However, by far not only (large scale) structural studies are of interest but, as outlined
above, especially an understanding of the evolution of baryonic matter within the dark
matter environment is a key challenge. Semi-analytical modeling techniques are a road to
theoretically incorporate interactions other than gravity in N -body simulations and hence
make predictions on baryonic galaxy properties (e.g. Kauffmann et al. 1999; Croton et al.
2006; Somerville et al. 2008). Direct hydrodynamical simulations are a valuable alternative
to the expense of substantially higher computational effort (e.g. Springel and Hernquist
2003, for an application of hydrodynamic simulations in a research area well connected to
this thesis). Generally, it is the vast complexity of physical processes underlying the intrin-
5
1. Introduction
sic growth and evolution of galaxies that limits any theoretical approach and explains the
necessity of testing model predictions against real data. Galaxy evolution and in particular
the processes through which stellar mass builds up over time therefore clearly needs to be
constrained observationally.
1.2.1. Redshift surveys and deep fields
Due to the variety of processes by which the baryonic constituents of a galaxy (mainly stars
as well as interstellar gas and dust) interact or evolve, different portions of the electromagnetic spectrum carry different information on the global state of a given galaxy and only
the multi-wavelength view reveals the full picture.
Given all aspects discussed so far an observational program to study the evolution of the
baryonic universe in broad variety and in detail requires in the ideal case
1. a survey over a large and possibly contiguous celestial area in order to
a) identify statistically meaningful samples of galaxy populations.
b) study aspects of large scale structure by weak lensing methods and by the directly observed clustering of individual galaxies.
2. panchromatic observations of this celestial area – hence requiring very different observing instruments in order to
a) characterize individual galaxies as well as their surrounding intergalactic medium
in detail.
b) determine redshifts and hence distances for large data sets of galaxies7 .
c) assure a certain lookback potential, implying that galaxies over a wide range of
cosmic epochs need to be traced which requires sufficiently high sensitivities at
all wavelength8 .
It is therefore apparent that panchromatic deep field surveys for lookback studies demand tremendous observational programs constituting one of the largest collaborative efforts in modern observational astronomy. Various such survey programs have been carried
out, especially over the last decade, differing in area, depth as well as in celestial position.
Despite the ideal survey design listed above, the variety of different survey programs has
a number of advantages. Survey design follows the ’wedding cake’ picture in which on top
small area (’pencil-beam’) observations are carried out to highest depth while very large
area and shallow surveys form the bottom. Very large lookback times can be assessed this
way even for rather normal galaxies (e.g. in the Hubble Ultra Deep Field (HUDF); Beckwith
et al. 2006) but, on the other hand, also a larger local volume can be sampled enabling a
virtually complete view of the (near) present day galaxy population (e.g. the Sloan Digital Sky Survey, SDSS; York et al. 2000). Intermediate panchromatic surveys typically aim
at a statistically meaningful sampling of the galaxy population residing at various cosmic
7
The concept of redshift and consequences for light emitted at a given wavelength are discussed in Appendices
B.1 and B.2.
8
Aspects concerning the choice of the depth of survey data are discussed in Chapter 3.1.
6
1.2. Tools to study cosmic evolution: Simulations and surveys
z=2, z=0.03
z=1, z=0.02
24.0
23.5
23.0
22.5
22.0
21.5
21.0
20.5
20.0
24.0
23.5
23.0
22.5
22.0
21.5
21.0
20.5
20.0
10Mpc/h
GOODS
1.4
HDFs
20Mpc/h
1.0
f814-f475
2.0
0.4
f814-f475
0.8
Figure 1.3. – Cosmological simulation results for two redshift slices over a 2 square degree
field of view (the angular extent of the COSMOS field). For comparison the areal coverage
of other prominent deep field surveys are indicated as well as the physical scale (normalized
to the dimensionless Hubble parameter h = H0 /(100 km s−1 Mpc−1 ) assumed to be h = 0.7
in this thesis). The simulations have been carried out in the ΛCDM framework by the Virgo
Consortium (Frenk et al. 2000). The background gray scale indicates the simulated dark
matter distribution, clearly showing the cosmic web consisting of overdense filaments and
underdense voids. Symbols denote individual galaxies that are color-coded according to their
colors predicted by semi-analytical models. The simulations motivate the comparatively large
observational time investment for surveying a 2 deg2 field in order to probe the effects of
large scale structure and avoid cosmic variance. Image taken from Scoville et al. (2007d).
epochs, hence enabling evolutionary studies of global galaxy properties. The most prominent surveys of this kind9 are based on observations of the survey field with the Hubble
Space Telescope (HST) in at least one band and completed by panchromatic observations
over a spatially coinciding area of similar size, typically from X-ray to far-infrared and radio wavelengths. The high angular resolution of HST observations allow for morphological
studies of galaxies at optical to ultraviolet wavelengths in their rest-frame, thereby revealing interacting or merging galaxy systems.
This thesis is based on the panchromatic data acquired in the COSMOS field (Scoville
et al. 2007d) which covers an on-sky area of 2 square degrees (deg2 in the following). It is
the largest of the prominent HST deep field surveys (see Figure 1.2). This size is motivated
9
To name a few, these are the GEMS (Galaxy Evolution from Morphologies and SEDs) survey (Rix et al. 2004)
with ancillary data from the COMBO-17 (Classifying Objects by Medium-Band Observations in 17 filters)
survey (Wolf et al. 2001), the Great Observatories Origins Deep Surveys (GOODS; Giavalisco et al. 2004)
with survey fields in the northern and southern sky and various ancillary observing programs as well as the
Cosmic Evolution Survey (COSMOS; Scoville et al. 2007d). Both, the GOODS-South as well as the GEMS
fields partially coincide with the (extended) Chandra Deep Field South ((E)CDFS; Giacconi et al. 2001) and
contain the Hubble Ultra Deep Field (HUDF; Beckwith et al. 2006). The GOODS-North field contains the
northern Hubble Deep Field (HDF; Williams et al. 1996).
7
1. Introduction
by cosmological simulations that predict the largest structures at a redshift of z = 1 to
show a comparable angular extent corresponding to about 40 Mpc in comoving units (see
Figure 1.3). COSMOS therefore traces cosmic structures at and above this redshift in a
representative way, thereby minimizing the effect of cosmic variance10 . The large number
of ∼ 2 × 106 galaxies residing in the COSMOS field and the vast panchromatic ancillary
data11 enable an unprecedented rich view of galaxy evolution at high statistical accuracy.
1.3. The global population of galaxies over time
Redshift surveys provide the opportunity to investigate changes of the galaxy population
over time in a statistical sense. Since we cannot directly follow the individual evolutionary
paths of galaxies we aim at selecting galaxies at different cosmic times based on the same
parameters and compare them with respect to other properties of interest.
Since galaxies are a diverse class of objects, various parameters, such as their morphology, their color or luminosity qualify for this selection. It is important to notice, however,
that broadly speaking the classification of galaxies in the local universe turns out to be
remarkably simple, placing individual objects either onto a relatively tight red sequence
of mostly massive sources or a somewhat broader distribution (the so-called blue cloud) in
the plane spanned by visual broad-band color and luminosity or stellar mass content (e.g.
Baldry et al. 2004). Interestingly, the perhaps most intuitive feature of galaxies – namely
their appearance (also known as morphology) – is also related to this color-magnitude distribution (e.g. Strateva et al. 2001). Red sequence objects are predominantly elliptically
shaped, i.e. of earlier Hubble types, while those that reside in the blue cloud cover later
types observed as spiral galaxies. Spiral galaxies are often also referred to as disks due to
their flat profiles when seen edge-on. Physically, they are rotationally supported systems
while elliptical galaxies are pressure supported.
Clearly, there are intermediate objects and complex phenomena but for the moment they
shall be of minor interest for our global picture. For this thesis two observations are of highest importance: First, the red sequence objects are generally dominated by older stellar
populations. They show little ongoing star formation activity and must hence have formed
their substantial amount of stars at earlier times. Star forming galaxies, in turn, are found
among the bluer objects. Indeed, galaxies show specific colors because their broad-band
spectral energy distributions (SEDs) are dictated by the composition of their dominant stellar populations. Stellar population synthesis modeling (e.g. Bruzual and Charlot 2003) is
hence a road to assemble the spectral footprints of galaxies allowing even for rough morphological information solely based on photometric observations.
Interestingly (and this is the second point of interest for this work), even at much higher
redshifts (e.g. Bell et al. 2004; Kriek et al. 2006; Williams et al. 2009; Marchesini et al. 2010)
and hence earlier cosmic times the apparent color bimodality is observed to persist, raising
questions of how the populations of blue and red galaxies are connected and whether there
10
Cosmic variance leads to different number counts and hence results for, e.g., luminosity functions of galaxies
for different survey fields that underscore the scales needed to trace overdensities and voids in a representative fashion.
11
For an overview on the observing programs see Chapter 4.2. Table 1 in Ilbert et al. (2009) lists the sensitivities
achieved in the ultraviolet to mid-infrared bands.
8
1.3. The global population of galaxies over time
are evolutionary paths from one family to the other.12 Since we already pointed out that
red elliptical galaxies are found to be massive13 the most appealing evolutionary direction
is from the star forming blue cloud to the quiescent red sequence. It is hence vital to
compare the number densities of color-selected galaxies as a function of their luminosity
or total stellar mass at different epochs in order to compare their differential evolution
as well as the evolution of the integrated luminosity or mass density.14 These are the
diagnostics that advanced our constantly growing understanding of galaxy formation and
evolution. Different evolutionary channels from the blue cloud to the red sequence have
been proposed from evolutionary luminosity function studies, all involving a shutdown of
star formation (known as star formation quenching) at some point (e.g. Faber et al. 2007).
Empirically, Peng et al. (2010) recently suggested alternative pathways to when and under
which conditions quenching occurs. We will cover these findings at a later stage in this
thesis when contextually appropriate. It should be noted that the question of what physical
processes cause galaxies to quench their star formation has not been definitely answered
to-date.
In addition to drawing inferences from the number density distributions of galaxies it is
the direct observation of the mass build-up through recent star formation at different times
which is of highest priority to constrain the evolution of galaxies. This is the subject to
be covered in this thesis. In the following we will first discuss the essential background
motivating the immediate goals of this thesis before we proceed to a brief outline of how
we actually measure star formation rates.
Clearly, there is much more to know about the population of galaxies, their properties
and their shapes etc. which cannot be covered in this introduction. For a profound and
comprehensive overview on galaxies and their evolution we refer the reader therefore to
the literature (in particular to the comprehensive textbook by Mo et al. 2010).
1.3.1. The growth of stellar mass through star formation
From the observational measurement of star formation rates (SFRs) in galaxies at various
cosmic epochs over the past 15 years the picture has emerged that the global star formation
activity in the universe is a rapidly evolving quantity. Lilly et al. (1996) as well as Madau
et al. (1996) first presented evolutionary measurements of the total and comoving volumenormalized SFR, a quantity referred to as an SFR density (SFRD) in the following.15 They
12
As one caveat to the simple color division in blue and red sources it should not be forgotten that galaxies can
also be reddened by dust extinction. Potentially, even those systems with substantial star formation activity
are covered by larger amounts of dust. The color-based selection of galaxies hence needs to be efficient
in selecting intrinsically red objects because of older stellar populations. This can be achieved by colorcolor techniques (e.g. Williams et al. 2009) or by selection via intrinsic colors inferred from fitting stellar
population synthesis models to the observed SED under the assumption of a reddening law (e.g. as used by
Ilbert et al. 2010, for the selection major parts of this thesis are based on).
13
The stellar mass content of galaxies is measured from the stellar mass-to-light ratio. In practice, this can
either be approximately determined from broad-band colors (Bell and de Jong 2001) or, as done in this
thesis, from stellar population modeling if a simple analytic form for the star formation history of the galaxy
as well as a dust extinction law (e.g. Calzetti et al. 1994, 2000; Charlot and Fall 2000) is assumed. Either
way the stellar mass estimates depend on the explicit assumption of the initial mass distribution function of
stars (the stellar IMF).
14
More information on luminosity and mass functions – in particular with respect to their visualization – is
found in Appendix B.3.
15
see Appendix B.1 for a definition and explanation on comoving distance measures.
9
1. Introduction
Figure 1.4. – The cosmic star formation history (CSFH) and the relation between star formation
rate and stellar mass in the local universe. Left: A recent measurement of the evolution of
the comoving SFR density (SFRD) over time which is based on ultraviolet emission. The
literature data span the redshift ranges z < 2 (black open squares; Schiminovich et al. 2005),
2 . z . 3 (green crosses; Reddy and Steidel 2009) as well as 3 . z . 10 (filled circles;
Bouwens et al. 2009, 2011b,a). The upper set of points with underlying orange shaded region
are the data after dust extinction corrections have been applied while the shaded blue region
shows the uncorrected trends. The steep decline of the SFRD since z ∼ 1 is observationally
well established. The CSFH at earlier epochs, in particular the continuous increase since the
highest redshifts is less well constrained to-date. Particularly, the minor importance of dustobscured star formation shown here is under debate. Right: The tight relation between SFR
and stellar mass as inferred from emission line diagnostics for galaxies without contribution
of an active galactic nucleus that reside in the local universe. The red dashed curve depicts
the average trend along with likelihood contours. The data shown are from the Sloan Digital
Sky Survey. Images taken from Bouwens et al. (2011b) and Brinchmann et al. (2004).
and a constantly growing number of other authors (see Hopkins and Beacom 2006, for a
compilation) concluded that the SFRD undergoes a rapid decline over the last ∼ 8 billion
years (corresponding to a redshift of z ∼ 1). The SFRD at even earlier cosmic times is
less well established. The currently preferred scenario from the observers’ side is that the
cosmic star formation activity reaches a maximum around 1 < z < 3 and steeply declines to
higher redshifts (see Figure 1.4).
Most evidence for this scenario comes from SFRD measurements that are based on ultraviolet (UV) emission. To be precise, the UV luminosity function has been constrained at
various epochs even out to z ∼ 10 (see in particular Bouwens et al. 2011b, for recent results) and the resulting, integrated UV luminosity densities has been converted into SFRDs
at the corresponding cosmic times. In the presence of interstellar dust surrounding the
emitting stars the UV light is absorbed (see Appendix B.5) so that empirically derived dust
extinction corrections have to be applied. These corrections are found to be substantial
as shown in Figure 1.4 at redshifts of z ≪ 4 highlighting the critical need for alternative
dust-unbiased measurements of the SFRD at these epochs.
Dust extinction can be inferred from the UV continuum properties of galaxies (e.g. Charlot and Fall 2000). At the high redshifts probed by, e.g., Bouwens et al. (2011b) the observed
near-infrared data trace the rest-frame UV continuum of the objects. Based on such diagnostics they infer that star forming galaxies at the highest redshifts observed to-date are
essentially dust-free. Hence they conclude that the uncorrected UV emission of such distant galaxies provides an unbiased measure of the SFRD in the early universe. Already
10
1.3. The global population of galaxies over time
at z ∼ 4 dust-obscured star formation appears to cease its importance in this scenario.
This stark contrast between the resulting dust correction factors applied to the global cosmic star formation activity from early to late times raises numerous questions that are of
high relevance for our understanding of the total stellar mass growth in the universe and
hence galaxy evolution as a whole. It is hence clear that sensitive and dust-unbiased star
formation estimates at high redshifts are critical (see also below).
With growing knowledge about the global cosmic star formation history (CSFH) questions on the main drivers of its rapid evolution have been and are still raised. One insightful finding was revealed by comparing SFRs of galaxies that are differently massive.
In the local universe it was found that star forming sources form a tight sequence in the
SFR/stellar mass plane (see Figure 1.4; and e.g. Brinchmann et al. 2004) while quiescent
galaxy – unsurprisingly – fall significantly below this trend at the high-mass end. Also at
higher redshift (see, e.g., Elbaz et al. 2007, for results at z ∼ 1) evidence for the existence
of such a ’main sequence’ of star forming galaxies exists while average SFRs follow the
global trend and substantially increase as we go back in time. These results are surprising
in that the mass that is contained in stars should intuitively have little effect on the stellar
mass growth. As Dutton et al. (2010) and Noeske et al. (2007a) argue it is the net rate
of cold gas accretion onto the dark matter halo which might shape the SFR-sequence at
any epoch since this quantity shows a similar evolution as the SFR-sequence. Hence in the
SFR-sequence the total stellar mass might act as a proxy for dark matter halo mass as the
one rises monotonically with respect to the other (e.g. Moster et al. 2010). Hence secular
processes are supposed to be responsible for supplying galaxies with molecular gas through
the gravitational interaction of baryonic gas and dark matter, providing a vital example for
the interplay between the baryonic and the dark universe.
It is, however, critical to obtain detailed observational insights into the evolutionary properties of this SFR-sequence. It has been argued that star formation in galaxies is supposed
to ’downsize’ (e.g. Cowie et al. 1996) which has been interpreted as a shift of the main
contribution to the global star formation activity from more to less massive galaxies over
time. The question if this is indeed the case and how it would affect the shape of the
SFR-sequence at different epochs is of high relevance.
Particularly SFR measurements from dust-unaffected tracers are needed as well as a
statistically representative galaxy sample even at comparatively low stellar masses out to
substantial redshifts. It is an important motivation for this thesis to accurately measure the
average evolutionary trends of differently massive galaxies and to determine the characteristic mass scales of galaxies in which star formation predominantly occurs.
1.3.2. The role of starbursts in galaxy evolution and observational
cosmology
The merging of galaxies is an alternative channel for the gas-supply of galaxies. Large
amounts of gas accumulate in galaxy interactions of similarly massive galaxies (so-called
major mergers) which typically leads to a starburst, i.e. a significant excess in star formation activity compared to normal star forming galaxies. In turn, starbursts are supposed
to be predominantly driven by galaxy interactions. It is established that local starbursts,
sources also known as (ultra-)luminous infrared galaxies ((U)LIRGs) due to their high luminosities of > 1011 (> 1012 ) L⊙ at infrared wavelengths, are interacting systems (e.g.
11
1. Introduction
Sanders et al. 1988)16 . Also infrared-luminous starbursts at higher redshifts, so-called
sub-millimeter galaxies (SMGs) have been found to be mostly driven by major galaxy interactions (e.g. Engel et al. 2010).
This poses the question whether (merger-driven) starburst activity contributes a significant fraction to the global star formation rate at different cosmic epochs. As mentioned
before, the existence of a tight star forming main sequence of galaxies favors secular trends
in which galaxies accrete their gas predominantly in a less stochastic way. A number of recent studies revealed indeed that major mergers are of minor importance for the global star
formation activity at redshifts of z < 1 (e.g. Robaina et al. 2009). Other recent studies (e.g.
Elbaz et al. 2011; Rodighiero et al. 2011; Williams et al. 2011), using different diagnostics,
also support a picture in which starbursts might contribute at most ∼ 10 % to the total
cosmic star formation at any epoch out to z ∼ 2.
It might appear tempting to extrapolate the minor importance of extreme star formation
out to higher redshifts. As we go back in cosmic time it is, however, reasonable to challenge
this paradigm. In a hierarchically forming and expanding universe that was substantially
denser at early epochs the seeds of the largest present-day overdensities are thought to
have been sown early on and should, in principle, be observable already at high redshift. It
is likely to find sites of extreme star formation in these denser environments (called protoclusters) where the starburst activity might be powered by gas-rich (major) galaxy mergers.
In turn, finding extreme starbursts at z > 4 is a road to reveal overdense regions within
only 1.5 Gyr after the Big Bang. Cosmological simulations predict the existence of these
proto-clusters at high redshifts, a paradigm that needs to be tested against observations.
This is why the search for massive starbursts at very high redshifts is critical to constrain
models of cosmological structure formation.
In the COSMOS field one proto-cluster at z = 5.3 could be recently revealed around a
massive starburst thereby constraining its baryonic mass content (Figure, 1.5; Capak et al.
2011). Also in the GOODS-North field one proto-cluster structure at z ∼ 4 could be identified after the serendipitous carbon monoxide (CO) detection of three extreme starbursts
(Daddi et al. 2009b,a).
The search for extreme starbursts at such high redshifts is also motivated by the observation of massive and no longer star forming galaxies lying on the red sequence even beyond
z ∼ 2 (e.g. Kriek et al. 2006, 2008a; Williams et al. 2009; Marchesini et al. 2010). Given
the comparatively short formation timescales at such high redshifts, it is likely that a substantial fraction of their mass has been rapidly build up (e.g. Kriek et al. 2008b). Massive
starbursts at even higher redshifts, triggered by major mergers and thereby shaping their
elliptical morphologies are hence likely the progenitors of the earliest massive quiescent
galaxies observed to-date. It is, however, an open question if the number densities of both
populations match (e.g. Coppin et al. 2009).
It is furthermore important to constrain the number density of z > 4 massive starbursts
since their individually high SFRs of typically several hundreds of solar masses per year
(e.g. Michałowski et al. 2010) might give rise to a significant contribution to the global
16
The same study suggests also a link between mergers and nuclear activity. This scenario has recently been
challenged by Cisternas et al. (2011) who found no significant statistical enhancement in black hole growth
through major mergers at redshifts 0.3 < z < 1. In parts of this thesis we will be dealing with active
galactic nuclei (AGN). We refer to the excellent reviews by Antonucci (1993) and Urry and Padovani (1995)
for essential background information on different types of AGN, their unification and their properties.
12
1.4. Essentials: Star formation and its measurement
SFRD at these early times. Given their large dust reservoirs (e.g. Michałowski et al. 2010)
there might hence be more dust-obscured star formation activity in the early universe than
currently assumed (see Figure 1.4). It should be noted that it is another challenge to explain
how the large amounts of interstellar dust observed in these extreme starbursts have been
produced at such early times (e.g. Michałowski et al. 2010; Dwek et al. 2011).
Figure 1.5. – Optical composite image of a confirmed high-redshift proto-cluster core that hosts
an extreme starburst. This area corresponds to a 2′ × 2′ region around the (sub-)millimeter
source AzTEC-3 (its optical counterpart is labeled with z = 5.3), a massive starburst that resides at a redshift of z = 5.3 in the COSMOS field. Broad-band dropout sources likely residing
at a similar redshift are denoted by white circles. A 2 Mpc comoving radius is indicated with
a green circle. Arrows point to foreground stars and to objects with spectroscopic redshifts
(labeled by their redshift values) including confirmed proto-cluster members as well as red
objects at much lower z . This example shows that massive starbursts at z > 4 qualify to reveal mass-overdensities at early times thereby paving the way to observationally map cosmic
structure formation. Image taken from Capak et al. (2011).
13
1. Introduction
Figure 1.6 – Modern view on the relation of the
surface densities of molecular gas and star formation rate in galaxies. Shown are regions
of local spiral galaxies (shaded; Bigiel et al.
2008), local spiral (crosses) and ultra-luminous
infrared galaxies (ULIRGs; filled triangles; Kennicutt 1998b), normal star forming galaxies out
to a redshift of z ∼ 1.5 (Daddi et al. 2010b;
Tacconi et al. 2010; red filled circles/triangles,
brown crosses) as well as distant massive starbursts (sub-millimeter galaxies, SMGs; light
green; Bouché et al. 2007; Bothwell et al. 2010).
The current data suggest that throughout cosmic time there is a bimodality in the star formation law between starbursts and average star
forming systems resembling the properties of
local ULIRGs and local disk galaxies respectively. Image taken from Daddi et al. (2010b).
1.4. Essentials for this work: star formation on galaxy scales
and its measurement at long wavelengths
How individual stars form is a matter of vast complexity and far from being fully understood
today. In short, (hot) baryonic gas around a galaxy is supposed to cool on cosmologically
short timescales, to reach the center of the galaxy, to subsequently become denser and
cooler and to finally collapse resulting in clouds of dense and cold gas. It is an observationally supported and generally accepted scenario that stars form in dense clouds of molecular
gas as there is a tight empirical correlation between the surface density of molecular gas
and that of star formation (Figure 1.7; see e.g. Schmidt 1959; Kennicutt 1998b; Leroy et al.
2008). Hence, molecular gas is supposed to be the material out of which stars form.17 This
relation is typically described by a power-law as already suggested in the seminal work
by Schmidt (1959). Observationally supported values for its power-law index are found
between N ∼ 1 (Bigiel et al. 2008) and N ∼ 1.4 (Kennicutt 1998b). Theoretical work discussing different possible underlying physical reasons for this empirical star formation law
is presented by Krumholz et al. (2009) and Dib (2011). The ratio of gas surface density to
star formation rate surface density is commonly used as a gas consumption timescale.
It has been suggested (see Daddi et al. 2010b; Genzel et al. 2010, for recent results) that
this star formation law comes in two flavors (see Figure 1.7). Star forming galaxies show
an apparent bimodality in the observed star formation surface density versus neutral gas
surface density suggesting that most galaxies (i.e. the constituents of the SFR-sequence)
have typical gas depletion timescales of a few billion years that are significantly larger than
those determined for starbursts. It is speculated that galaxy major mergers are the main
cause for this observed bimodality as during the merging process the available gas is very
efficiently compressed and subsequently transformed into stars explaining the higher star
17
Note that recent simulations (Glover and Clark 2011) challenged this logically appearing and commonly
accepted paradigm in that they showed that essentially atomic gas suffices to form stars. They point out
that only the physical conditions found in dense molecular clouds – in particular a sufficient shielding from
the interstellar radiation field – might be required for star formation.
14
1.4. Essentials: Star formation and its measurement
formation efficiency observed in starbursts (e.g. Bournaud et al. 2010). This bimodality is
supposed to persist out to high redshift while especially for average star forming objects
currently only limited data exist at z > 1.18
Since this thesis is not directly concerned with the theoretical framework behind star
formation numerous question remain open in this introduction. We therefore refer the
interested reader to the excellent reviews by Mac Low and Klessen (2004) and McKee and
Ostriker (2007).
1.4.1. Measuring star formation rates of galaxies from their (far-)infrared
emission
In this work we measure SFRs from far-IR and radio continuum emission. Both have advantages compared to other prominent SFR tracers (see, e.g., Kennicutt 1998a, for a review
on SFR tracers). Both are unaffected by the effects of dust obscuration while the far-IR
emission even demands the presence of interstellar dust. Provided there is dust in a galaxy
especially the ultraviolet (UV) light of massive (young) stars is absorbed and thermally reemitted at far-infrared (far-IR) wavelengths. Therefore the far-IR emission alone is a good
tracer of the star formation rate provided that all UV photons are thermally processed.
As Kennicutt (1998a) points out, far-IR emission is best tracing the SFR in dense (local)
starbursts which offer the ideal conditions for an almost calorimetric measurement due to
young stars dominating the radiation field and the presence of large amounts of (opaque)
dust. While it is not clear a priori that extreme starbursts at high redshift provide the same
dense interstellar environments as their local cousins the presence of large dust reservoirs
and predominantly young stellar populations is a valid working assumption. We therefore
use the integrated far-IR luminosity for our best estimate of the SFR in an extreme starburst
at z = 4.622.19
Essentially no tracer provides a perfect measure of the SFR under all possible conditions.
Also the far-IR emission ceases its near-perfection if environments much different from
those found in starbursts are concerned. If the dust is not entirely optically thick or if it
is also significantly heated by the visible light emitted by older stars the far-IR emission
becomes probably a less reliable SFR tracer (see, e.g., Kennicutt 1998a, and references
therein for a discussion).
No matter which SFR tracer is used the calibration from the observed luminosity in a
given spectral range is converted into an SFR with the help of stellar population synthesis
models. This furthermore requires an assumption of the initial mass function (IMF) of stars.
For the influence of different choices of IMFs on various SFR tracers in an extragalactic
context we refer the reader to Wilkins et al. (2008).
1.4.2. The (far-)IR/radio correlation in star forming galaxies
The origin of radio emission from star forming galaxies will be outlined in more detail at a
later stage (see Section 4.1). For a general profound and comprehensive introduction into
radio emission from galaxies we refer the reader to the excellent review by Condon (1992).
18
19
Information on how the molecular gas content in (distant) galaxies is measured is provided in Appendix. B.4.
The measurement of IR luminosities from dust emission at far-IR wavelengths is outlined in Appendix B.5.
15
1. Introduction
Figure 1.7 – Early results on the
relation between (far-)infrared
and radio continuum emission in
nearby galaxies with extended
emission detected at 1.4 GHz that
reside either in the Virgo cluster
(circles) or the field (triangles).
Nearby starbursts are shown as
well and follow the general trend.
Image taken from Helou et al.
(1985).
Here we want to recap the underlying observational paradigms allowing for estimates of
SFRs from radio continuum emission.
Radio continuum emission at frequencies up to a few gigahertz is predominantly of nonthermal nature (e.g. Condon 1992). Its spectrum can be well described by a power-law
Fν ∝ ν αrc . In case of an ensemble of relativistic electrons spiraling in a static and homogeneous magnetic field such a power-law synchrotron spectrum is produced if the electron
energy distribution also follows a power-law. Thermal free-free emission from HII regions
contributes to the radio emission but clearly underscores the non-thermal emission in the
low GHz regime.
Surprisingly, it is empirically well established that the radio emission (not solely) in star
forming galaxies is tightly correlated with their thermal emission at far-IR wavelengths (e.g.
Helou et al. 1985; Condon 1992; Yun et al. 2001; Bell 2003a). Physically, this relation raises
a number of questions that largely remain open to-date. Most important for our work is
that this relation leads to an alternative radio-based way of estimating SFRs based on wellknown calibrations and that this seems to hold true grossly over the redshift range probed
in this thesis (e.g. Sargent et al. 2010a,b).
The intrinsic dispersion of this relation in the local universe is very low (< 0.3 dex) and
places it among the tightest relations in observational astrophysics. The relations holds
over several orders of magnitude in luminosity, hence being valid also over a wide range of
SFRs.
It is suggestive to infer that this tight relation points to a common origin of both IR and
radio emission within galaxies while it is an ongoing effort to constrain the physical origin
of this relation and to trace the regimes where it might break down. Insightful suggestions
have been made to explain its physical drivers by a calorimeter model (e.g. Lisenfeld et al.
1996; Voelk 1989) or by postulating a conspiracy (Bell 2003a). The far-IR/radio relation
has been challenged on sub-kpc scales in nearby spiral galaxies (e.g. Dumas et al. 2011)
which revealed that it is not uniform across the disk and deviated from a linear behavior in
16
1.5. Observatories and instruments
Figure 1.8. – The IRAM 30 m telescope located near the city of Granada on Pico Veleta in the
Spanish Sierra Nevada. The left picture shows the 30 m dish during a pooled observing run in
the evening hours in November 2008 during which sources discussed by Martínez-Sansigre
et al. (2009) were observed. The right picture was taken at the Mirador San Nicolás in the
old Arabic quarter of Granada facing towards Pico Veleta. The trained eye will recognize
the telescope as a tiny white point in the foreground of the cloud’s shadow (at the lower
central part of the shadow in the image center). If the picture extended more to the right, the
Alhambra would be seen.
certain regions. A detailed model is provided by Lacki et al. (2010) and useful implications
for higher redshift applications are discussed by Lacki and Thompson (2010).
The far-IR/radio correlation has typically been calibrated based on 1.4 GHz radio continuum data. In order to apply the calibrations that have been established in the local universe
(e.g. Condon 1992; Yun et al. 2001; Bell 2003a) at higher redshifts one needs to scale the
radio-continuum luminosity appropriately under the assumption of a spectral index value
for the radio continuum. How this should be done for distant objects is derived in Appendix
B.2.
1.5. Observatories and instruments
While data from multiple observing instruments are used in this thesis, three facilities are
of special importance for our radio-focussed work.
The Very Large Array (VLA; Thompson et al. 1980, for an early review), operated by the National Radio Astronomy Observatory (NRAO) is a Y-shaped radio interferometer located in
New Mexico/USA near the town of Magdalena. Its 27 antennas (each dish has a diameter of
25 m) can be arranged in four different configurations from the most extended (A-array) to
the most compact one (D-array) thereby covering baselines between more than 35 km and
35 m. Here we use L-band continuum data at an observed frequency of 1.4 GHz (an effective wavelength of 20 cm) obtained in A and C configuration observed in the VLA-COSMOS
project (Schinnerer et al. 2007, 2010).
The 30 m telescope (Mauersberger 2003, for an overview) is located on the Pico Veleta
mountain in the Spanish Sierra Nevada at an altitude of 2850 m (see Figure 1.8). It is
17
1. Introduction
operated by the Instituto de Radioastronomía Milimétrica (IRAM).20 Until recently it was
equipped with the second generation MAx-Planck Millimeter BOlometer camera (MAMBOII; Kreysa et al. 1998), a 117 pixels array observing at a frequency of 250 GHz (an effective
wavelength of 1.2 mm). Data from this camera are used in this thesis. The same holds
true for the privately funded 128 element Goddard-IRAM Superconducting 2-Millimeter
Observer (GISMO; Staguhn et al. 2008) that is currently installed at the 30 m telescope. It
features next generation superconducting Transition Edge Sensor (TES) based bolometer
technology and observes at a frequency of 150 GHz (an effective wavelength of 2 mm).
The Plateau de Bure Interferometer (PdBI; Guilloteau et al. 1992) is also operated by the
IRAM consortium. This interferometer array consists of six 15 m antennas and is located
in the French Hautes-Alpes to the south of the city of Grenoble on the Plateau de Bure
at an elevation of 2550 m. It can be arranged in four different configurations (A, B, C,
D) with baselines up to 760 m in the most extended A configuration. In this thesis we
present emission line and continuum data observed in the 3 mm band using the B, C and D
configurations.
20
IRAM is sponsored by the Spanish Instituto Geográfico Nacional, the German Max-Planck-Gesellschaft and
the French Centre National de la Recherche Scientifique (CNRS). Its headquarters are located in SaintMartin-d’Hères suburb of Grenoble/France. The French, English and German translations of the institute’s
name are chosen to match the IRAM acronym.
18
2. Overview
In the following this thesis is structured as follows. Each Chapter starts with a context
outline which is followed by a detailed introduction into the technical or scientific matter.
Chapter 3 provides methodological background. The image stacking technique that is extensively used in this work is introduced (Sections 3.1 and 3.2) and its implementation into
a newly developed software during this thesis is detailed (Section 3.3). The ongoing development (Section 3.3.3) and scientific applications (also those not further presented in this
thesis; Section 3.3.4) of this software are discussed. Statistical background is provided in
the Appendices A.1 and A.2.
Chapter 4 describes the stellar-mass based selection and evaluation of an extensive
panchromatic galaxy sample (Section 4.2) that is used as input to the imaging stacking
routine in order to perform stacks at radio continuum wavelengths (Section 4.3) in bins
of stellar mass and photometric redshift. A newly developed method to assess the statistical representativeness of these sub-samples is described in Appendix A.3. The resulting
radio-based evolution of the average (specific) star formation rate of galaxies at redshifts
0.2 < z < 3 as a function of stellar mass is discussed and compared to literature work from
a variety of star formation rate tracers in Section 4.4. The influence of sample selection
parameters on the results for star forming sources is discussed in Section 4.5.
Chapter 5 builds on the results presented in Chapter 4 and literature measurements of
the evolution of the stellar mass distribution function for star forming galaxies. These ingredients enable the study of the global evolution of the cosmic star formation rate with
respect to the relative importance of differently massive galaxies (Section 5.2). The results are compared to literature measurements that use multiple star formation diagnostics
(Section 5.3). Appendix B.3 provides mathematical background on the visualization of luminosity functions and related quantities.
Chapter 6 takes the step from average levels of star formation to highly elevated ones and
bridges the gap to even earlier cosmic times. To this end a single extreme starburst at z =
4.622 is studied in detail with respect to its star forming properties, molecular gas content
and its hidden nuclear activity (Section 6.3) using a variety of diagnostics including optical
spectroscopy and millimeter interferometry (Section 6.2). The star formation process at
such early times is finally compared to that in objects with highly elevated star formation
activity at later times (Section 6.4).
Chapter 7 provides a detailed summary of the other Chapters with a focus on the most
important findings. Prospects for future work as well as ongoing projects are also discussed
in this Chapter
Fundamental background information on the 12 CO line as well as dust continuum emission properties in a high redshift context are given in the Appendices B.4 and B.5, respectively. Appendix B.4 also provides information on convenient units used in the context of
19
2. Overview
12 CO
line emission and hence also in this thesis. More fundamental constants, units and
conversions used in this thesis are found in Appendix C.
During this PhD work the author of this thesis contributed to other studies that are not
presented here but that are of special value for the scientific Chapters of this thesis. Among
those is a publication on the millimeter properties of obscured quasars (Martínez-Sansigre
et al. 2009) which provides fundamental results for the content of Chapter 6. The work
of Capak et al. (2011) yields important insights into why extreme starbursts like the one
presented in Chapter 6 are of high relevance to constrain and actually observationally map
cosmic structure formation in the early universe. The work of Dwek et al. (2011) thereby
provides valuable insights into the estimation of star formation rates in such objects and
the process of dust production at early times. Further (ongoing) projects are highlighted
where contextually appropriate.
20
3. Seeing through the noise: Pushing
observational limits via image stacking
This Chapter introduces an idl-based multi-purpose image stacking algorithm that has been
successfully applied at radio wavelengths in order to produce the scientific results presented in the next Chapters. It has been fully designed and implemented throughout the
course of this thesis and currently finds applications at radio and various other (shorter)
wavelengths to address a variety of scientific questions in the context of galaxy evolution.
Parts of this Chapter are published in
A. Karim, E. Schinnerer, A. Martínez-Sansigre, M. T. Sargent, A. van der Wel, H.-W. Rix,
O. Ilbert, V. Smolčić, C. Carilli, M. Pannella, A. M. Koekemoer, E. F. Bell & M. Salvato, 2011,
ApJ, 730, 61, The star formation history of mass-selected galaxies in the COSMOS field
3.1. Introduction
Multi-wavelength deep field look-back surveys – providing large data-sets of galaxies – are
the key element for studying cosmic evolution. Typically, the number of galaxies a survey
finds depends on the wavelength and hence varies – for a given survey – from catalog to catalog resulting from observations with individual instruments in various bands. This effect
would occur even if the sensitivities were chosen to be the same in all bands observed because, clearly, the spectral energy distribution of a galaxy does not follow a flat distribution
across the electromagnetic spectrum. In other words, for the observed differential flux density of a galaxy as a function of observed frequency generally holds Sνobs (νobs ) 6= const. The
effect of surface-brightness dimming generally1 causes a galaxy to fade with increasing distance/redshift, eventually pushing it below a given sensitivity limit. Moreover, the spectral
shapes of galaxies vary with galaxy type and potentially with redshift due to evolutionary
effects. These might not only be changes in the stellar populations a given galaxy type hosts
at different cosmic times but also an evolving composition of the interstellar medium leading to different (wavelength-dependent) dust-extinction laws and different dust-emission
properties at infrared wavelengths.
In reality it is observationally unfeasible to design a multi-wavelength survey in such
a way that the sensitivities in a ll bands are matched to the lowest possible flux level expected across all galaxy types and a substantial redshift range due to the unrealistically
long observing times required. For a given band a survey therefore generally remains fluxlimited. Often open questions in the field of galaxy evolution deal with relations between
two distinct (global) galaxy properties or calibrations between two quantities derived from
observables. In such cases deriving average trends has the highest priority.
1
Unless (under certain circumstances) observed at (sub-)mm wavelengths (see Appendix B.2).
21
3. Seeing through the noise: Pushing observational limits via image stacking
These, however, can already be studied if
a given galaxy population is represented in
a statistically complete sense only with respect to one observable or derived galaxy
property. While then many or even most of
the galaxies detected in one band (A) do not
have a significant counterpart in the other
band (B), co-adding postage stamp cutout
images of the survey-map obtained in band
B at the positions of sources in the sample
resulting from band A it is possible to estimate the typical properties for a specific
galaxy population with respect to band B.
Usually referred to as stacking, this technique has proven to be a powerful tool to
estimate the typical flux density of galaxies with respect to a given galaxy property,
not only in the radio (e.g. White et al. 2007;
Carilli et al. 2008; Dunne et al. 2009; Pannella et al. 2009; Garn and Alexander 2009;
Bourne et al. 2010; Messias et al. 2010)
but also in the mid-IR (e.g. Zheng et al.
2006, 2007a,b; Martin et al. 2007a; Bourne
et al. 2010), far-IR (e.g. Lee et al. 2010;
Rodighiero et al. 2010a; Bourne et al. 2010)
as well as sub-mm (e.g. Greve et al. 2010;
Martínez-Sansigre et al. 2009). The list can
be extended to other wavebands always requiring a galaxy sample in the other band
representative for the underlying population.
Figure 3.1. – Illustration of an image stacking experiment. First, individual cutout images
(gray scale), centered at the positions of catalog
sources detected at a different wavelength, are
retrieved from a survey image. Subsequently,
the individual cutouts are stacked, i.e. a single co-added map (colored foreground image)
is produced by averaging over all pixels that
are located at the same position in each cutout.
This illustration, also shown on the cover page
of this thesis, is based on a test stacking experiment at 1.4 GHz of ∼ 11, 000 massive galaxies at redshifts of z > 1 in the COSMOS field
which results in a ∼ 40σ detection from median
statistics. Despite the extraordinarily deep radio imaging used the vast majority of objects is
individually undetected at 1.4 GHz. The input
galaxy sample is culled from the mass-selected
galaxy catalog presented in Ilbert et al. (2010)
and the 1.4 GHz VLA-COSMOS map (Schinnerer et al. 2007, 2010) used has a resolution of
1.5′′ × 1.4′′ . The images shown here have sizes
of 40′′ × 40′′ (i.e. (115 × 115) pixels). The stacked
map resembles well the synthesized beam (comparable to a point spread function) of the VLACOSMOS image.
A major limitation of the image stacking
approach is that deeper insights into intrinsic properties of a given relation, such as
its dispersion, remain largely unexplored.
Via a bootstrapping approach this limitation
might be partially circumvented but only at
the expense of largely unprobed assumptions about the intrinsic shape of the flux
density distribution of the galaxies at the
wavelength stacked. In short, the image
stacking technique provides a highly important tool for modern galaxy evolution studies while it cannot be regarded as a substitute for
newer observing instruments enabling even deeper observations.
22
3.2. Image stacking techniques
3.2. Image stacking techniques
There are several ways to perform an image stack and not all involve the stacking of actual
images but instead rely on averaging of a single pixel column (e.g. Dunne et al. 2009;
Bourne et al. 2010). In order to retrieve the full average photometric information for a given
galaxy population stacked, the retrieval of postage stamp cutout images each centered on
the position of a catalog source, however, is a prerequisite. A full stacking routine should
therefore be capable of processing the input imaging in two ways. Either the cutout images
are readily available and need to be processed by the algorithm or the routine itself should
be able to retrieve the individual cutout images from a full survey image. Given typical
pixel scales and image dimensions of deep field surveys the latter should be regarded as
a common option because mostly standard computer memory suffices to temporarily load
these full images. Specific scientific problems often require to process many input samples
at a time and it is therefore desirable for the user to be left only with the task to produce
the individual catalogs as input for the stacking algorithm.
An important question regards the statistical method to estimate the typical flux density
of an input sample at the wavelength stacked. More precisely, stacking means averaging
over pixels located at the same position in each postage stamp in a statistically appropriate
way. This problem can be approached by computing either the mean or the median of the
mentioned set of pixels. Ideally, the resulting stamp then shows the spatial distribution of
the average emission for the sample studied. For an input sample of N galaxies its back√
ground noise level should correspond to ∼ 1/ N of the noise measured in a single radio
stamp. Non-uniform noise properties within the input map can be addressed by applying a
weighted scheme to compute the mean but also the median (see Appendix A.1).
Any sample of galaxies likely contains also a fraction of sources with detections at the
wavelength stacked. Even if this fraction is small, the mean is sensitive to the large excess
in flux density compared to the average emission of the individual non-detections. On the
other hand, setting a threshold and excluding detections from the stack artificially changes
the sample and the results, hence, depend on the threshold applied. In addition, foreground
objects and other extended bright features need to be handled with care and might be a
source of contamination affecting the noise in the final stamp but also potentially the signal itself. It is therefore beneficial to exclude stamps showing these features from a mean
stack. By resorting to the median, the stacking technique becomes more robust against
outliers allowing the use of the entire input sample. While it is often argued that there is
no straight-forward way of interpreting the sample median compared to the sample mean,
White et al. (2007) showed that the median is a well-defined estimator of the mean of the
underlying population in the presence of a dominant noise background, a typical situation,
e.g., at radio wavelengths.
The key capabilities an image stacking routine should have can be summarized as follows:
• Efficient handling of cutout postage stamps and their direct retrieval from an input
image based on user-defined coordinates.
• Multiple options of average estimators including median and mean statistics also in a
noise-weighted fashion.
23
3. Seeing through the noise: Pushing observational limits via image stacking
• Optional (automated or manual) rejection of cutout stamps showing bright and extended noise features or being heavily contaminated by foreground interlopers.
3.3. Full implementation of an image stacking algorithm
The development of a new multi-purpose image stacking routine is a major achievement of
this thesis. Originally designed for a specific scientific purpose (the radio-based and massdependent cosmic star formation history) and implemented along the guidelines described
above it has been improved several times for extended and more flexible use. The resulting
idl-package StackAttack provides a multi-functional and computationally efficient stacking environment whose various options are steered by a simple input ascii file.
3.3.1. Workflow and performance
The elements in the workflow of StackAttack are:
1. Processing of the user-defined input parameters.
2. Evaluating the imaging input (pre-extracted cutout stamps or an input image).
In case an entire survey image is used:
a) Creating a basic fits-header by extracting only the relevant information out of
the fits-header of the input survey map. Processing of the input coordinate list
(StackAttack is capable of processing both, an ascii coordinate list2 as well as
an array of structures written to a fits table).
b) Extracting cutout images centered at a given input catalog position with cutout
dimensions specified by the user and correct fits-header information.
3. Building a data cube from the individual cutouts with parallel storage of their individual fits-headers.
4. Estimation and storage of the background noise level in each cutout stamp for weighted
stacking methods and to monitor the noise-decrease during a stacking experiment.
Additional transformations of individual cutout stamps are optionally available (e.g.
subtracting a local sky background or rotations about a random multiple of π in case
of large-scale noise distortions in the input image). Optionally, quality checks on individual cutouts can be performed and individual cutouts can be subsequently flagged
automatically if not already manually flagged by the user.
5. Averaging over all pixel columns located at the same position in each cutout according
to the user-defined statistic of choice and storage of the final stacked map.
6. Updating the astrometric information in the fits-header such that the central pixel in
the stacked map acts as the new reference pixel (defining at the same time the new
origin in coordinate space such that positions in pixel space correspond to relative
offsets to the central position). This eases later visual inspection of the stacked map.
2
StackAttack processes decimal coordinate formates in degrees (J2000).
24
3.3. Full implementation of an image stacking algorithm
7. Measuring the background noise level as well as the peak signal in the stacked map
and estimating its uncertainty via a bootstrapping technique (see Appendix A.1). Including these measurements in the new fits-header via dedicated keywords.
8. Writing the stacked map along with the new fits-header and other (optional) output
to disk. File names are chosen to resemble that of the input sample. Optional outputs includes the full data cube of cutouts including all corresponding fits-headers in
order to enable later visual inspection of individual input sample members.
9. Optionally, keeping the input survey map in the computer memory if multiple stacks
on the same image should be performed.
As outlined above, it was necessary to achieve flexible input image processing including
correct astrometric operations. Therefore the final stacking routine needs to retrieve the
essential fits-header information of a given input survey image and extract the astrometric
parameters. Often fits-headers carry extensive additional information that is not required
for the stacking experiment, including imaging and data acquisition as well as reduction
history information. One has to be aware that the footprint data reduction pipelines leave
in a fits-header might cause memory problems if many cutout images with individual fitsheaders are extracted at a time. As the example of the VLA-COSMOS image shows, the
assembly of a data cube of cutouts would be restricted to sample sizes smaller than usually
needed for a stacking experiment even if the computer memory is comparatively large.
StackAttack therefore builds a basic fits-header from the survey map input including
only the essential keywords containing, e.g., astrometry parameters as well as physical
units, scalings and observing facility information. Some of the fits image and header
processing is handled using external routines provided within the idl Astronomy Library3 .
Even though StackAttack is implemented in idl, the user is free to chose the preferred
working environment with respect to sample selection and to embedding StackAttack in
the own workflow. The ascii file containing the user defined input parameters can be prepared by the user using any text editor or, e.g., shell-based text manipulation thereby also
setting the output path. The entire stacking package can be compiled at once such that
a single call suffices to start StackAttack from shell as a background process, requiring
only an idl installation and license as well as a local copy of the idl Astronomy Library. As a
result, the way StackAttack is implemented eases the handling of large numbers of input
samples and different survey images and can be smoothly embedded in any environment of
choice. This is a prerequisite, e.g., for extensive stacking simulations carried out currently
in a hybrid workflow of StackAttack, perl and shell-scripting (Sargent, Karim et al. in
prep.). Extensive stacking experiments in which multiple large data sets need to be processed furthermore require a high computational efficiency. The StackAttack algorithm
is optimized to assure fast computation. Even if the input image is large (≫ 1 gigabyte) and
a standard workstation4 is used, the routine processes an input sample of ∼ 10, 000 galaxies
in less than two minutes. It thereby produces a mean and a median stacked map in parallel
3
We thank Wayne Landsman and the NASA Goddard Space Flight Center for making the library publicly
available at http://idlastro.gsfc.nasa.gov.
4
The term standard refers to the processor power of a modern but usual personal workstation. The computer
should, however, posses enough memory reserves. As a rule of thumb, the random access memory should
correspond to the input image size plus 1 gigabyte and for extraordinarily large sample sizes it should be as
large as twice the image size.
25
3. Seeing through the noise: Pushing observational limits via image stacking
including error estimation for both statistics via bootstrapping (see Section A.2).
Given its flexibility with respect to input image processing StackAttack is a wavelengthindependent, i.e. a pan-chromatic, image stacking tool. It still offers dedicated options that
are useful only for specific wavelengths.
3.3.2. Measurement of flux densities and error estimation
Along the way from the input sample to the final average result the measurement of total
flux densities and an estimation of the errors is certainly critical. How to best measure
a flux density, however, depends on the input imaging and, generally, cannot not be automated. It is hence up to the user to perform the final image processing part in a stacking experiment. For the most general case of flux measurement via aperture photometry
StackAttack offers build-in capabilities that only need to be adjusted to the needs at the
wavelength of choice. For example, aperture photometry and unit conversions have been
pre-implemented for the processing of Spitzer/MIPS images according to the MIPS user
manual5. This example shows that imaging obtained with a given instrument needs specific
treatment even in the simple approach of measuring flux densities via aperture photometry.
Perhaps the most non-trivial flux density measurement needs to be performed if (radio)
interferometric imaging is used. Flux density units at radio continuum wavelengths are typically reported in Janskys per beam. The total flux density of a point source can therefore be
measured by retrieving solely the flux density at the brightest pixel. However, especially if
the interferometric imaging has a high angular resolution, the point source limit turns out
to be an oversimplification in a stacking experiment of extragalactic sources even if they
are intrinsically point-like as detailed in the next Chapter (see Section 4.3.2). Extensive and
well-tested software to treat radio interferometric imaging is publicly available and should
be used in the workflow. As outlined above, a major advantage of StackAttack is that it is
optimized to process large numbers of input samples and that it can be embedded smoothly
in different computing environment. In order to assure this flexibility up to the final step
from the input to the resulting flux density even in the photometrically exotic case of radio interferometric imaging we implemented an external shell-based routine that uses the
aips6 pipeline. Another dedicated and newly implemented external shell-based routine is
finally used to translate the extensive human-readable aips output into a machine-readable
ascii table. Both routines drastically improve the efficiency of the workflow in extensive
radio stacking experiments. The individual steps to be performed in case of radio input
imaging and the parameters typically used are detailed in Section 4.3.2.
While flux density measurement depends on the input imaging used the same, in principle, holds true for the estimation of measurement errors. In other words, if standard
photometric techniques are used also error estimation can be performed in a standard way
when dealing with a stacked map. However, in a stacking experiment not only the pure
measurement uncertainty is of interest but also the effects caused by the intrinsic flux dispersion of the input sample. How large this dispersion is depends on the homogeneity of
5
The manual and other image processing as well as calibration requirements for Spitzer/MIPS data are found
at http://irsa.ipac.caltech.edu/data/SPITZER/docs/mips/.
6
aips is available from the National Radio Astronomy Observatory (NRAO) at http://www.aips.nrao.edu/ and
copyrighted by Associated Universities, Inc. using the GNU copright form.
26
3.3. Full implementation of an image stacking algorithm
the pre-selected galaxy population but also on the quality of the sample selection methods
which often depends on properties that themselves are affected by measurement errors
(e.g. colors). The user should be free to select the input sample so that restrictions of any
kind would neither be useful nor helpful since also very homogeneously selected samples
will show a minimum flux dispersion. It should rather be the aim to find a most objective
way to incorporate sample-dependent uncertainties in the final error estimation.
StackAttack therefore uses a bootstrapping approach (see Appendix A.2) that handles
both median and mean statistics as well as noise-weighted estimators (see Appendix A.1).
Our method is a simplification in that it uses the central pixel in each cutout stamp and
hence assumes that the dispersion of the peak signal is trivially related to that of the total
signal7 . A total flux measurement for each individual object and subsequently bootstrapping the set of total flux densities is, however, typically unfeasible since the bulk of objects
is undetected in a stacking experiment. It might be performed only if standard aperture
photometry with a single aperture extent is used but it is out of reach for more complicated
situations, e.g., in a (radio) interferometric stacking experiment as discussed above. Overall
our approach is a fair and efficient compromise that yields realistic insights in the dispersion of the input sample. Generally, it might not be straight forward to incorporate this
intrinsic sample dispersion in the total error budget of the integrated flux density. Exemplarily we discuss a way to treat the most important case for this thesis of radio continuum
stacking in the next Chapter (see Section 4.3.2).
3.3.3. Additional software features and prospects
Especially in case of mean-stacking experiments, concepts of outlier rejection are worth to
explore. This affects direct detections within a sample at the wavelength stacked as well as
noise distortions due to imaging artifacts and (extended) foreground structures. Not all of
these problems are actually related and hence different solution strategies are needed.
Perhaps simplest is the handling of spatially well separated direct detections at the wavelength stacked. If those are catalogued, a cross-match between input sample and survey
catalog suffices to exclude the detections from the stack. In order to arrive at a representative signal for the input sample, however, the contribution of both, detections and
non-detections, needs to be accounted for. A useful way of combining stacked signal and
individual detections is to average them in a way that accounts for the typically very different numbers of sources on both sides of the detection threshold.8 A noise-weighted
average is an appropriate choice since the decrease in background-noise in a correct stacking experiment is proportional to the inverse square-root of the number of sources stacked.
By definition the noise-weight is thus directly proportional to the number of undetected
sources.
As a caveat, the handling of direct detections based on a source catalog will always
7
Another assumption is that the astrometry is well behaved in the sense that the position in the input sample
neither has a systematic offset to the corresponding position of an object in the stacked map nor that the
flux in the two bands intrinsically peaks at distinct positions. Since the sources are generally unresolved the
latter point is of minor importance while the former point was tested for the radio imaging used to obtain
the results presented in this thesis (see Section 4.3.1 in the next Chapter).
8
While typically the bulk of the sources will be undetected at the wavelength stacked the signal contributed by
the rare detections is substantially larger which leads to an imbalance of flux contribution if not accounted
for by a number-weighted averaging scheme.
27
3. Seeing through the noise: Pushing observational limits via image stacking
Figure 3.2. – Cutout images affected by noise distortions, e.g., through foreground objects.
The examples shown here are taken from the test radio stacking experiment presented in
Figure 3.1. Mostly seen are lobes from bright radio galaxies at different foreground distances.
Examples a) and b) will barely affect the stacked signal measured at the center but enhance
the background noise level which complicates the total flux measurement. Other examples
(especially e) but also c) ) artificially add signal at the image center which significantly affects
a mean stacking experiment even given the fact that foreground distortions – as shown here
– are generally rare in the stacking experiments presented in this thesis.
be biased to some extent due to the detection threshold chosen for the catalog and the
user might want to test the robustness of the stacking experiment against the choice of
different thresholds. StackAttack provides the functionality to identify sources above a
user-defined detection threshold and to store the corresponding cutouts in an alternative
data cube that can be processed later by the user. In order to avoid the identification of
pure noise-peaks, the routine measures the average signal-to-noise ratio over 3 × 3 pixel
apertures within the central region of each cutout after determining if adequately bright
pixels exist within the same region. This part of the implementation has been developed
independently of the stacking algorithm for efficient and successful 1.4 GHz counterpart
search to distant star forming galaxies (see Chapter 6). It should be noted that testing of
this software feature was so-far restricted to the radio regime and that evaluation of its
performance at different wavelength is an ongoing effort.
The source finding capabilities of StackAttack can also be used to detect extended foreground structures in a given cutout stamp that might contribute to the signal in its central
region (see Figure 3.2). In a stacking experiment at radio wavelengths such structures
28
3.3. Full implementation of an image stacking algorithm
could be lobes of radio galaxies that are clearly not related to the actual source stacked.
These typically very bright structures might only affect the off-center regions of a cutout in
which case they leave a footprint in a final mean-stacked map, leading hence to significant
background distortions, artificially boosted noise levels and often even to an apparent loss
of information (e.g. Garn and Alexander 2009). Rejecting also cutouts that show off-central
bright structures might hence be beneficial but this needs to be evaluated separately for
different wavelength regimes and cannot be generalized. This is hence not an automatic
feature of StackAttack. In case of radio stacking, however, significantly less than 1 % of
objects in a sample are rejected on average and the effect of this artificial cut on the sample
thus is negligible.
Finally, direct detections might cause another important complication in case of a high
projected source density. If a source in the survey image happens to be close enough to
a source in the input sample signal confusion occurs. Depending on the input sample it
might even happen that two or more of its constituents might be blended into one in the
survey image, thereby counting the total signal twice in the stack. While crowded fields are
generally problematic, the situation degrades especially in combination with large beam
sizes. It is hence fair to say that a stacking experiment suffers from low angular resolution
as well as from increasing survey sensitivity.
Various strategies have been proposed to address these issues mainly at infrared (e.g.
Bourne et al. 2010; Chary and Pope 2010) and sub-mm (e.g. Greve et al. 2010) wavelengths,
typically starting from subtracting detected sources above a given threshold from the survey image and hence working with a residual map. Chary and Pope (2010) sort the sources
in the selection band by decreasing flux and retrieve cutouts centered at the catalog positions. In parallel they mask out all pixels in the survey map that are within a source
aperture centered at the position of a catalog source. A subsequent cutout that includes
this area will hence include no signal contribution from the masked pixels. The size of the
source aperture thereby is the same as used for extracting the photometry in the stacked
map. While there are several risks going along with such an image manipulation, a main
problem of this approach is the assumption of a strong correlation between source intensity in the selection band and at the wavelength stacked. It might not be the case for every
stacking experiment that brighter sources in one band are always brighter in the other.
Moreover, this method is restricted to stacking the entire galaxy population in the selection
band at once, hence not allowing to cull sub-populations based on other galaxy properties.
This is caused by the fact that only sources that are actually contained in the input sample
will be masked out while other objects might still lead to source confusion. To account for
all objects in a given selection band a complicated deblending strategy has been applied by
Greve et al. (2010) that involves the identification of a chain of neighbors when considering
the relative distances of sources in an input sample in relation to the beam size of the survey map. This chain leads to a system of equations connecting measured (i.e. blended) and
intrinsic fluxes of all sources contained in the chain to be solved for the intrinsic signal of
the source of interest. Based on stacking simulations it has been shown by Kurczynski and
Gawiser (2010) that such a deblending strategy indeed provides a vast improvement over
other methods if the survey map resolution is so coarse that source blending becomes the
dominant source of errors (e.g. at (sub-)mm wavelengths). An alternative strategy is to exploit the knowledge about the source clustering properties of the input sample (e.g. Bourne
et al. 2010). This involves an autocorrelation analysis of the positions in the input sam-
29
3. Seeing through the noise: Pushing observational limits via image stacking
ple and leads to an estimate of the average flux excess expected in a stacking experiment
as detailed by Bourne et al. (2010). The limitations of this approach are the assumption
that source clustering follows the same laws in both the selection and the stacking band as
well as the fact that only a global (i.e. common) correction factor for subsequent stacks of
sub-samples can be obtained.
It is certain that not all methods discussed above apply equally well to any stacking experiment since their limitations prohibit to use them in a general context. Any artificial
source rejection from an input sample as well as any deblending strategy hence needs to
be chosen with care and applied wisely depending not only on resolution and sensitivity
but also on the choice of input sample as well as the stacking method. It is also noteworthy that radio interferometric imaging offers practically ideal conditions for image stacking
experiments. The high angular resolution of radio images fruitfully combines with the comparatively low detection rate even deep radio surveys show. Source confusion issues are
hence marginalized and constitute a negligible source of uncertainty for the results of a
radio stacking experiment.
Clearly, further stacking simulations that involve artificial sources placed into residual
maps at various wavelengths are needed to explore further the potential biases of stacking
experiments with respect to the various parameters mentioned. Thanks to its efficient
implementation StackAttack qualifies well for extensive simulations that are currently
underway (Sargent, Karim et al. in prep.).
3.3.4. Panchromatic applications of the image stacking routine
The newly implemented image stacking routine StackAttack has been used in the 1.4 GHz
band of the VLA-COSMOS survey for an extensive radio continuum stacking study of stellar
mass-selected galaxies in the COSMOS field to reveal their average star formation properties (Karim et al. 2011a). Further details on stacking and flux measurements at radio
wavelengths as well as the scientific results are presented in the upcoming Chapters of this
thesis.
At radio wavelengths the routine is currently also used in a very different scientific context (Smolčić, Karim et al. in prep.) constraining the evolution of the 1.4 GHz luminosity
function for massive quiescent galaxies, the main hosts of active galactic nuclei (AGN)
with substantial radio emission (radio-AGN) since z ∼ 3 (Figure 3.3). The luminosity functions are used to observationally constrain the total mechanical energy output of radio-AGN
(Figure 3.4) that sets the rate by which radio-AGN heat their surrounding interstellar media thereby preventing further star formation (a process called ’radio-mode feedback’).
These results extend the initial findings by Smolčić et al. (2009b) and can be directly compared to theoretical predictions (e.g. Croton et al. 2006). Further radio continuum stacking
studies are under-way: Selecting galaxies based on their rest-frame ultraviolet continuum
properties (the so-called UV-slope) enables insights into the evolution of the average dustextinction. Moreover, comparing the average UV-derived star formation rates with radiostacking based ones at various redshifts the appropriate dust extinction correction factors
can be evaluated in a stellar-mass dependent way.
StackAttack is also extensively utilized at infrared wavelengths using Spitzer/MIPS and
Herschel/PACS maps of the COSMOS field (Sargent, Karim et al. in prep.). The goals of
this study are twofold. On the one hand thorough numerical as well as stacking simulations
30
3.3. Full implementation of an image stacking algorithm
Figure 3.3. – Evolution of the radio luminosity function (LF) for quiescent galaxies with stellar
masses M∗ & 3 × 1010 M⊙ in the COSMOS field. These results by Smolčić, Karim et al. (in
prep.), to be submitted to The Astrophysical Journal, have been constrained with the help of
StackAttack at low radio luminosities.
Left: Local (0.1 < z < 0.3) LF (open thick symbols). Volume densities that have been derived
based on a volume limited radio detected sample are denoted by black open squares, while
the volume density that is based on stacked data is shown by an open black circle. The LFs
derived based on literature data (SDSS, 2dF, NGC catalog; Sadler et al. 2002; Best et al.
2005; Filho et al. 2006; Mauch and Sadler 2007) are also shown, and labeled in the panel.
Two analytic LFs (Sadler et al. 2002; Mauch and Sadler 2007; S02, M07) are also displayed.
Right: Evolution of the LF in four redshift bins out to z = 3. Here stacked data are indicated as
filled black circles. In the 0.3 < z < 0.6 redshift range we show literature results (Sadler et al.
2007; Donoso et al. 2009). The displayed lines show the best fit evolution to the COSMOS
data using the S02 LF (full dark-grey curve: pure luminosity evolution; full light-gray curve:
pure density evolution), and the M07 LF (black dashed curve: pure luminosity evolution). For
comparison we also show the assumed evolution of the low-power radio AGN by Willott et al.
(2001) as a light-gray dash-dotted curve.
of artificial sources are carried out in order to investigate potential stacking biases and
especially how stacking-derived flux ratios (such as colors) are affected. A second aim is to
explore the evolution of the radio/infrared relation at faint (low-mass) levels based on the
galaxy samples used in Karim et al. (2011a) in order to extend previous studies of galaxies
detected in the COSMOS field (Sargent et al. 2010a,b).
At millimeter wavelengths StackAttack is used to explore the cold dust emission properties at the faint end of the star forming galaxy population on an initial 2 mm deep field
image taken in the GOODS-North field (Walter et al. in prep.). This map was recently
obtained with the privately funded Goddard-IRAM Superconducting 2-Millimeter Observer
(GISMO), a next generation bolometer array camera currently operated at the IRAM 30 m
telescope.
31
3. Seeing through the noise: Pushing observational limits via image stacking
Figure 3.4. – Comoving volume averaged heating rate (Ω) done by quiescent massive galaxies
in the COSMOS field as a function of redshift. These results by Smolčić, Karim et al. (in
prep.), to be submitted to The Astrophysical Journal, have been constrained with the help
of StackAttack in order to observationally constrain the effect of ’radio-mode feedback’
to galaxy evolution. Ω was derived by first converting the luminosity functions shown in
Figure 3.3 into kinetic energy density functions and then integrating the latter over radio
luminosity (see Bîrzan et al. 2008 and Smolčić et al. 2009b for details). Both panels show
the COSMOS data points derived by assuming pure density (PDE; filled circles), and pure
luminosity (PLE; open squares) evolution that best fit the data in a given redshift bin. The
(dotted and dashed) lines in the top panel illustrate the discrepancy in Ω if various lower
boundary integral values are assumed (indicated in the panel). The thick solid line shows the
’radio-mode feedback’ heating rate drawn from the Croton et al. (2006) cosmological model,
and required to reproduce observed galaxy properties.
32
3.4. Summary
3.4. Summary
A major time invest during the course of this thesis was the development and implementation of an idl-based multi-purpose image stacking routine. The resulting software package
StackAttack is an efficient, flexible and portable image stacking tool capable of processing arbitrary survey imaging and input samples using various statistical estimators.
StackAttack has been intensively tested and applied at radio continuum wavelengths
while it is already used to produce scientific results also at infrared and millimeter wavelengths. Clearly, not all features of this software have been fully developed and exploited
in a panchromatic fashion given the vast diversity of requirements demanded by different input samples at different wavelengths. Especially the implementation of deblending
strategies is an ongoing effort as well as the exploration of biases introduced in a stacking
experiment via numerical and stacking simulations.
33
3. Seeing through the noise: Pushing observational limits via image stacking
34
4. Star formation at 0.2 < z < 3 in
mass-selected galaxies in the COSMOS
field
In this chapter the newly developed image stacking routine introduced above is used at
radio continuum wavelengths to study the average (specific) star formation rate ((S)SFR)
of > 105 stellar mass-selected galaxies in the 2 deg2 COSMOS field. We separately consider
the total sample and a subset of galaxies that shows evidence for substantive recent star
formation in the rest-frame optical spectral energy distributions. At redshifts 0.2 < z < 3
both populations show a strong and mass-independent decrease in their SSFR towards
the present epoch. It is best described by a power- law (1 + z)n , where n ∼ 4.3 for all
galaxies and n ∼ 3.5 for star forming (SF) sources. The decrease appears to have started
at z > 2, at least for high-mass (M∗ & 4 × 1010 M⊙ ) systems where our conclusions are
most robust. Our data show that there is a tight correlation with power-law dependence,
SSFR ∝ M∗ β , between SSFR and stellar mass at all epochs. The relation tends to flatten
below M∗ ≈ 1010 M⊙ if quiescent galaxies are included; if they are excluded from the
analysis a shallow index βSFG ≈ −0.4 fits the correlation. On average, higher mass objects
always have lower SSFRs, also among SF galaxies. At z > 1.5 there is tentative evidence
for an upper threshold in SSFR that an average galaxy cannot exceed, possibly due to
gravitationally limited molecular gas accretion. It is suggested by a flattening of the SSFRM∗ relation (also for SF sources), but affects massive (> 1010 M⊙ ) galaxies only at the
highest redshifts. Since z = 1.5 there thus is no direct evidence that galaxies of higher
mass experience a more rapid waning of their SSFR than lower mass SF systems. In this
sense, the data rule out any strong ’downsizing’ in the SSFR. This chapter is part of the
publication
A. Karim, E. Schinnerer, A. Martínez-Sansigre, M. T. Sargent, A. van der Wel, H.-W. Rix,
O. Ilbert, V. Smolčić, C. Carilli, M. Pannella, A. M. Koekemoer, E. F. Bell & M. Salvato, 2011,
ApJ, 730, 61, The star formation history of mass-selected galaxies in the COSMOS field
4.1. Introduction
Over the last years multi-waveband surveys of various wide fields have lead to estimates
of star formation rates (hereafter SFRs) and stellar masses for large numbers of galaxies
out to high redshifts. Both quantities are crucial for understanding galaxy evolution. On
the one hand an evolution of the observed number density of galaxies as a function of
stellar mass, i.e. the mass function, reveals how the stars are distributed among galaxies at
different cosmic epochs. If, on the other hand, an increase in stellar mass of any population
of galaxies can solely be explained by the rate at which new stars are formed within these
systems or if other mechanisms are dominant can only be discussed if the corresponding
35
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
SFRs themselves are known.
A number of studies (e.g. Lilly et al. 1996; Madau et al. 1996; Chary and Elbaz 2001;
LeFloc’h et al. 2005; Smolčić et al. 2009a; Dunne et al. 2009; Rodighiero et al. 2010b;
Gruppioni et al. 2010; Bouwens et al. 2011b; Rujopakarn et al. 2010 and for a compilation
Hopkins 2004 and Hopkins and Beacom 2006) revealed that the star formation rate density
(hereafter SFRD), i.e. the SFR per unit comoving volume, rapidly declines over the last
∼ 10 Gyr following the purported maximum of star formation activity in the universe. The
question of whether the stellar mass content of galaxies could be a major driver for this
decline has gained significant interest after the discovery of a tight correlation of SFR and
stellar mass for star forming (hereafter SF) galaxies with an intrinsic scatter of only about
0.3 dex (e.g. Brinchmann et al. 2004; Noeske et al. 2007b; Elbaz et al. 2007). This relation
was studied in the local universe (Brinchmann et al. 2004; Salim et al. 2007) suggesting an
apparent bimodality in the SFR-M∗ plane if all galaxies are taken into account. It was also
found to exist for SF galaxies at z . 1.2 (e.g. Noeske et al. 2007b; Elbaz et al. 2007; Bell
et al. 2007; Walcher et al. 2008) and further out to z ≈ 2.5 (Daddi et al. 2007; Pannella et al.
2009).1 Consequently the stellar mass normalized SFR (hereafter specific SFR or SSFR),
i.e. the SFR at a given epoch divided by the stellar mass the galaxy possesses at the same
cosmic epoch, shows a tight (anti-)correlation.
By studying the SSFR galaxies of different stellar masses can be directly compared. The
SSFR itself defines a typical timescale that can be interpreted as a current efficiency of
star formation within a galaxy compared to its past average star formation activity. The
compilation of the studies mentioned (e.g. Pannella et al. 2009; González et al. 2010; Dutton
et al. 2010), not using a common tracer for star formation nor selection technique for
separating the SF galaxy fraction and data originating from various wide fields, suggests
a steep evolution of the normalization of the SSFR-M∗ relation2 for SF galaxies. Studies,
covering a broad dynamical range in stellar mass, have been carried out for all galaxies
and confirmed the SSFR, as a function of redshift, to be even more rapidly increasing from
z = 0 to z ≈ 1 (e.g. Feulner et al. 2005b; Zheng et al. 2007a; Damen et al. 2009b, 2010)
as well as throughout an even wider range in redshift (e.g. Feulner et al. 2005a; PérezGonzález et al. 2008; Dunne et al. 2009; Damen et al. 2009a). It has been claimed that the
steepness of the SSFR-increase with redshift might be a challenge for a cold dark matter
concordance model (ΛCDM) suggested by comparisons to predictions from semi-analytical
models (SAMs) (see Santini et al. 2009; Damen et al. 2009a; Firmani et al. 2010 and, e.g.,
Guo and White 2008, for theoretical results based on a SAM).
It was recently discussed by Stark et al. (2009) and González et al. (2010), at least for
moderately massive SF galaxies (M∗ ∼ 5 × 109 M⊙ ), that the rapidly evolving SSFR might
turn constant in the early universe. Their data show constant SSFRs up to the highest
redshift ranges (z ≈ 7 − 8) probed so far. This significant deviation of the SSFR-evolution
from a power-law (SSFR ∝ (1 + z)n ), fitting well the data below z ≈ 2, could be a hint
for different physical mechanisms regulating star formation in the early universe (González
et al. 2010). However, this deviation could also be a result of observational data significantly
underestimating the SSFRs at these high redshifts (Dutton et al. 2010) caused by selection
1
It needs to be mentioned that at z ∼ 2 Erb et al. (2006) only found a weak correlation between SFR and
stellar mass. However, their galaxy sample selection at ultraviolet wavelengths preferentially traces SFR
rather than stellar mass, thus potentially biasing their results towards a flatter SFR-M∗ relation.
2
In the following we will refer to this relation for SF galaxies as the SSFR-sequence.
36
4.1. Introduction
biases 3 . Recent theoretical models propose an enhanced merger rate (Khochfar and Silk
2010) at high z in order to account for the purported constancy of the SSFR. This is in
contrast to pure steady cold-mode gas accretion above a limiting dark matter halo mass
(the so-called ’mass floor’ of MDM ∼ 1011 M⊙ ; Bouché et al. 2010) reproducing well the
observed slope of the SSFR-sequence at all redshifts z < 2.
It was generally found that at z < 2 all galaxies show a significant (negative) slope of the
SSFR-M∗ relation leading to lower SSFRs in more massive galaxies. Star forming galaxies
also seem to show this behavior but the trend tends to be significantly weaker especially at
z > 1 where, based on the sBzK selection technique, the slope was found to be practically
vanishing (Daddi et al. 2007; Pannella et al. 2009). It therefore is an ongoing debate if this
phenomenon of a decreasing slope of the SFR-M∗ relation for SF galaxies with redshift is
real or just an artifact (for an introduction and a summary of the conflicting observational
results see, e.g., Fontanot et al. 2009). This effect is commonly interpreted as star formation
efficiency being shifted from higher mass objects in the cosmic past to lower mass objects
in the present and sometimes referred to as ’cosmic downsizing’ (Cowie et al. 1996). Most
recently, based on first Herschel/PACS far-infrared data, even the opposite effect, the socalled SSFR-upsizing at z & 1.5, has been proposed (Rodighiero et al. 2010a).4
More measurements are needed to understand the relation of SFR and stellar mass and
its evolution with redshift. This holds especially true for the population of SF galaxies. An
accurate measurement of the (S)SFR-sequence at all epochs is key for a better understanding of galaxy evolution. As it was claimed (e.g. Noeske et al. 2007b) a tight correlation of
SFR and stellar mass disfavors star formation histories (SFHs) of individual normal galaxies that are mainly driven by stochastic processes, such as mergers. Quite contrarily it
favors smooth SFHs in such a way that the SFH at any cosmic epoch of a galaxy is solely
determined by its stellar mass content measured at the corresponding redshift unless the
galaxy becomes subject to quenching of star formation. In this sense the SFR-M∗ relation
at a given redshift is regarded an isochrone for galaxy evolution in the same manner the
Hertzsprung-Russel-Diagram is an isochrone for the evolution of a stellar population at a
given age.5 It should be mentioned, however, that Cowie and Barger (2008) disagree with
this conclusion which underlines the importance of future studies that use a sufficiently
deep direct SFR tracer to study the intrinsic dispersion of the SSFRs .6
Several tracers across the electromagnetic spectrum are used to estimate the star formation rate of a normal galaxy7 . While rest-frame ultraviolet (UV) light originates mainly
from massive stars and thus directly traces young stellar populations it will be strongly at3
Note the very small number of galaxies currently studied in the extreme high redshift regime. Also note the
highly discrepant SSFR-estimates presented by Yabe et al. (2009) and Schaerer and de Barros (2010) at the
most extreme redshifts as summarized by Bouché et al. (2010) in their Figure 13.
4
This trend is weakly supported by the earlier findings of Oliver et al. (2010).
5
The (S)SFR-mass relation is therefore also sometimes referred to as ’the galaxy main sequence’ (Noeske
et al. 2007b) that is, for an individual galaxy of stellar mass M∗ , connected by evolutionary tracks (e.g. the
so-called tau-model discussed in Noeske et al. 2007a) at distinct cosmic epochs (see also Noeske 2009, for
a summary).
6
Cowie and Barger (2008) cannot confirm the low level of intrinsic dispersion in the SSFR-M∗ plane found
by Noeske et al. (2007b) and they discuss other hints they find supporting SFHs to be rather dominated by
episodic bursts. We emphasize that the larger dispersion of SSFRs might be caused by the relatively broad
bins in redshift used by Cowie and Barger (2008) given the steep increase with redshift of SSFRs at z < 1.5
while studying all massive galaxies.
7
’Normal’ galaxies are defined as systems that do not host an active galactic nucleus.
37
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
tenuated by dust. The absorbed UV emission is thermally reprocessed by heating the dust
which in turn reemits at infrared (IR) wavelengths. Star formation also leads to emission
in the radio continuum since charged cosmic particles are accelerated in shocks within
the remnants of supernovae (SNR) leading to non-thermal synchrotron radiation (e.g. Bell
1978a and e.g. Muxlow et al. 1994, for observations of individual SNRs). Thermal free-free
emission (Bremsstrahlung) in general contributes only weakly to the 1.4 GHz signal (see
e.g. Condon 1992) but might become dominant in low-mass systems where the synchrotron
emission was empirically found to be strongly suppressed (Bell 2003a). Also empirically
the phenomenon of radio emission triggered by star formation results in its well known
strong correlation with the far-IR output of a given SF galaxy (e.g. Helou et al. 1985; Condon 1992; Yun et al. 2001; Bell 2003a) that appears to persist out to high (z > 2) redshifts
in a non-evolving fashion (e.g. Sargent et al. 2010a,b).
A major advantage of radio emission as a tracer for star formation is its obvious independence of any correction for dust attenuation. Due to well known underlying physical
processes the spectral energy distribution of a normal galaxy in the low (. 5) GHz regime
shows a Fν ∝ ν αrc shape (e.g. Bell 1978a). While αrc = −0.8 is found to be a typical value
for the radio spectral index (e.g. Condon 1992; Bell 2003a, for a summary but also, e.g.,
Scheuer and Williams 1968; Bell 1978b, for early results) no further spectral features are
expected in this frequency range thus leading to a robust K-correction up to high (z . 3)
redshifts.8 Both advantages directly confront the rather uncertain dust attenuation coefficient for UV light and the presence of polycyclic aromatic hydrocarbon (PAH) emission
features redshifted (at z & 0.8) into the 24 µm band commonly used as an estimator for
the total infrared (TIR) emission. Also the combination of UV and mid-IR emission tracing
star formation is limited since it is typically tested in moderately SF systems at low redshift
(for a summary see Calzetti and Kennicutt 2009) which might not resemble high redshift
galaxies with higher SFRs and larger dust content. Finally, even at a resolution of ∼ 5′′
achieved by current UV and IR telescopes blending of sources becomes a severe issue for
the faint end of the sources (see, e.g., Zheng et al. 2007b). Current radio interferometers
such as the (E)VLA and (e)Merlin achieve resolutions of . 2′′ that are needed to unambiguously identify optical counterparts. This unambiguity is particularly important in a stacking
experiment as otherwise flux density from nearby sources might contribute to the emission of an individual object. A drawback of using radio emission to trace star formation
is the generally low sensitivity to the normal galaxy population even in the deepest radio
surveys to-date which usually limits the analysis to a stacking approach. Therefore, current
radio surveys allow one to study average SFR properties while they cannot shed light on
the intrinsic dispersion of individual sources. This situation will improve with future EVLA
surveys.
Studying the stellar-mass dependence of the SFH requires a mass-complete sample in
order to prevent inferred evolutionary trends from being mimicked by sample incompleteness. Early type galaxies containing predominantly older stellar populations and showing
therefore a prominent 4000 Å break (see e.g. Gorgas et al. 1999) are likely to be excluded
in optical surveys above z ∼ 1 even at deep limiting magnitudes as the break is redshifted
into the selection band. Optical selection, thus, potentially limits any study of a stellar
mass-complete sample to the bright (i.e. high-mass) end or is effectively rather a selection
8
Unless radiative losses, e.g. inverse Compton scattering against the cosmic microwave background, steepen
the spectral index to values ∼-1.3.
38
4.2. The pan-chromatic COSMOS data used
by unobscured SFR than by stellar mass if the full sample is considered for the analysis.
Channel 1 of the IRAC instrument onboard the Spitzer Space Telescope provides us with
the 3.6 µm waveband that samples the rest-frame K -band at z ∼ 0.5 to the rest-frame z band at z ∼ 3. It is therefore ideal in probing mainly the light from old low-mass stars
while not being severely affected by dust. For the analysis presented here, hence, a deep
and rich (∼ 100, 000 sources at z ≤ 3) 3.6 µm galaxy sample in combination with accurate
photometric redshifts and stellar-mass estimates has been used (Ilbert et al. 2010). With
a sky coverage of 2 deg2 the Cosmic Evolution Survey9 (COSMOS) provides the largest
cosmological deep field to-date (see Scoville et al. 2007d, for an overview). The uniquely
large COSMOS 3.6 µm galaxy sample offers uniform high-quality pan-chromatic data for
all sources enabling us to study the SSFR in small bins in both stellar mass and redshift.
Additionally the evolution of the stellar mass-functions has been studied already based on
the same sample and its SF sub-population (Ilbert et al. 2010). As it was argued (e.g. in
Daddi et al. 2010a) the combination of the individual evolutions of the mass function and the
(S)SFR-sequence might be the most important observational constraints for understanding
the stellar mass build-up on cosmic scales jointly resulting in a potentially peaking and
declining SFRD. We will discuss further implications in the next Chapter.
This Chapter is organized as follows. In Section 4.2 we present our principle and ancillary
COSMOS data sets and the selection of our sample. Sec 4.3 contains a detailed description of the application of our stacking algorithm at radio wavelengths and the derivation of
average SFRs from 1.4 GHz image stacks. Additional methodological considerations pertaining to both sample selection and flux density estimation by image stacking are to be
found in the Appendices. Readers who wish to directly proceed to our results and their
interpretations can find those regarding the relation of SSFR and stellar mass in Section
4.4.
Throughout this and the following Chapter all observed magnitudes are given in the AB
system. We assume a standard cosmology with H0 = 70 (km/s)/Mpc, ΩM = 0.3 and ΩΛ = 0.7
consistent with the latest WMAP results (Komatsu et al. 2009) as well as a radio spectral
index of αrc = −0.8 in the notation given above if not explicitly stated otherwise. A Chabrier
(2003) initial mass function (IMF) is used for all stellar mass and SFR calculations in this
Chapter. Results from previous studies in the literature have been converted accordingly.10
4.2. The pan-chromatic COSMOS data used
In order to study the redshift evolution of galaxies in general, and the evolution of their
SFRs in particular, a complete and large sample of normal galaxies is needed as it not only
provides representative but also statistically significant insights.
The large area of 2 deg2 covered by the COSMOS survey, fully imaged at optical wavelengths by the Hubble Space Telescope (HST; Scoville et al. 2007a; Koekemoer et al. 2007),
is necessary to minimize the effect of cosmic variance. Deep UV GALEX (Zamojski et al.
2007) to ground-based optical and near-infrared (NIR) (Taniguchi et al. 2007; Capak et al.
2007) imaging of the equatorial field11 yielded accurate photometric data products for
9
http://cosmos.astro.caltech.edu
Logarithmic masses and SFRs based on a Salpeter (1955) IMF, a Kroupa (2001) IMF and a Baldry and Glazebrook (2003) IMF are converted to the Chabrier scale by adding -0.24 dex, 0 dex and 0.02 dex, respectively.
11
The COSMOS field is centered at RA = 10 : 00 : 28.6 and Dec = +02 : 12 : 21.0 (J2000)
10
39
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
∼ 1 × 106 galaxies down to 26.5th magnitude in the i-band (Ilbert et al. 2009; Capak et al.
2007). Thanks to extensive spectroscopic efforts at optical wavelentghs using VLT/VIMOS
and Magellan/IMACS (Lilly et al. 2007; Trump et al. 2007) the estimation of photometric
redshifts for all these sources could be accurately calibrated. Ongoing deep Keck/DEIMOS
campaigns (PIs Scoville, Capak, Salvato, Sanders and Karteltepe) extent the spectroscopically observed wavelength regime to the NIR which is critical to improve the photometric
calibration for faint sources at high redshifts. In addition to observations of the whole or
parts of the COSMOS field in the X-ray (Hasinger et al. 2007; Elvis et al. 2009) and millimeter (Bertoldi et al. 2007; Scott et al. 2008), imaging by Spitzer in the mid- to far-IR
(Sanders et al. 2007) as well as interferometric radio data (Schinnerer et al. 2004, 2007,
2010) covering the full 2 deg2 have been obtained.
4.2.1. VLA-COSMOS radio data
Radio observations of the full (2 deg2 ) COSMOS field were carried out with the Very Large
Array (VLA) at 1.4 GHz (20 cm) in several campaigns between 2004 and 2006. The entire field was observed in A- and C-configuration (Schinnerer et al. 2007) where the 23
individual pointings were arranged in a hexagonal pattern. Additional observations of the
central seven pointings in the most extended A-configuration (Schinnerer et al. 2010) were
obtained in order to achieve a higher 1.4 GHz sensitivity in the area overlapping with the
COSMOS MAMBO millimeter observations (Bertoldi et al. 2007). In both cases the data
reduction was done using standard procedures from the Astronomical Imaging Processing
System (aips; see Schinnerer et al. 2007, for details). At a resolution of 1.5′′ × 1.4′′ the final
map has a mean rms of ∼ 8 µJy/beam in the central 30′ × 30′ and ∼ 12 µJy/beam over the
full area, respectively. Using the SAD algorithm within aips, a total of 2,865 sources were
identified at more than 5σ significance in the final VLA-COSMOS mosaic (Schinnerer et al.
2010). As the outermost parts of the map are not covered by multiple pointings the noise
increases rapidly towards the edges. In this study we therefore exclude these peripheral
regions resulting in a final useable area of 1.72 deg2 .
4.2.2. A 3.6 µm selected galaxy sample within the COSMOS photometric
(redshift) catalogs
Deep Spitzer IRAC data mapping the entire COSMOS field in all four channels have been
obtained during the S-COSMOS observations (Sanders et al. 2007). The data reduction
yielding images and associated uncertainty maps for all the four channels is described in Ilbert et al. (2010) (I10 hereafter). For the 3.6 µm channel a source catalog has been obtained
by O. Ilbert and M. Salvato (private communication) using the SExtractor package (Bertin
and Arnouts 1996). Given the point spread function (PSF) of 1.7” a Mexican hat filtering of
the 3.6 µm image within SExtractor was used in order to assure careful deblending of the
sources.
The resulting sample of 3.6 µm sources down to a limiting magnitude of mAB (3.6 µm) =
23.9 in the 2.3 deg2 field, not considering the masked areas around bright sources (Ks < 12),
areas of poor image quality and the field boundaries, consists of 306,000 sources.12
12
As a stacking analysis depends on the input sample prior masked areas consequently reduce further the
effective area for this study. All space densities reported in this work are therefore computed for an effective
40
4.2. The pan-chromatic COSMOS data used
As detailed in I10 photometric redshifts (hereafter photo-z ’s) were assigned to all 3.6 µm
detected sources. The vast majority of sources is also detected at optical wavelengths
and therefore contained in the COSMOS photo-z catalog13 (Ilbert et al. 2009) so that in
general photometric information from 31 narrow-, intermediate and broad-band FUV-tomid-IR filterbands was available.14 Within the remaining 4 % (i.e. a total of 8507) of the
3.6 µm sources 2714 are also contained in the COSMOS K−band selected galaxy sample
(McCracken et al. 2010) and are also regarded as real sources. I10 assigned photo-z’s to
these extremely faint objects using the available NIR-to-IRAC photometry.
The quality of the photo-z ’s was estimated (for details see I10) by using spectroscopic redshifts for a total of 4,148 sources at mAB (i+ ) < 22.5 from the zCOSMOS survey (Lilly et al.
2009). At a rate of < 1 % of outliers the accuracy was found to be σ(zphot −zspec )/(1+zspec ) =
0.0075 down to the magnitude limit of the spectroscopic sample. For all objects within the
3.6 µm selected catalog – regardless of i-band magnitude the accuracy was derived by using
the 1σ uncertainty on the photo-z’s from the probability distribution function which yields
a conservative estimate of the photo-z uncertainty as detailed in Ilbert et al. (2009). At
1.25 < z < 2 the relative photo-z uncertainty is 0.08 and thus higher by a factor of four
compared to the median value for the full (mAB (3.6 µm) ≥ 23.9) sample.15 We account for
this when binning the data in redshift by choosing increasing bin widths with increasing
redshift.16 It is worth noting that the photo-z accuracy is degraded at magnitudes fainter
than mAB (i+ ) = 25.5 (See Figure 12 in Ilbert et al. (2009)). Our choice of lower stellar mass
limits (see Section 4.2.6) and our stellar mass binning-scheme (see Section 4.2.6) automatically ensures a low fraction (< 15 %) of these optically very faint objects within the lowest
mass-bin above our mass limit at any redshift. The fraction of such faint objects effectively
vanishes towards higher masses as also pointed out by I10.17
4.2.3. Estimation of stellar masses
Stellar masses for all objects within the 3.6 µm selected parent sample have been computed
by I10. Here, we briefly summarize the method and the important findings. For the estimation of stellar masses based on a Chabrier IMF stellar population synthesis models generated with the package provided by Bruzual and Charlot (2003) (BC03) have been used.
Furthermore an exponentially declining SFH and a Calzetti et al. (2000) dust extinction
law have been assumed. Spitzer MIPS 24µm flux densities (from LeFloc’h et al. 2009) have
been included in the SED template fitting as an additional constraint on the stellar mass.
field size of 1.49 deg2 .
This optically deep sample has a limiting magnitude of 26.2 in the i+ selection band (see Table 1 in Salvato
et al. (2009)).
14
As described in detail by I10 all photo-z’s used in our study were obtained using a χ2 template-fitting procedure implemented in the code Le Phare (Arnouts et al. 2002; Ilbert et al. 2006) and a library of 21 templates.
Additional stellar templates were used to reject stars (i.e. sources with a lower χ2 values for the stellar compared to the galaxy templates) from the final galaxy sample.
15
For a color-selected sub-set of galaxies for which spectroscopic redshifts from the zCOSMOS-faint survey
(Lilly et al., in prep.) were available the photo-z accuracy was directly tested at 1.5 < z < 3. This yields an
accuracy of σ∆z/(1+z) = 0.04 with 10% of catastrophic failures.
16
It should be mentioned, however, that the projected-pair analysis by Quadri and Williams (2009) independently shows that photo-z ’s from data sets with broad- and intermediate band photometry like the COSMOS
catalog are not expected to have very different photo-z errors at z > 1.5 than at lower redshifts.
17
I10 use comparable mass limits and their Figure 8 shows the strong decline of the fraction of optically faint
objects with mass at all z .
13
41
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
Systematic uncertainties on the stellar masses, caused by the use of photo-z’s, the choice
of the dust extinction law and library of stellar population synthesis models, have been investigated. No systematic effect due to the use of photo-z’s is apparent. Stellar masses
derived from the BC03 templates are systematically higher by 0.13-0.15 dex compared to
the newer Charlot & Bruzual (2007) versions (Bruzual 2007) that have an improved treatment of thermally pulsing asymptotical giant branch (TP-AGB) stars. As BC03 models are
commonly used in the literature, both studies, I10 and this work, are based on BC03 mass
estimates.
4.2.4. Spectral classification
A number of studies suggest the existence of a bimodality in the SSFR-M∗ plane (e.g. Salim
et al. 2007; Elbaz et al. 2007; Santini et al. 2009; Rodighiero et al. 2010a) leading to a tight
SSFR-sequence to be in place only for SF galaxies. Therefore a deselection of quiescent,
i.e. non SF, objects is needed.
Following I10 we classify galaxies with a best-fit BC03 template that has an intrinsic (i.e.
dust unextincted) rest-frame color redder than (NUV − r + )temp = 3.5 as quiescent. Several
authors (e.g. Wyder et al. 2007; Martin et al. 2007b; Arnouts et al. 2007) suggest this color
to be an excellent indicator for the recent over past average SFR as it directly traces the
ratio of young (light-weighted average age of ∼ 108 yr) and old (≥ 109 yr) stellar populations.
Seeking for a color bimodality that discriminates galaxies with currently high from those
with low star formation activity the NUV−r color appears therefore to be superior to purely
optical rest-frame colors such as U − V (e.g. Bell et al. 2004).
Using a dust uncorrected NUV − r + versus r + − J rest-frame color-color diagram18 I10
showed that in the range 0 ≤ z ≤ 2 for (NUV −r + )temp > 3.5 quiescent galaxies are well separated from the parent sample without severe contamination by dust-obscured SF galaxies.
This quiescent population is therefore comparable to the one classified by Williams et al.
(2009) based on a U − V versus V − J rest-frame color-color diagram.
Furthermore our quiescent population shows a clear separation from the parent sample with respect to galaxy morphology. I10 visually classified a subset of 1,500 isolated
and bright galaxies from the 3.6 µm parent sample using HST/ACS images and found the
quiescent population among those to be clearly dominated by elliptical (E/S0) systems. A
further cut ((NUV − r + )temp < 1.2) was shown to efficiently separate late type spiral and
irregular galaxies from early type spirals as well as the remaining tail of elliptical systems.
As any such color cut effectively is a cut in star formation activity we discuss the spectral
pre-classification of SF systems in more detail in Section 4.5.
4.2.5. AGN contamination
A major concern arising in the context of using radio emission to trace star formation is
contaminating flux from active galactic nuclei (AGN). For some galaxies the total radio
signal might even be dominated by an AGN. For our study, ideally, we should therefore
remove all galaxies hosting an AGN from our sample.
18
Here the absolute magnitudes were inferred from the observed magnitudes not accounting for dust reddening.
42
4.2. The pan-chromatic COSMOS data used
Cross-matching the most recent XMM-COSMOS photo-z catalog (Salvato et al. 2009;
Brusa et al. 2010) with the 3.6 µm selected parent sample delivered a total of 1,711 (i.e.
∼ 1 %) X-ray detected objects. Most of these sources exhibit best-fit composite AGN/galaxy
SEDs19 while a minor fraction is well fitted by an SED showing no AGN contribution. However, here all X-ray detections are treated as potential AGN contaminants and thus removed
from our sample.20
Studies of the radio luminosity function (e.g. Sadler et al. 2002; Condon et al. 2002) agree
that radio-AGN contribute half of the radio light in the local universe at radio luminosities
slightly below L1.4 GHz ∼ 1023 W/Hz and outnumber SF galaxies above ∼ 2 × 1023 W/Hz.
Detailed multi-wavelength studies (Hickox et al. 2009; Griffith and Stern 2010) yield that
radio-AGN are hosted by red galaxies. The evolution out to z ≈ 1.3 of the radio-AGN fraction
for luminous (i.e. L1.4 GHz > 4 × 1023 W/Hz) radio-AGN as a function of stellar mass has
been presented by Smolčić et al. (2009b) who selected a parent sample of red galaxies with
rest-frame U − B colors in a range close to our quiescent galaxy fraction. The derived AGNfractions at a given stellar mass within the red galaxy population are therefore applicable
to our sample.
According to Smolčić et al. (2009b) (see their Figure 11) the luminous radio-AGN fraction
at 0.7 < z < 1.3 is well below 25 % at all log (M∗ [M⊙ ]) < 11.5 where it drops quickly to
∼ 1 % at log (M∗ [M⊙ ]) = 11 and continuously to lower levels as stellar mass decreases. At
masses lower than log (M∗ [M⊙ ]) = 11 the radio-AGN fractions are subject to non-negligible
evolution between 0 < z < 1 while the fractions at higher masses increase only mildly.
However, given that the radio-AGN fractions are well below 1 % in the former (i.e. low)
mass range out to z ∼ 1.3 it is unlikely that they rise above 10 % at z ≫ 1. The evolution
of the radio-AGN fraction at the high-mass end is much slower but the fractions are high
already in the local universe. We therefore set an arbitrary but reasonable threshold and
exclude all quiescent objects above log (M∗ [M⊙ ]) = 11.6, where the expected radio-AGN
fraction exceeds 50 %, from our stacking analysis. As the radio-AGN fraction sharply drops
below this limit the remainder of our full galaxy sample should be generally free from radioAGN contamination. Within the highest mass bin probed here (M∗ > 1011 M⊙ ; see Figure
4.2), however, the average fraction of radio AGN among the quiescent galaxies could still
be ∼ 25 % at z > 1. This fraction appears high but among the entire galaxy population
(quiescent and SF sources) the percentage drops to at most 10 % within our highest massbin at z ∼ 1. As shown by I10 globally, but in particular at M∗ > 1011 M⊙ the fraction
of quiescent galaxies among the entire sample decreases strongly towards higher redshifts
(see also Taylor et al. 2009).21 An upper bound of 10 % to the potential fraction of radio-AGN
within our highest mass-bin hence is a well justified number at z > 1.
Due to prominent spectral features we regard the SED-fits for quiescent objects as most
19
Based on the Salvato et al. (2009) classification that uses an enhanced set of AGN/galaxy templates in order
to fit the FUV-to-mid-IR SED and that includes further priors (e.g. variability information) in the fitting
procedure while delivering accurate photometric redshifts for all these sources.
20
Note that Hickox et al. (2009) and Griffith and Stern (2010) yield strong evidence that X-ray and radio selected
AGN are mutually distinct populations such that it is actually questionable to remove X-ray selected objects
from our samples. We confirmed that our results do not change significantly when including those objects
and urge caution to remove more objects if deeper X-ray data compared to the XMM imaging used here is
at hand.
21
The global stellar mass density of quiescent galaxies at z = 1.5 is about an order of magnitude lower than the
SF one.
43
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
Figure 4.1. – Observed 3.6 µm flux versus stellar mass from SED fits. The 12 panels show photometric redshift bins, as 0.2 ≤ zphot ≤ 3 indicated in the upper left part of each panel. Flux
densities relate to AB-magnitudes via mAB (3.6 µm) = −2.5 log10 (F3.6 µm [µJy]) + 23.9 (23.9 is
the magnitude limit of the catalog). Blue points denote highly active SF systems, with intrinsic rest-frame template colors (NUV − r+ )temp < 1.2; red points denote quiescent (low star
formation activity) galaxies with (NUV − r+ )temp > 3.5. Green points are objects of intermediate intrinsic rest-frame color (and hence star formation activity). Horizontal dashed lines
mark the levels of the detection completeness, estimated through Monte Carlo simulations of
artificial sources (see Section 4.2.6). The vertical dashed-dotted line in each panel denotes
the lower mass limit, to which the sample of SF systems (i.e. the union of all blue and green
points) is representative of the underlying SF population and the SFR is not affected by the
intrinsic catalog incompleteness. The solid vertical line in each panel denotes the mass limit
to which the entire sample is regarded as representative.
44
4.2. The pan-chromatic COSMOS data used
trustworthy such that also the SED-derived SFRs are expected to be accurate for individual
objects. These SFRs therefore serve as a prior for revealing potential radio-AGN among
the radio-detections in our sample. Hence we correlated our sample with the latest version
of the VLA-COSMOS catalog (Schinnerer et al. 2010) and excluded those objects showing
radio-derived SFRs more than twice as large as the SED-derived values. We find that the
overall number of objects excluded in each sample to be stacked is negligible. The same
holds for very luminous (L1.4 GHz > 1025 W/Hz) radio sources among the radio-detections
that are most likely high-power radio-AGN. We therefore excluded also these objects relying on individual photo-z’s in order to estimate the radio luminosity. The total fraction of
galaxies among all objects in a given bin that we exclude by these two criteria amounts –
on average – to less than 0.3 % such that only a fraction of radio detections is rejected.
We stress the smallness of this percentage as the advantage of our radio-approach is its
insensitivity to dust obscuration which might be challenged by relying on individual optical best-fit SEDs as we partially do when removing some of the radio-detected objects. It
should be noted that the high-power radio-AGN candidates are exclusively hosted by red
galaxies within our sample. Hence, X-ray detected sources are the only objects that have
been removed from our SF samples.
As the radio-based SFR-results presented in this chapter (see Section 4.4) are based on a
median stacking approach (see Chapter 3) a minor fraction of contaminating outliers such
as AGN is even tolerable. We conclude that contamination of the stacked radio flux densities
caused by AGN emission at radio frequencies is not a siginifcant source of uncertainty in
the context of this study and that our conclusions would not change if we included the
radio-AGN candidates in our analysis.
4.2.6. Completeness considerations
In the following we will discuss the completeness of our (sub-)samples. It is important to
distinguish between two kinds of effects. While the full 3.6 µm-selected source catalog (1)
is subject to a flux density-dependent level of detection incompleteness we are interested
in (2) how representative for the underlying population a given subset of galaxies is at a
given mass. Our lower mass limits hence need to be chosen such that the objects at hand
remain sufficiently representative.
I10 evaluated the efficiency of the source extraction procedure (and hence the detection
completeness) with Monte Carlo simulations of mock point-sources inserted into the 3.6 µm
mosaic. At the flux density cut of 1 µJy (mAB (3.6 µm) = 23.9) the catalog was found to be
55 % complete; 90 % completeness is reached at F3.6 µm ≈ 5 µJy (mAB (3.6 µm) = 22.15).
This rather shallow decline in detection completeness towards the magnitude limit is due
to source confusion.
Figure 4.1 shows the distribution of 3.6 µm flux density with stellar mass in narrow redshift slices for our source catalog, color coded by the spectral type of the galaxies (see
Section 4.2.4). The Monte Carlo detection completeness levels of the catalog are indicated
by horizontal dashed black lines starting from the flux density limit at the bottom to the
95 % completeness limit at the top in each panel. Each sub-population shows a clear correlation between 3.6 µm flux density and stellar mass, and the quiescent population residing
at the high-mass end at all flux densities. While SF sources (the union of all blue and green
data points) span the entire range of 3.6 µm flux densities at all redshifts, hardly any qui-
45
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
escent objects with low flux densities are observed at intermediate and high redshifts. We
consequently find fewer and fewer low-mass quiescent objects as redshift increases. This is
certainly the combined effect of a general absence of such sources at higher redshifts plus
the loss of these objects at low flux densities due to the global detection incompleteness of
our catalog.
Detection incompleteness affects all sources at a given 3.6 µm flux density, regardless of
their spectral type. However, the different distribution of quiescent and SF sources with
respect to 3.6 µm flux density necessitates that a different lower mass limit (‘representativeness limit’, hereafter) be adopted, depending on whether we consider the redshift evolution
of SF galaxies or that of the entire galaxy population. We now discuss how the limiting mass
is set for these two samples:
• In the case of the entire galaxy population, it is important to be working with a sample
in which the fractional contribution of quiescent and SF sources reflects the true population fractions as closely as possible. The probability that this is the case becomes
larger, the better the underlying population is sampled; i.e. it rises with increasing detection completeness. We therefore require an intrinsic catalog completeness of 90 %
(corresponding mAB (3.6 µm) = 22.15) at all masses considered. This is an arbitrary
but reasonable threshold as the intrinsic catalog completeness rises rapidly towards
higher flux densities.
In order to evaluate the actual mass representativeness limit we need to define yet another type of completeness level, which we shall refer to as statistical completeness.
By applying the analytical scheme described in detail in Appendix A.3 we ensure that
the statistical completeness of our sample always reaches at least 95 %. This value
sets the actual level of representativeness of a given sub-sample. In the following we
will also present results for sub-samples below the evaluated mass-limits which will
be indicated separately. Those results represent strict upper limits in (S)SFR.
• For studying the SF population we need not be as conservative because we are dealing
with a single sub-population that is subject to less internal variation of SF activity
as a (bimodal) sample including both quiescent and SF systems. We thus consider
sources down to the limiting flux density of the 3.6 µm catalog when we compute
the mass limits at a given redshift. Since this implies that at low stellar masses the
flux distribution is sharply cut due to the magnitude limit of our catalog, we still
need to use the scheme presented in Appendix A.3 to identify stellar mass limits that
provide a representative flux density distribution for SF galaxies. As visible in all
panels of Figure 4.1, the lowest mass bin always contains objects over the full range
of detection completeness, from 55 % to 100%. One might expect – and the SED fits
confirm this – that among galaxies of a given mass, those with the fainter fluxes have
lower SSFRs. Failure to include them (due to detection incompleteness) would thus
yield average radio-derived SSFRs that are biased towards higher values. We wish to
emphasize, however, that our choice of the statistical completeness level ensures that
this bias is small above our mass limit and that our samples hence are ‘representative’
in the sense that they can be expected to render a meaningful measurement of, e.g.,
the average SSFR of the underlying population.
The stellar mass representativeness limits for the whole sample and the SF systems are
marked in Figure 4.1 as vertical lines for each redshift bin in the range 0.2 < zphot < 3 and
46
4.2. The pan-chromatic COSMOS data used
Table 4.1.
Stellar mass limits for all/SF galaxies
All galaxies
SF systems
z
log(M∗ [M⊙ ])lim
log(M∗ [M⊙ ])lim
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
2.3
2.5
2.7
2.9
9.7
9.8
10.0
10.1
10.2
10.4
10.4
10.5
10.8
10.8
10.8
10.9
11.0
11.1
8.8
8.9
9.1
9.1
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.9
10.1
10.2
Note. — The lower stellar mass limits
above which our samples are regarded representative. Those limits are as shown in
Figure 4.1 and A.1 and have been derived
based on the scheme that is detailed in Appendix A.3.
listed in Table 4.1. Note that they increase with redshift. As a consequence, our results will
be based on fewer mass bins at high redshift and the aforementioned bias in the lowest mass
bin may therefore have a larger impact on fitting trends. Very conservatively speaking, our
results for SF objects presented in the following should generally be regarded as most
robust at z . 1.5 while evolutionary trends inferred at the high mass end are robust out to
our redshift limit of z = 3. We will also show results for SF galaxies obtained at masses
lower than the individual mass limits and treat them as not entirely representative. Such
measurements will be indicated with different symbols in our plots and we will discuss any
further implications in Section 4.4.4.
The final sample of galaxies with mAB (3.6 µm) = 23.9 and zphot < 3 consists of 165,213
sources over an effective area of ∼ 1.5 deg2 . Figure 3 in I10 shows the redshift distribution
with a median of zphot ∼ 1.1. After adopting a lower redshift limit of zphot = 0.2 in order to
account for the small local volume sampled by our effective area and our binning scheme
113,610 sources22 (90,957 SF galaxies) enter our analysis. This is by far the largest galaxy
sample used for studying the dependence between SFR and stellar mass throughout cosmic
time. Figure 4.2 shows the adopted binning scheme and the number of galaxies contained
in each stellar mass and photo-z bin.
22
This number already considers the upper limiting mass for quiescent galaxies as discussed in Section 4.2.5
and excludes further 328 sources (i.e. 0.3 %) classified as radio-AGN.
47
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
Figure 4.2. – Binning scheme in stellar mass and photometric redshift for the entire (left) and
the SF (right) sample. Hatched bins lie below the corresponding limits denoted in Figure 4.1
and are hence regarded representative of the underlying galaxy population. The top number
in each box is the total number of galaxies used in the radio stack; the bottom number shows
the signal to noise ratio achieved in the radio stack. In the left panel, the middle number is
the amount of potential radio-AGN (not detected in the X-ray) that has been excluded from
the stack. In the right panel this number gives the amount of optically very faint sources
only detected redwards from the K-band. No radio-AGN candidate has been found among the
radio-detected sources in the SF sample and only X-ray detected objects have been removed.
The total number of galaxies per redshift bin is given below the panels.
4.3. Image stacking at radio continuum wavelengths
The bulk of objects in our 3.6 µm selected sample is not individually detected in the 1.4 GHz
continuum. An estimation of the SFR based on the radio flux density for every object in the
sample is therefore impossible. On the other hand, studying only radio-detected galaxies in
this sample yields effectively a selection by SFR and not by stellar mass since only radiobright, i.e. highly active star forming, normal galaxies remain.23 As outlined in the previous
chapter similar situations occur frequently in modern galaxy evolution research and are
ideally addressed by an image stacking approach.
4.3.1. Median stacking and error estimates
We use the input imaging processing options of our stacking routine to retrieve cutouts
with sizes of 40′′ × 40′′ , centered on the position of the optical counterpart. Since the
COSMOS astrometric reference system was provided by the VLA-COSMOS observations
23
The currently deepest radio surveys (e.g. Owen and Morrison 2008, with rms1.4
detect galaxies with SFRs & 50 M⊙ /yr at a redshift of z = 1.
48
GHz
∼ 3 µJy) individually
4.3. Image stacking at radio continuum wavelengths
the positional accuracy between radio and optical sources should be well within the errors
of both datasets. As detailed in Schinnerer et al. (2007) the relative and absolute astrometry
of the VLA data are 130 and < 55 mas, respectively. In other words the average distribution
of radio flux follows the one at optical wavelengths and the central pixel in any stacked
image was always the brightest one. Averaging over pixels located at the same position in
each stamp hence is an astrometrically well-defined problem.
In this study median stacking is our method of choice. As outlined in the previous chapter compared to the mean the stacking experiment becomes more robust against outliers
allowing the use of the entire input sample.24 . Non-uniform noise properties within the
radio map can also be addressed by applying a weighted scheme to compute the median
(see Appendix A.1). White et al. (2007) showed that the median is a well-defined estimator
of the mean of the underlying population in the presence of a dominant noise background.
Although, strictly speaking, these arguments only apply to the case of pure point sources,
the condition of a dominant noise background is given in our study. One has to be aware of
the fact that there is in principle no possibility to access the intrinsic distribution of radio
peak fluxes of the underlying population as a whole. The observed distribution merely
is the intrinsic one as smeared out by the gaussian noise background. However, it still
contains information that needs to be used in order to find proper confidence limits for any
statistic applied. Based on the above arguments, we expect the broadened distribution to
be not only shifted but also skewed towards positive flux density values. As a result, the
uncertainty for the obtained peak flux density is poorly estimated by the background noise
in the final stamp. Using a bootstrapping technique (see Appendix A.2) allows us to obtain
more realistic, asymmetric error bars for our measured peak flux densities.
4.3.2. Integrated flux densities, luminosities and SFRs from stacked radio
images
So far we considered only the average peak flux density which, to first order, would not
require to stack individual cutouts but only their central pixel. However, the typical galaxy
of a given sample might exhibit extended radio emission. In that case the peak flux density
is no longer equivalent to the total source flux but underestimates the typical radio flux
density and hence all other quantities derived from it.
The effect of bandwidth smearing (BWS), chromatic aberration caused by the finite bandwidth used during the VLA-COSMOS observations leads to a spatial broadening of a source
even if it is intrinsically point-like. Within a single pointing the BWS increases with increasing radial distance from the pointing center and the effect is analytically well determined
(e.g. Bondi et al. 2008). For a mosaic like the VLA-COSMOS map that consists of many
overlapping pointings the effect becomes analytically unpredictable due to the varying uncertainties introduced by the calibration and observing conditions.
24
We applied the different stacking techniques discussed above to some of our sub-samples. We found the
median flux densities obtained to be within . 7 % of those obtained when using a mean stacking technique
that excludes radio-stamps including extended foreground features. For the mean stack we co-added objects
in a given sub-sample that are not individually detected in the radio imaging and the flux density of the
detected sources has been added to the flux density obtained from the stack in a noise-weighted fashion.
This ensures that those objects that are not individually radio-detected – i.e. the bulk of our sources – are
most strongly weighted
49
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
5,763
4,402
9.4−9.8
2,700
9.8−10.2
1,586
10.2−10.6
484
10.6−11.0
> 11.0
Figure 4.3. – Examples for 40′′ × 40′′ (i.e. (115 × 115) pixels) 1.4 GHz postage stamp images
obtained via median stacking of star forming galaxies (see Section 4.2.4) in the redshift bin
between 1.6 < z < 2. The number of galaxies for which individual radio cutout images from
the VLA-COSMOS map (resolution of 1.5′′ × 1.4′′ ) have been co-added is given at the upper
left of each stamp in the top row while the number at the lower right denotes the bin extent
in log(M∗ [M⊙ ]). Due to the high signal-to-noise ratios (SNRs) achieved, generally, a clear
(dirty) beam pattern is visible. The bottom row shows the corresponding CLEANed stamps
(see Section 4.3.2, for details). Contour levels are at 2, 4, 5σbg and followed by steps of
5σbg . (The individual SNRs are given in Figure 4.2 and flux densities measured as well as the
background noise levels reached are listed in Table 4.3).
For all our samples we constructed median co-added cutout images (Figure 6.7) and determined accurate RMS-noise estimates (hereafter σStack ) for the image stacks by averaging
over adequate off-centure aperture tiles. These (115×115) pixel2 dirty maps were processed
within aips.25
We used the task PADIM to make the stacked images equal in size to a (512 × 512) pixel2
image of the VLA-COSMOS synthesized (dirty) beam by filling the outer image frame with
additional pixels of constant value The task APCLN with a circular CLEAN box of radius of
seven pixels (i.e. 2.45′′ ) around the central component was then used to CLEAN each dirty
map down to a flux density threshold of 2.5 × σStack 26 .
Integrated flux densities, as well as source dimensions and position angles after deconvolution with the CLEAN beam were obtained by fitting a single-component Gaussian elliptical
model to the CLEAN image within a quadratic box of (15×15) pixel2 around the central pixel
using the task JMFIT. Errors on the integrated flux densities have been estimated according
to Hopkins et al. (2003) and rely on the combined information on the best-fit source model
25
Note that only bright (> 45 µJy) radio sources have been CLEANed in the individual pointings prior to the
assembly of the final mosaic. Hence, a stack of fainter sources will display a clear beam pattern as seen in
Figure 6.7 which must be deconvolved.
26
This is a conservative threshold. We confirmed that this choice does not lead to systematic biases by CLEANing individual stacked images down to 1 × σStack . Integrated flux densities obtained from both approaches
do not differ by more than 3 % and do not lead to mass-dependent effects. The mentioned fluctuations are
well within the error margins.
50
4.3. Image stacking at radio continuum wavelengths
and the bootstrapping results from the image stacking:
σTotal
=
hFTotal i
s
σdata
hFTotal i
2
+
σfit
hFTotal i
2
,
(4.1)
where (Windhorst et al. 1984; Condon 1997 and also the explanations in Schinnerer et al.
2004, 2010)
σdata
hFTotal i
σfit
hFTotal i
=
s
S
N
−2
+
1
100
v
u
u2
θB θb
= t
+
ρS
θM θm
2
(4.2)
!
2
2
+ 2 .
ρ2ψ
ρφ
(4.3)
θM = 1.5′′ is the major axis and θm = 1.4′′ the minor axis of the beam while θM and θm are
the major and minor axis of the measured (hence convolved) flux density distribution. In
order to include the bootstrapping error estimates we set S/N = hFpeak i/σbs , i.e. the ratio
of the peak flux density in the stacked dirty map and the 68 % confidence interval resulting
from the bootstrapping. The same applies to the parameter-dependent estimators of the fit
entering equation (4.3) that are given by:
ρ2X =
θM θm
4 θB θb
1+
θB
θM
a 1+
θb
θm
b S
N
2
(4.4)
and a = b = 1.5 for ρF , a = 2.5 and b = 0.5 for ρM as well as a = 0.5 and b = 2.5 for ρm .
For a given sub-sample centered at a given median redshift hzphot i the average (median
stacking based) integrated flux density hFTotal i observed at 1.4 GHz can be directly converted into a rest-frame 1.4 GHz luminosity using a K-correction that depends on the radio
spectral index αrc (here αrc = −0.8, e.g. Condon 1992):
hL1.4 GHz i [W/Hz] = 9.52 × 1012 hFTotal i [µJy]
−(1+αrc )
2 ×
DL [Mpc] 4π 1 + hzphot i
(4.5)
with DL the luminosity distance at this median photo-z of all objects inside the bin.
It was pointed out by Dunne et al. (2009) that the median redshift might not be appropriate for estimating the radio luminosity if the peak of the radio flux density distribution does
not coincide with the median of the photo-z distribution. They overcame this problem by
deriving (and subsequently effectively stacking) luminosities according to Eq. (4.5) for all
objects relying both on the individual photo-z ’s and peak flux density measurements at the
pixel corresponding to the position in the input catalog. At z > 0.2 they afterwards applied
a common (i.e. redshift independent) factor to the median of all obtained luminosities to
correct for the difference between peak and total flux density as well as for the effect of
BWS. A similar approach was recently also used by Bourne et al. (2010). The method by
Dunne et al. (2009) is justified given their data as they find for z > 0.2 that the ratio of total
to peak flux density does not change significantly, in particular not as a function of K-band
magnitude. However, our data does not yield such a uniform behavior with respect to mass
in the correction factor as Figure 4.4 shows. Indeed, if we were to state an average peak
to total flux density conversion it would be a function of mass.
51
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
Figure 4.4. – Ratio of integrated to peak flux density at 1.4 GHz of the stacked radio images
for different sample sub-sets. The left panel shows results for the entire sample, the right
panel the sub-set of blue (SF) galaxies. The data is color-coded by redshift and the dashed
black line depicts the uniform correction factor used in the radio stacking study by Dunne
et al. (2009). It is evident that the extent of radio emission is not uniform across our samples
because our radio imaging has a higher angular resolution compared to the VLA map used by
Dunne et al. (2009). All measured data points are listed in Table 4.2 and 4.3.
An explanation for the discrepancy of our findings compared to Dunne et al. (2009) can
be found in the use of higher resolved A-array data in our case compared to the B-array
data constituting their radio continuum imaging. Hence, both results are correct given
the respective data used and show that higher resolution radio data needs to be treated
differently. The spread in conversion factors within our sub-samples is large and lower
redshift objects show a significantly larger hFTotal i/hFPeak i ratio27 (see Figure 4.4). Moreover, further variations might arise depending on the galaxy population studied. Hence, if
high-resolution data is used, results are more robust when first total flux densities are individually derived for any radio stacking experiment before computing radio luminosities. As
it is apparent from the Dunne et al. (2009) results their method should be considered, how27
Note that a larger conversion factor is equivalent to a larger source extent. Since it is unlikely that the
varying number counts in our sub-samples are responsible for mass- or redshift-dependent source sizes
we infer that higher mass objects are intrinsically more extended at all redshifts compared to their lower
mass siblings. The larger correction factors at lower z can be explained by the increasing angular diameter
distance towards higher z .
52
4.4. The evolution of the specific SFR
ever, if stacking is used to infer the average radio luminosity of an entire galaxy population
with a broad redshift distribution (∆z & 1). As our broadest bins in redshift have ∆z = 0.5
– and this only at z ≫ 1 where they span a much smaller range in time – it is indeed more
accurate to rely on our approach given our radio imaging.
In order to convert the derived average 1.4 GHz luminosities into average SFRs we use
the calibration of the radio-FIR correlation by Bell (2003a) scaled to a Chabrier IMF28 :
hSFRi [M⊙ /yr] =
(
3.18 × 10−22 L , L > Lc
3.18×10−22 L
, L ≤ Lc
0.1+0.9 (L/Lc )0.3
(4.6)
where L = hL1.4 GHz i is the average radio luminosity derived from the median stack according to Eq. (4.5) and Lc = 6.4 × 1021 W/Hz is the radio luminosity of an L∗ -like galaxy. As Bell
(2003a) empirically argues the low-luminosity population needs to be treated separately
from higher values of radio luminosities since non-thermal radio emission might be significantly suppressed in these galaxies. Even though our work exploits the radio-faint regime
our derived average 1.4 GHz luminosities lie generally above this threshold. Only at the
lowest masses and z . 0.8 we find hL1.4 GHz i < Lc (see Table 4.2 and 4.3). Any study relying
on the calibration by Yun et al. (2001) is, consequently, directly comparable to our results
as Yun et al. (2001) used a uniform normalization very similar to the case L > Lc in Eq.
(4.6).29 According to Bell (2003a) individual objects scatter about the average calibration
by about a factor of two. It is not necessary to include this dispersion in the estimation of
the final uncertainty on the SFR computed from the stack since the latter involves a sufficiently large number of sources to ensure that the average relation is representative. We
do not attempt to take the differences of the derived SFRs caused by the discrepancy of the
mentioned calibrations into consideration for the error estimates of our results. We also
neglect any uncertainty on the median photo-z so that all errors on the derived SFRs result
from propagation of the errors derived using equation (4.1).30
Finally, for a given sample, specific SFRs are computed as the ratio of the SFR and the
median stellar mass. Based on the same arguments as before we neither take into account
an uncertainty in the median mass for the error estimates of our derived SSFRs. As we exclusively deal with average quantities in this work we omit the hi-notation in the following.
4.4. The Specific SFR (SSFR) of mass-selected galaxies over
cosmic time from radio stacking
In the remaining parts of this chapter we present our measurements of the SSFR-M∗ relation (this Section) and discuss their implications for the evolution of the cosmic SFR density
(see Section 5.1).
28
Bell (2003a) adopts a Salpeter initial mass function with IMF ∝ M −2.35 in the mass range from 0.1 to 100 M⊙
so that we divide his normalization by 1.74.
29
A radio luminosity independent calibration has also been presented by Condon (1992). We refer to Dunne
et al. (2009) who present all their results using both the Bell (2003a) and Condon (1992) calibration.
√
30
This is justified as this error scales with the number of objects as 1/ N where N ≫ 102 given our binning
scheme.
53
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
Table 4.2.
Radio stacking results for the entire mass-selected sample
∆ log(M∗ )
M∗ [M⊙ ]
hlog(M∗ )i
M∗ [M⊙ ]
∆zphot
9.3-9.6
9.45†
0.2-0.4
0.27
9.44†
0.4-0.6
0.49
9.44†
0.6-0.8
0.69
9.45†
0.8-1.0
0.89
9.44†
1.0-1.2
1.11
9.45†
1.2-1.6
1.40
9.47†
1.6-2.0
1.78
9.6-9.9
9.9-10.2
†
0.2-0.4
0.27
9.74†
0.4-0.6
0.49
9.74†
0.6-0.8
0.69
9.74†
0.8-1.0
0.89
9.75†
1.0-1.2
1.10
9.73†
1.2-1.6
1.41
9.75†
1.6-2.0
1.82
9.75†
2.0-2.5
2.21
9.76†
2.5-3.0
2.65
10.04⋆
0.2-0.4
0.27
10.05⋆
0.4-0.6
0.49
10.04†
0.6-0.8
0.68
10.05†
0.8-1.0
0.89
10.05†
1.0-1.2
1.09
10.04†
1.2-1.6
1.39
10.04†
1.6-2.0
1.87
†
2.0-2.5
2.28
10.04†
2.5-3.0
2.73
10.35
0.2-0.4
0.29
10.34
0.4-0.6
0.49
10.35⋆
0.6-0.8
0.68
10.35⋆
0.8-1.0
0.89
10.35⋆
1.0-1.2
1.09
10.34†
1.2-1.6
1.38
†
1.6-2.0
1.81
10.33†
2.0-2.5
2.36
9.74
10.04
10.2-10.5
10.33
10.5-10.8
10.8-11.1
> 11.1
hzphot i
10.34†
2.5-3.0
2.81
10.63
0.2-0.4
0.28
10.64
0.4-0.6
0.48
10.63
0.6-0.8
0.69
10.64
0.8-1.0
0.89
10.64
1.0-1.2
1.09
10.64⋆
1.2-1.6
1.37
10.63⋆
1.6-2.0
1.78
10.64†
2.0-2.5
2.27
10.62†
2.5-3.0
2.76
10.95
0.2-0.4
0.27
10.92
0.4-0.6
0.48
10.92
0.6-0.8
0.69
10.91
0.8-1.0
0.90
10.92
1.0-1.2
1.10
10.91
1.2-1.6
1.36
10.92
1.6-2.0
1.79
10.93⋆
2.0-2.5
2.21
10.93†
2.5-3.0
2.72
11.20
0.2-0.4
0.27
11.23
0.4-0.6
0.48
11.20
0.6-0.8
0.69
11.20
0.8-1.0
0.90
11.20
1.0-1.2
1.10
11.20
1.2-1.6
1.35
11.20
1.6-2.0
1.78
11.22
2.0-2.5
2.22
11.23⋆
2.5-3.0
2.71
hFPeak i
[µJy/beam]
hFTotal i
[µJy]
[µJy/beam]
hL1.4 GHz i/Lc
Lc = 6.4 × 1021 W/Hz
hSFRi
[M⊙ /yr]
1.7+0.3
−0.4
4.9+1.4
−2.2
0.399+0.015
−0.002
0.2+0.0
−0.1
0.6+0.1
−0.2
+0.2
1.4−0.3
2.2+1.2
−1.9
0.276+0.004
−0.006
0.6+0.4
−0.6
1.5+0.6
−1.0
2.0+0.4
−0.3
1.3+0.2
−0.3
+0.3
1.1−0.2
0.7+0.2
−0.1
+0.2
0.5−0.3
3.9+0.6
−0.2
+0.3
3.6−0.4
+0.2
2.4−0.3
2.1+0.3
−0.2
+0.3
2.7−0.3
1.9+0.2
−0.3
+0.2
1.3−0.2
1.3+0.2
−0.3
+0.2
0.9−0.3
+0.6
5.1−0.5
5.4+0.5
−0.5
5.3+0.2
−0.5
3.9+0.2
−0.4
4.0+0.3
−0.4
3.3+0.2
−0.2
2.9+0.2
−0.2
2.2+0.2
−0.3
1.7+0.3
−0.3
+0.5
7.5−0.4
7.9+0.4
−0.4
+0.5
4.8−0.5
5.1+0.4
−0.4
5.4+0.3
−0.3
4.6+0.4
−0.3
4.2+0.4
−0.2
3.7+0.4
−0.4
3.3+0.3
−0.6
+0.7
9.8−0.7
+0.8
8.1−0.4
6.4+0.4
−0.6
+0.4
6.3−0.5
5.6+0.4
−0.4
6.2+0.5
−0.4
6.9+0.4
−0.3
5.2+0.3
−0.3
4.9+0.5
−0.6
+1.0
9.6−1.0
9.2+0.6
−0.4
6.7+0.7
−0.7
7.1+0.5
−0.3
7.6+0.5
−0.4
6.3+0.6
−0.6
7.8+0.3
−0.3
6.9+0.5
−0.4
6.8+0.5
−0.7
9.2+0.9
−1.9
10.3+2.0
−3.2
7.3+1.2
−1.2
8.6+0.9
−1.0
+0.7
10.1−0.8
11.1+0.9
−1.1
14.3+0.7
−1.0
13.7+1.1
−0.9
+0.9
11.3−0.8
2.5+1.1
−1.0
1.9+0.5
−0.9
1.9+1.6
−1.2
0.9+0.5
−0.4
0.9+0.8
−1.0
9.6+2.5
−1.0
+1.3
7.4−1.9
5.4+0.9
−1.3
4.5+1.4
−0.9
4.0+1.4
−1.3
2.3+1.1
−1.4
2.1+1.0
−1.0
2.0+0.7
−0.8
+0.5
1.0−0.6
13.8+2.9
−2.4
11.8+2.1
−2.2
+0.7
8.5−1.7
+0.8
5.7−1.5
7.0+1.4
−1.6
4.7+1.0
−1.0
5.5+0.8
−0.8
3.2+0.9
−1.1
2.5+1.3
−1.2
+2.4
18.1−1.7
+1.9
16.4−1.8
+2.2
9.8−2.1
9.5+1.7
−1.6
9.2+1.3
−1.2
8.3+1.5
−1.4
9.3+1.7
−1.0
6.2+1.5
−1.5
5.8+1.2
−2.3
+3.1
23.9−2.9
+3.4
18.6−2.0
+1.6
13.3−2.7
+1.5
11.1−2.0
+1.7
11.3−1.7
+2.0
11.4−1.9
+1.6
11.8−1.1
+1.2
10.0−1.4
+2.6
11.6−2.6
+5.4
32.7−5.1
+2.6
22.5−2.0
+3.2
15.5−3.0
+1.8
12.8−1.1
+1.8
13.6−1.6
+2.5
13.7−2.5
+1.4
15.9−1.2
+2.0
13.8−1.6
+2.0
14.0−3.0
+5.5
36.0−10.8
22.6+8.4
−13.0
+6.1
24.4−6.5
+3.6
16.6−4.0
+2.8
21.6−3.1
19.6+3.5
−4.3
28.7+3.0
−4.0
25.0+4.1
−3.6
23.2+3.8
−3.5
rms
0.388+0.006
−0.006
0.246+0.007
−0.013
0.275+0.005
−0.010
0.179+0.001
−0.003
0.243+0.004
−0.006
0.469+0.017
−0.033
+0.010
0.455−0.004
0.341+0.028
−0.002
0.265+0.002
−0.010
0.320+0.022
−0.005
0.216+0.006
−0.007
0.232+0.003
−0.015
0.271+0.015
−0.008
+0.005
0.293−0.005
+0.014
0.504−0.008
0.472+0.016
−0.022
0.360+0.011
−0.013
0.288+0.005
−0.009
0.364+0.002
−0.004
0.260+0.003
−0.006
0.274+0.005
−0.003
0.277+0.006
−0.003
0.308+0.004
−0.007
0.534+0.016
−0.005
0.495+0.010
−0.018
+0.025
0.386−0.009
0.311+0.005
−0.006
0.375+0.020
−0.009
0.279+0.001
−0.012
0.325+0.008
−0.009
0.330+0.025
−0.006
0.343+0.009
−0.005
0.594+0.027
−0.019
+0.010
0.555−0.026
0.420+0.006
−0.020
+0.002
0.331−0.010
0.391+0.013
−0.016
0.308+0.004
−0.004
0.378+0.017
−0.009
0.400+0.008
−0.008
0.437+0.003
−0.012
+0.009
0.882−0.007
0.733+0.030
−0.009
0.556+0.034
−0.013
0.412+0.025
−0.014
0.509+0.008
−0.011
0.417+0.010
−0.008
0.479+0.003
−0.005
0.523+0.012
−0.009
0.583+0.013
−0.036
1.250+0.047
−0.038
+0.008
1.227−0.025
0.897+0.010
−0.007
0.681+0.013
−0.009
+0.018
0.881−0.013
0.762+0.012
−0.022
0.835+0.022
−0.009
0.737+0.023
−0.025
0.767+0.021
−0.030
0.3+0.1
−0.1
1.0+0.3
−0.5
1.7+1.4
−1.1
1.4+0.9
−0.6
2.6+2.3
−2.8
0.3+0.1
−0.0
+0.2
1.0−0.2
1.6+0.3
−0.4
2.4+0.8
−0.5
3.5+1.3
−1.2
3.7+1.8
−2.3
6.2+3.0
−3.1
8.9+3.0
−3.8
+3.3
6.9−4.2
+0.1
0.5−0.1
1.5+0.3
−0.3
2.4+0.2
−0.5
3.1+0.4
−0.8
6.1+1.2
−1.4
7.3+1.6
−1.5
17.0+2.6
−2.4
15.9+4.3
−5.5
18.8+9.3
−8.8
0.7+0.1
−0.1
2.1+0.2
−0.2
+0.6
2.8−0.6
5.1+0.9
−0.9
8.1+1.1
−1.0
12.5+2.3
−2.1
26.8+4.8
−2.9
33.0+8.1
−7.8
45.5+9.4
−18.5
0.9+0.1
−0.1
2.4+0.4
−0.2
3.9+0.5
−0.8
+0.8
6.0−1.1
9.8+1.5
−1.5
17.1+3.0
−2.8
32.6+4.4
−3.0
48.3+6.0
−6.6
+19.6
88.4−20.0
+0.2
1.1−0.2
2.8+0.3
−0.2
4.5+0.9
−0.9
7.0+1.0
−0.6
12.1+1.6
−1.5
20.2+3.7
−3.7
44.5+3.9
−3.4
63.1+8.9
−7.4
+14.6
102.3−21.7
+0.2
1.2−0.4
2.8+1.0
−1.6
7.1+1.8
−1.9
9.2+2.0
−2.2
+2.5
19.3−2.8
28.2+5.1
−6.2
79.7+8.4
−11.0
+18.9
115.3−16.5
+27.8
169.4−25.7
0.9+0.3
−0.3
2.1+0.5
−1.0
3.5+2.8
−2.3
2.8+1.8
−1.2
5.2+4.6
−5.7
0.9+0.2
−0.1
+0.3
2.0−0.4
3.2+0.6
−0.8
4.9+1.6
−0.9
7.2+2.6
−2.4
7.6+3.6
−4.7
12.7+6.0
−6.2
18.2+6.1
−7.6
+6.6
14.1−8.6
1.2+0.2
−0.2
3.1+0.6
−0.6
5.0+0.4
−1.0
6.3+0.9
−1.7
12.5+2.5
−2.9
14.8+3.2
−3.0
34.6+5.2
−4.9
32.4+8.8
−11.2
+18.9
38.2−17.9
1.6+0.2
−0.1
4.3+0.5
−0.5
+1.3
5.7−1.2
10.5+1.9
−1.8
16.6+2.3
−2.1
25.4+4.7
−4.2
54.5+9.7
−5.9
+16.4
67.1−15.9
+19.2
92.6−37.6
1.8+0.2
−0.2
4.8+0.9
−0.5
7.9+0.9
−1.6
+1.6
12.2−2.2
20.0+3.0
−3.0
34.7+6.1
−5.7
66.3+9.0
−6.1
+12.3
98.3−13.4
+39.8
179.7−40.6
2.2+0.4
−0.4
5.7+0.7
−0.5
9.2+1.9
−1.8
14.3+2.0
−1.3
24.6+3.2
−3.0
41.0+7.4
−7.5
90.5+7.8
−6.8
+18.1
128.4−15.1
+29.6
207.9−44.1
2.5+0.4
−0.8
5.7+2.1
−3.3
14.4+3.6
−3.8
18.7+4.0
−4.5
+5.1
39.2−5.7
+10.3
57.4−12.5
+17.1
162.0−22.4
+38.5
234.4−33.6
+56.5
344.4−52.3
Note. — Median stacking-based average 1.4 GHz radio flux densities and derived average quantities for all our bins in mass and redshift for the entire
mass-selected sample . A Chabrier (2003) IMF is assumed. Radio luminosities are stated in units of Lc , the threshold luminosity below which Bell (2003a)
empirically found the non-thermal radio emission to be suppressed (see Eq. (4.6)). Resulting SFRs from bins with lower radio luminosity are hence boosted
compared to, e.g., the calibration of the radio-IR relation by Yun et al. (2001). The median stellar mass and median z for any given bin are also stated.
†
Mass bin contains data below the limit of mass representativeness and yields an upper limit to the average SFR (see Section 4.2.6 for further details.)
⋆
First mass bin above the limit of representativeness (see Section 4.2.6) which contains a low fraction (< 15 %) of optically faint objects with mAB (i+ ) ≥
25.5 for which the photo-z accuracy is degraded (see Section 4.2.2 for further details).
54
4.4. The evolution of the specific SFR
Table 4.3.
∆ log(M∗ )
M∗ [M⊙ ]
hlog(M∗ )i
M∗ [M⊙ ]
∆zphot
9.4-9.8
9.58
0.2-0.4
9.8-10.2
10.2-10.6
> 11.0
hzphot i
0.28
9.58
0.4-0.6
0.49
9.58
0.6-0.8
0.69
9.58
0.8-1.0
0.89
9.58⋆
1.0-1.2
1.10
9.58†
1.2-1.6
1.40
9.60†
1.6-2.0
1.79
9.62†
2.0-2.5
2.17
9.99
0.2-0.4
0.28
9.99
0.4-0.6
0.49
9.98
0.6-0.8
0.68
9.99
0.8-1.0
0.89
9.99
1.0-1.2
1.09
9.97⋆
1.2-1.6
1.39
9.98⋆
1.6-2.0
1.85
9.98†
2.0-2.5
2.25
9.99†
2.5-3.0
2.71
10.37
0.2-0.4
0.29
10.37
0.4-0.6
0.49
10.39
0.6-0.8
0.68
10.38
0.8-1.0
0.89
10.40
1.0-1.2
1.10
10.38
1.2-1.6
1.38
10.37
1.6-2.0
1.81
10.37⋆
2.0-2.5
2.32
10.38
10.6-11.0
Radio stacking results for star forming systems
⋆
2.5-3.0
2.78
10.74
0.2-0.4
0.28
10.75
0.4-0.6
0.48
10.75
0.6-0.8
0.69
10.75
0.8-1.0
0.89
10.75
1.0-1.2
1.10
10.75
1.2-1.6
1.37
10.77
1.6-2.0
1.79
10.77
2.0-2.5
2.22
10.76
2.5-3.0
2.72
11.10
0.2-0.4
0.29
11.10
0.4-0.6
0.48
11.10
0.6-0.8
0.69
11.10
0.8-1.0
0.89
11.13
1.0-1.2
1.10
11.11
1.2-1.6
1.36
11.11
1.6-2.0
1.80
11.15
2.0-2.5
2.22
11.17
2.5-3.0
2.71
hFPeak i
[µJy/beam]
hFTotal i
[µJy]
[µJy/beam]
hL1.4 GHz i/Lc
Lc = 6.4 × 1021 W/Hz
hSFRi
[M⊙ /yr]
3.1+0.5
−0.5
8.7+2.3
−2.2
0.408+0.001
−0.002
0.3+0.1
−0.1
0.9+0.2
−0.2
2.4+0.2
−0.4
2.1+0.3
−0.2
1.7+0.2
−0.2
2.1+0.3
−0.2
1.1+0.2
−0.2
0.8+0.2
−0.2
1.1+0.2
−0.2
+0.4
6.9−0.8
6.2+0.5
−0.5
5.4+0.3
−0.6
3.9+0.2
−0.4
+0.3
3.7−0.3
3.2+0.2
−0.2
2.5+0.2
−0.2
+0.2
2.0−0.1
+0.2
1.6−0.2
12.2+0.8
−0.3
11.5+1.1
−0.6
8.2+0.3
−0.3
+0.3
7.8−0.4
6.5+0.3
−0.3
+0.2
5.3−0.2
4.9+0.3
−0.3
4.0+0.2
−0.3
3.5+0.3
−0.3
18.8+1.3
−1.7
13.8+1.2
−1.3
13.3+1.1
−0.6
10.5+0.6
−0.5
8.1+0.3
−0.4
+0.4
8.6−0.4
7.9+0.4
−0.3
6.3+0.7
−0.5
5.6+0.3
−0.4
19.8+3.7
−4.1
18.1+1.2
−1.8
12.7+1.1
−1.4
13.8+1.4
−1.7
13.4+1.5
−1.3
13.4+1.0
−0.8
+1.1
15.6−1.6
11.9+0.6
−0.5
11.1+0.7
−1.1
5.1+1.4
−2.0
3.6+1.2
−0.7
3.2+0.7
−1.0
3.2+1.0
−0.7
1.4+0.5
−0.5
1.5+0.9
−1.3
1.4+0.6
−0.7
17.7+2.0
−3.5
12.6+2.0
−1.9
+1.2
9.3−2.2
6.2+0.9
−1.5
+1.4
6.6−1.3
4.4+1.0
−1.0
4.6+1.0
−0.8
2.8+1.0
−0.5
+1.4
2.0−1.5
29.0+3.5
−1.4
23.3+4.4
−2.6
16.0+1.4
−1.3
14.5+1.4
−1.5
12.0+1.3
−1.1
+0.9
9.7−0.8
+1.1
9.8−1.3
7.0+0.7
−1.1
6.6+1.2
−1.3
53.8+6.4
−8.3
30.2+5.0
−5.4
27.7+4.4
−2.5
19.5+2.6
−2.2
15.8+1.2
−1.7
16.8+1.6
−1.8
14.8+1.7
−1.1
11.9+2.6
−1.9
13.3+1.2
−1.6
+20.8
75.4−23.1
+6.2
56.3−9.3
32.6+5.1
−6.4
32.0+5.6
−6.7
26.9+5.6
−4.9
27.7+4.1
−3.1
+4.3
30.3−6.3
21.8+2.3
−1.8
22.5+2.9
−4.6
rms
0.372+0.016
−0.033
0.258+0.009
−0.002
0.219+0.004
−0.006
0.246+0.006
−0.009
0.169+0.001
−0.004
0.210+0.004
−0.004
0.237+0.001
−0.000
+0.019
0.523−0.011
0.441+0.011
−0.016
0.336+0.022
−0.029
0.264+0.002
−0.005
+0.010
0.305−0.006
0.225+0.014
−0.001
0.228+0.006
−0.004
0.248+0.012
−0.002
+0.001
0.256−0.001
0.592+0.014
−0.014
0.542+0.007
−0.011
0.415+0.026
−0.009
0.324+0.006
−0.002
0.358+0.013
−0.004
+0.005
0.267−0.004
0.298+0.007
−0.000
0.302+0.010
−0.001
0.311+0.010
−0.009
+0.017
0.851−0.014
0.707+0.012
−0.015
0.573+0.035
−0.023
0.433+0.009
−0.001
0.454+0.005
−0.018
0.333+0.002
−0.003
0.387+0.011
−0.009
0.397+0.002
−0.004
0.428+0.005
−0.020
1.640+0.084
−0.100
+0.071
1.364−0.048
1.086+0.040
−0.011
0.907+0.039
−0.007
0.881+0.013
−0.009
0.734+0.023
−0.027
+0.013
0.701−0.014
0.594+0.023
−0.044
0.645+0.007
−0.004
0.7+0.2
−0.3
1.0+0.3
−0.2
1.7+0.4
−0.5
2.9+0.9
−0.6
2.2+0.8
−0.8
4.2+2.6
−3.7
6.3+2.5
−2.9
+0.1
0.6−0.1
1.7+0.3
−0.3
2.7+0.3
−0.6
3.4+0.5
−0.8
+1.2
5.8−1.1
6.8+1.5
−1.5
14.0+3.0
−2.6
13.6+4.8
−2.6
+10.1
14.5−11.2
1.2+0.1
−0.1
3.0+0.6
−0.3
4.6+0.4
−0.4
7.9+0.8
−0.8
10.6+1.1
−1.0
+1.3
14.7−1.2
28.2+3.2
−3.7
35.6+3.5
−5.8
50.9+8.9
−10.2
+0.2
2.0−0.3
3.9+0.6
−0.7
8.1+1.3
−0.7
10.5+1.4
−1.2
14.1+1.0
−1.5
25.0+2.3
−2.7
41.3+4.9
−3.0
+11.9
55.2−8.7
+9.0
97.6−11.9
2.9+0.8
−0.9
6.9+0.8
−1.2
9.6+1.5
−1.9
17.1+3.0
−3.6
24.2+5.0
−4.4
40.5+6.0
−4.5
+12.1
85.9−17.9
+10.6
100.1−8.5
+20.8
164.5−33.7
1.5+0.3
−0.5
2.1+0.7
−0.4
3.6+0.8
−1.1
5.9+1.9
−1.2
4.5+1.7
−1.7
8.5+5.4
−7.4
12.7+5.1
−5.9
1.5+0.1
−0.2
3.4+0.5
−0.5
5.4+0.7
−1.3
6.8+1.0
−1.6
+2.4
11.9−2.2
13.9+3.1
−3.1
28.5+6.2
−5.2
27.6+9.8
−5.2
+20.6
29.5−22.7
2.4+0.3
−0.1
6.2+1.2
−0.7
9.4+0.8
−0.7
16.0+1.5
−1.6
21.5+2.3
−2.0
+2.7
29.9−2.5
57.3+6.5
−7.5
72.5+7.0
−11.7
+18.1
103.5−20.8
4.0+0.5
−0.6
7.9+1.3
−1.4
16.4+2.6
−1.5
21.3+2.8
−2.4
28.7+2.1
−3.1
50.9+4.7
−5.4
83.9+9.9
−6.1
+24.2
112.3−17.7
+18.2
198.4−24.2
5.9+1.6
−1.8
14.1+1.6
−2.3
19.5+3.1
−3.8
34.9+6.1
−7.3
+10.2
49.2−9.0
+12.2
82.3−9.2
+24.6
174.6−36.4
+21.6
203.5−17.2
+42.4
334.4−68.5
Note. — Median stacking-based average 1.4 GHz radio flux densities and derived average quantities for all our bins in mass and redshift for star forming
systems within our mass-selected sample . For details see caption of Table 4.2.
†
Mass bin contains data below the limit of mass representativeness and yields an upper limit to the average SFR (see Section 4.2.6 for further details.)
⋆
First mass bin above the limit of representativeness (see Section 4.2.6) which contains a low fraction (< 15 %) of optically faint objects with mAB (i+ ) ≥
25.5 for which the photo-z accuracy is degraded (see Section 4.2.2 for further details). The average SFR measured in this bin might be slightly overestimated
towards higher values (see Section 4.2.6).
55
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
Figure 4.5. – Radio stacking based measurement of the SSFR as a function of stellar mass
at 0.2 < z < 3.0 for our entire galaxy sample (left) and SF systems (right). Open symbols
depict samples containing galaxies less massive than the individual limits denoted in Figure
4.1 and are regarded as not representative for the underlying galaxy population and rather
β
represent upper SSFR limits. Dashed lines are two-parameter fits of the form c × M∗ to
the mass-representative data depicted by filled symbols (see Table 4.4). The horizontal red
band sketches the inverse dynamical time of (370 ± 50) Myr measured in local disk galaxies
(Kennicutt 1998b) and also found in massive disk galaxies at z ∼ 1.5 (Daddi et al. 2010b).
Galaxies with such high levels of SSFR effectively double their mass within a dynamical time.
As detailed in Section 4.4.1 this might represent an upper bound to the average SSFR. All
measured data points are listed in Table 4.2 and 4.3. The derivation of error bars involves a
bootstrapping analysis combined with the uncertainties to the best-fit model of each stackingderived average radio source (see App. A.2 and Section 4.3.2; for further details). We do not
account for uncertainties associated with the SFR-calibration, the photometric redshift and
stellar mass estimates as the large number of objects stacked for each data point ensures that
even the joint error budget is statistically reduced to a low level that would not substantially
enhance our uncertainty ranges.
4.4.1. The relation between SSFR and stellar mass
We first consider the whole sample including all galaxies and show the redshift dependent
radio-based SSFRs that are distributed in the logarithmic SSFR-M∗ plane as seen in the left
panel of Figure 4.5. It is clear that the SSFR for a given stellar mass increases with redshift
and that it generally decreases with increasing stellar mass.
The data at the high-mass end (above log(M∗ ) ≈ 10.5) within all considered redshift slices
suggest power-law relations between SSFR and stellar mass of the form
SSFR(M∗ , z) = c(z) × M∗ β(z) .
(4.7)
In the following we will refer to the index β also as slope since the relation is commonly
shown in log -space. The dashed lines in Figure 4.5 depict the best fit to the data in the massrepresentative regime (see Section 4.2.6) and indicate that only the normalization evolves
while the power-law index βALL of the individually fitted relations shows minor fluctuations
but no clear evolutionary trend. Only at z & 1.5 there is tentative evidence for a somewhat
shallower slope. However, at the highest redshifts probed too few mass-representative data
points exist to perform the linear fit. Our evidence is solely supported by the offset between
56
4.4. The evolution of the specific SFR
the SSFR of the most massive galaxies and those of intermediate mass remaining the same
as at z ∼ 1.8. Based on our data it therefore is justified to consider the index βALL in Eq.
(4.7) a constant at least for all z < 1.5 and log(M∗ ) & 10.5 .
At log(M∗ ) < 10 − 10.5 we see at practically all epochs that the measured SSFRs significantly deviate from the relation fitted to the high-mass end. The extrapolation towards
lower masses over-predicts the measurement. In Section 4.2.6 we argued that all these data
points – lying below the mass representativeness limits – likely represent upper limits. We
hence believe this is a genuine deviation that is reminiscent of the bimodality (whereby quiescent galaxies preferentially populate the high-mass end) in the SSFR-M∗ plane confirmed
at various redshifts for galaxy samples with individually measured SFRs (e.g. Brinchmann
et al. 2004; Salim et al. 2007; Elbaz et al. 2007; Santini et al. 2009; Rodighiero et al. 2010a).
Using our spectral classification scheme we separately study the SF galaxy population
in order to break the afore mentioned bimodality. The right panel in Figure 4.5 shows
that a power-law relation according to Eq. (4.7) holds over the entire mass range probed,
once quiescent galaxies are excluded. Linear fits exclusively to the mass-representative
regime show that, at z . 1.5: (i) SSFR declines towards higher mass, and that (ii) the slope
βSF G is constant, as it was the case for the entire galaxy population. Compared to the
entire sample, the slope is significantly shallower.31 All theses conclusions also hold at all
other epochs probed but are supported by fewer data points significantly above the massrepresentativeness limits that enter the fits. Hence we regard our conclusions as most
robust at z < 1.5.
Above z ∼ 1.4 and below log(M∗ ) ≈ 9.5 − 10, we again find that measurements in the
regime not regarded as mass-representative lie significantly below the linear fits. Since
quiescent galaxies are even less frequent at these redshifts32 , the bimodality argument is
obviously insufficient to explain this observed trend. A possible explanation is that the magnitude limit of our catalog leads to a loss of dust-dominated systems with low masses but
high star formation activity. If this were the case our previous statement that SSFRs in the
under-represented mass-regime are upper limits would not necessarily hold. However, we
do not expect a sufficiently high number density of low-mass dusty starbursts to make this
scenario plausible. Another explanation could lie in the dynamical considerations presented
in Section 4.4.2.
4.4.2. A potential upper limit to the average SSFR of normal galaxies
The fact that the aforementioned deviations from the linear fits at low masses steadily grow
with redshift hints at a solid upper limit to the average SSFR. Local spiral galaxies have
on average a dynamical timescale – i.e. the rotation timescale at the outer radius of a disk
galaxy – of τdyn ∼ 0.37 Gyr (Kennicutt 1998b). Daddi et al. (2010b) show that this still
holds at z ∼ 1.5. The inverse of this dynamical timescale, 1/τdyn ∼ 2.7 Gyr−1 , is similar
to the threshold that seems to prevent our average SSFRs from rising continuously with
decreasing mass. Note also that this dynamical timescale approximately equals the free31
At high masses, the radio-derived SSFRs for SF galaxies lie significantly above those for all galaxies demonstrating that the SED-based pre-selection is efficient.
32
Also at high z there is evidence for the existence of quiescent systems that are predominantly massive (e.g.
Cimatti et al. 2004; Kriek et al. 2006, 2008b; Brammer et al. 2009). However, as our spectral classification
of SF systems is efficient to exclude passive galaxies (see I10) and as these systems are also rare we do not
expect them to cause the observed trend.
57
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
Table 4.4.
Two parameter fits to the mass dependence of the SSFR
All galaxies
SF systems
∆z
log(cALL [1/Gyr])
βALL
χ2 /d.o.f
log(cSFG [1/Gyr])
βSFG
χ2 /d.o.f
0.2-0.4
0.4-0.6
0.6-0.8
0.8-1.0
1.0-1.2
1.2-1.6
1.6-2.0
2.0-2.5
2.5-3.0
−1.63 ± 0.04
−1.22 ± 0.04
−0.96 ± 0.08
−0.81 ± 0.07
−0.53 ± 0.05
−0.33 ± 0.13
0.04 ± 0.08
−0.73 ± 0.03
−0.75 ± 0.04
−0.57 ± 0.08
−0.73 ± 0.06
−0.58 ± 0.05
−0.61 ± 0.12
−0.33 ± 0.07
0.11
0.24
0.17
0.07
0.64
0.12
1.47
−0.67 ± 0.02
+0.34
−0.08
−0.44 ± 0.03
−0.42 ± 0.03
−0.40 ± 0.03
−0.38 ± 0.03
−0.46 ± 0.03
−0.30 ± 0.03
−0.41 ± 0.07
−0.42 ± 0.05
−0.44 ± 0.15
−0.40 ± 0.01
0.03
0.78
1.37
1.42
0.61
1.08
2.21
0.19
0.81
hβALL i =
−1.27 ± 0.03
−0.90 ± 0.03
−0.67 ± 0.03
−0.48 ± 0.03
−0.38 ± 0.03
−0.12 ± 0.03
0.10 ± 0.07
0.22 ± 0.06
0.43 ± 0.16
hβSFG i =
+0.10
−0.06
Note. — A power-law fit of the form c × (M∗ /1011 M⊙ )β (Eq. (4.7)) was applied to the radio stackingbased SSFRs as a function of mass within any redshift slice. Fits have only been applied if more than two
data points remained above the mass limit where the individual sample is regarded mass-representative.
The results for all galaxies are shown in the left half of the table while those for star forming systems
(see Section 4.2.4) are given in the right half. The weighted average power-law index (over all accessible
redshifts) found for each population is stated at the bottom along with the formal standard error and the
scatter range yielding a more realistic uncertainty estimate.
fall time (Genzel et al. 2010) which is commonly used to relate SFR volume density with gas
volume density (e.g. Schmidt 1959; Kennicutt 1998b; Krumholz and McKee 2005; Krumholz
et al. 2009; Leroy et al. 2008).
As indicated in Figure 4.5 the population of z > 1.5 galaxies reaches average levels of
star formation that enable these normal SF systems to double their mass within a dynamical
time scale. Generally, star formation is thought to be limited by the rate at which cold gas
is accreted onto the galaxy (e.g. Dutton et al. 2010; Bouché et al. 2010 and also e.g. Kereš
et al. 2005; Macciò et al. 2006, where simulations actually show the cold gas inflow) while
the efficiency of star formation does not appear to change out to the highest redshifts
accessible to molecular gas studies in normal disk galaxies to-date (Daddi et al. 2010a;
Tacconi et al. 2010). Consequently, even the highly elevated gas fractions – i.e. the amount
of gas available for star formation over the sum of gas and stellar mass – compared to
local disk systems (e.g. Daddi et al. 2010a, who find up to 60 % at z = 1.5) might not
suffice to sustain a star formation activity that proceeds faster than gravity permits. As
average galaxies reach inverse SSFRs comparable to their inverse dynamical – and, most
importantly, free fall – time it is hence likely that an effective gas accretion threshold is
reached. Hence the SSFR should stop its growth with redshift at some point. Lower mass
galaxies reach this threshold at lower redshifts than the more massive systems leading to
the flattening of the relation we observe at the lower mass end. We will henceforth refer to
the transition from an inclined to a flat SSFR-sequence as ‘crossing mass’ .
It is clear that carbon monoxide ALMA-studies at z > 1.5 of typical SF systems with
M∗ ≤ 1010 M⊙ are required to understand their molecular gas properties and to test the
star formation law of this population.
58
4.4. The evolution of the specific SFR
Figure 4.6. – Redshift evolution of the SSFRs for all galaxies (left) and SF systems (right)
in logarithmic stellar mass bins. Two-parameter fits of the form C × (1 + z)n are applied
only to data points derived from samples regarded as representative for the given underlying
galaxy population which are depicted by filled symbols (see Table 4.5). The black long-dashed
line gives the mass-doubling limit above which galaxies are able to double their mass until
z = 0 assuming a constant SFR and it therefore equals the inverse lookback-time. The black
dashed-dotted line depicts the inverse age of the universe at any given redshift and hence
makes measured SSFRs comparable to the past average star formation activity. The SEDderived measurement of Magdis et al. (2010) for LBGs at z ∼ 3 with log(M∗ ) ∼ 10 is shown as
a filled star. All data results are listed in Table 4.2 and 4.3.
4.4.3. The redshift evolution of SSFRs as a function of mass
The redshift evolution of our data is shown in Figure 4.6 for all galaxies and for the SF
population. Both panels suggest a co-evolution of the considered mass-bins at least out to
z ∼ 1.5; while all measured SSFRs increase with redshift, the high-mass end does not evolve
faster compared to lower masses and it always has the lowest SSFRs. An offset between the
typical SSFRs of different mass bins is also evident for SF galaxies but it is smaller than for
the entire galaxy population which shows a wider spread of SSFRs at fixed mass. Clearly,
all these aspects are the direct result of our previous findings:
• A constant slope β of the SSFR-M∗ relation is observed for all galaxies (at the highmass end) as well as for SF galaxies alone at least out to z ∼ 1.5.
• The slope βSFG is shallower for SF systems.
In Figure 4.6 we also plot the mass doubling line33 (long dashed line) and the inverse age
of the universe at any given redshift (dashed-dotted line). Our measurement clearly shows
that virtually all SF galaxies display a higher star formation activity than is required if their
entire mass had been build up at a constant rate over the whole age of the universe.34 All
galaxies, generally, cross the dashed-dotted line sooner or later depending on their stellar
33
At a given redshift, the mass-doubling threshold is given by the inverse lookback time. A SSFR in excess of
this limit is hence a mass-independent indicator for the potential of a galaxy to double its mass by z = 0 if it
were to maintain its current SFR.
34
This does not necessarily imply that an individual galaxy maintains a high level of star formation activity. All
statements we make here refer to an average galaxy of a given mass and cosmic epoch having a well-defined
59
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
Table 4.5.
∆ log(M∗ )
M∗ [M⊙ ]
10.2-10.5
10.5-10.8
10.8-11.1
> 11.1
Two parameter fits to the redshift evolution of the SSFR
All galaxies
log(CALL )
CALL [Gyr−1 ]
nALL
χ2 /d.o.f
−1.53 ± 0.56
−1.76 ± 0.93
−1.92 ± 1.48
−2.12 ± 3.93
hnALL i =
4.18 ± 0.05
4.28 ± 0.05
4.27 ± 0.05
4.53 ± 0.07
4.29 ± 0.03
3.05
1.48
1.75
2.37
+0.24
−0.11
∆ log(M∗ )
M∗ [M⊙ ]
9.4-9.8
9.8-10.2
10.2-10.6
10.6-11.0
> 11.0
SF systems
log(CSFG )
CSFG [Gyr−1 ]
nSFG
χ2 /d.o.f
−0.92 ± 0.45
−0.92 ± 0.33
−1.11 ± 0.28
−1.28 ± 0.47
−1.41 ± 0.82
hnSFG i =
3.02 ± 0.15
3.42 ± 0.07
3.62 ± 0.04
3.48 ± 0.04
3.40 ± 0.06
3.50 ± 0.02
0.65
1.63
5.24
1.73
1.52
+0.12
−0.48
Note. — A power-law fit of the form C × (1 + z)n was applied to the radio stacking-based SSFRs as a function
of redshift within any mass bin. Fits have only been performed if more than two data points remained above
the mass limit where the individual sample is regarded mass-representative. The results for all galaxies are
shown in the left half of the table while those for star forming systems (see Section 4.2.4) are given in the right
half. The weighted average power-law index (over all accessible masses) found for each population is stated
at the bottom along with the formal standard error and the scatter range yielding a more realistic uncertainty
estimate.
mass. The most massive systems enter the stage of sub-average star formation activity
already at z ∼ 0.8.
At the high-mass end (log(M∗ ) & 11) the SSFR for SF galaxies increases by almost a
factor of 50 and is about twice as much for all galaxies within 0.2 ≤ z ≤ 3. For a given
mass-bin the redshift evolution is well described by a power law g(z) ∝ (1 + z)n as depicted
by the dashed lines in Figure 4.6.35 For the most massive SF galaxies this relation holds
out to the highest redshifts probed, thus no flattening is observed. However, towards lower
masses and z & 2 significant deviation of the data from the best-fit relation with lower
SSFR towards lower masses is apparent. Again the argument of an upper SSFR limit due to
dynamical reasons might explain such a deviation. For reference we also show the recent
SED-based measurement by Magdis et al. (2010) for a Lyman Break Galaxy (LBG) sample
at z ≈ 3. Their study probes M∗ ≈ 1010 M⊙ and we see that their SSFR-measurement is
significantly below the extrapolation given by our evolutionary fit in the same mass-regime
even for SF galaxies. Basically, their data point is extending our measured data at the lowmass end if evolution were to stop at about z ≈ 1.5 (a scenario suggested by the data of
Stark et al. 2009 and González et al. 2010).
Summarizing our findings a separable function of the form
SSFR(M∗ , z) ∝ f (M∗ ) × g(z) = M∗β × (1 + z)n
(4.8)
describes well the mass-dependent evolution of the SSFR given our data within the restrictions discussed. For SF galaxies we find βSFG ≈ −0.4 and nSFG ≈ 3.5. We emphasize
again that the dynamical arguments discussed in Section 4.4.2 would give rise to a value
SSFR thanks to the SSFR-M∗ relation. Star formation might still be subsequently quenched in an individual
system so that its evolutionary track does not need to coincide with those shown in Figure 4.6.
35
We fitted only data in the representative mass range.
60
4.4. The evolution of the specific SFR
of βSFG = 0 below the crossing mass of the average SSFR and the upper limiting SSFR.
The results of the individual fits to our data yielding the parameters β and n for all and SF
galaxies are presented in Tables 4.4 and 4.5.
It is worth noting that at z > 1 – where angular diameter distance is approximately
constant – the evolutionary trend we find is very close to the redshift dependence of the
radio luminosity of about (1 + z)3.8 (see Section 4.3.2). As the SSFR is proportional to
the radio luminosity this is yet another argument to support that our inferences are not
challenged by systematic errors to the median redshift even in our broader bins at z > 1
(see also the corresponding discussion in Section 4.3.2).
In order to alternatively probe our inferences in the redshift range below z = 1.5 where
our data yields the most robust results we also stacked the same bins in redshift and mass
into the Spitzer 24 and 70 µm COSMOS maps. We inferred SFRs from the total (8-1000 µm)
IR luminosity predicted by the best-fitting IR SED (Chary and Elbaz 2001) given the joint
flux density information. The results do not deviate significantly from those derived from
the radio emission so that all our conclusions remain robust also when derived from the IR
data. All these and further results will be presented and discussed in detail in a separate
publication (Sargent et al., in prep.).
4.4.4. Comparison to other studies
In this Section we compare our findings with results in the literature, with a particular
focus on those least dependent on extinction corrections because they use either radio
stacking or stacking of IR imaging by Spitzer and, most recently, Herschel. Literature data
we show in the Figures belonging to this Section are based on a Salpeter IMF and have
been converted to the Chabrier scale.
The evolutionary power law we derived for all mass-selected galaxies is in excellent
agreement with the results presented by Damen et al. (2009a), both in terms of the evolutionary exponent and the normalization of the trend. We hence concur, in particular, with
those findings of Damen et al. (2009a) resulting from a detailed comparison of their results
with predictions from the semi-analytical model of Guo and White (2008). The study of
Damen et al. (2009a), which is based on SFRs from 24 µm and UV detections in conjunction
with deep K -band observation in the Chandra Deep Field South, is also in broad agreement
with the 24 µm stacking analysis of Zheng et al. (2007a) at z < 1 in the same field. Consistent findings have also been presented recently in the Spitzer/MIPS stacking analysis at 70
and 160 µm by Oliver et al. (2010) whose data covers the largest on-sky area of all aforementioned surveys, albeit at a reduced depth of F3.6 µm = 10 µJy (an order of magnitude
shallower compared to our sample) which prevents them from reliably constraining the
evolution beyond z ∼ 1. Based on a deep rest-frame NIR bolometric flux density selected
galaxy sample in the northern Great Observatories Origins Deep Survey (GOODS Giavalisco
et al. 2004) field Cowie and Barger (2008) measure extinction corrected UV-based SSFRs
for all individual objects out to z = 1.5. Their average trends with mass agree well with our
results for all galaxies in the comparable redshift ranges and also on absolute scales both
studies are consistent at all masses.
Radio-based measurements of the SSFR-M∗ relation have been presented by Dunne et al.
(2009). In terms of the evolution of the SSFR-sequence both their and our study show a
good agreement. The findings by Dunne et al. (2009) differ from ours (see Figure 4.7) as
61
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
Figure 4.7. – Left Panel: Comparison of our results (dashed and solid lines of different color)
of the mass dependence of the SSFR for SF systems at different redshifts to Dunne et al.
(2009); grey diamonds, Elbaz et al. (2007); red circles at z ∼ 1, as well as Pannella et al.
(2009); blue squares at z ∼ 2. The mass limits above which our sample is representative
are denoted as black dashed lines in the upper left. Right Panel: The corresponding measurements by Oliver et al. (2010); grey shaded bands and Rodighiero et al. (2010a); black
diamonds at various redshifts along with our results (color bands with mean redshift scale
at the right hand side). The Herschel/PACS based SSFR-sequence (Rodighiero et al. 2010a)
suggests a mild ’upsizing’ trend and appears to stop its evolution at z > 1.5 where the only
(apparent) deviation from our data occurs. See Section 4.4.4 and Appendix 4.5 for a discussion of effects introduced by selection biases. For immediate comparison our data are shown
as open symbols in both panels, rebinned in z in order to cover the same range in redshift as
each referenced study. The inverse horizontal red band sketches the inverse dynamical time
as detailed in Section 4.4.1.
well as from most other studies not restricted to SF galaxies only in that they report an
almost non-existent slope βALL at all reliably probed epochs. Their analysis and ours share
some methodological similarities (e.g. the use of a mass- (in their case: K-) selected sample36 and a radio stacking approach) and should therefore be directly comparable. Despite
the technical differences in the exact implementation of the image stacking as already discussed (see Section 4.3.2) it seems unlikely that an explanation for the different trends can
be found in the radio data used. It appears more likely that the derivation of individual stellar masses causes the differences as Dunne et al. (2009) use a direct conversion from the
rest-frame K-band magnitudes as measured from the best-fitting SED templates to stellar
mass which exclusively depends on redshift. Such a conversion should not only be different
for SF and quiescent sources (Arnouts et al. 2007) but even ceases to be applicable towards
lower mass SF sources as discussed in App. D of I10. It is hence likely that low-mass SF
sources with higher SSFRs have migrated to higher masses producing artificially elevated
SSFRs at the high-mass end. This explanation is consistent with the generally higher deviations from our results at higher masses (see Figure 4.7). Since neither we nor Dunne
et al. (2009) find a significant evolution of the slope βALL in the SSFR-M∗ plane the pure
evolutionary behavior reported in both studies is largely consistent.
36
It is, however, worth noting that our number statistics are larger by about a factor of four.
62
4.4. The evolution of the specific SFR
The SSFR-M∗ relation for sBzK – and hence SF K-band selected – galaxies in the COSMOS
field was derived by Pannella et al. (2009) based on radio stacks from the same VLA image.
Our results for SF galaxies are (necessarily) in good agreement with their findings at z ≈ 2
(left panel of Figure 4.7) where they do not probe the highest mass-range presented here.
A main conclusion of Pannella et al. (2009) is, however, a mass-independent SSFR at z > 1.5
which is mainly inferred from a measurement on their entire SF sample (not further divided
by redshift) and a measurement at z ≈ 1.6 both covering the same mass-range as considered
here. A similar tendency at z ∼ 2 has previously also been reported by Daddi et al. (2007)
in a study carried out in the GOODS fields. Their work is based on 24 µm detected galaxies
down to log(M∗ ) ≈ 9.5 but also based on radio stacks of their K-band selected sample. As
galaxies at 1.3 < z < 1.5 substantially contribute to the photometric redshift distribution
of the Pannella et al. (2009) sample, it is likely that the sBzK criterion no longer selects
all SF objects at these low redshifts. In this context we also refer to Section 4.5 where
the upper left panel in Figure 4.9 shows that the sBzK criterion by construction fails to
select all SF sources at z < 1.5. As we already pointed out, our SSFR-M∗ relation for our
SF sample tends to flatten towards lower M∗ . When considering only low to intermediate
masses, all measurements based on stacking into the VLA-COSMOS 1.4 GHz map are thus
in good agreement. The steeper slope βSFG of the SSFR-M∗ relation for SF galaxies found
in this study is thus a consequence of the fact that we span a larger mass range at z ≈ 2.
The left panel of Figure 4.7 also shows the results at z ≈ 1 presented by Elbaz et al.
(2007) based on 24 µm detection resulting from deep Spitzer/MIPS observations of the
GOODS fields and UV-corrected SFRs. Although this study too infers a nearly constant
relation between SSFR and mass, the figure shows that the radio-derived results agree
with the mid-IR measurements remarkably well. This illustrates that measurements of the
slope βSFG of the SSFR-M∗ for SF galaxies are quite sensitive to deviations at the edges
of the mass range even if measurements at individual masses do not significantly differ
between different studies. Finally, it is also worth noting that, towards lower redshifts, our
slope βSFG agrees well with the measurements by Noeske et al. (2007b) which are based
on SFRs from emission lines, UV as well as 24 µm imaging for a K-band selected sample
of the DEEP2 spectroscopic survey. Also in the local universe GALEX/UV-based values
around β = −0.35, consistent with our study, have been reported for galaxies taken from
the Sloan Digital Sky Survey (SDSS) (Salim et al. 2007; Schiminovich et al. 2007). It should
be mentioned that, based on the SDSS emission lines study of Brinchmann et al. (2004),
Elbaz et al. (2007) found a slightly shallower slope βSFG = −0.23 for SF galaxies in the local
universe.
Image stacking results using Herschel/PACS data at 160 µm have been presented by
Rodighiero et al. (2010a). Their GOODS-North Spitzer/IRAC data is only slightly shallower
compared to our COSMOS imaging. As the right panel of Figure 4.7 shows, individual measurements by Rodighiero et al. (2010a) at z < 1 are in good agreement with our findings.
(The one exception being their lowest redshift which extends to z = 0, explaining the overall
slightly lower SSFRs.) At z > 1.5 the Rodighiero et al. (2010a) results suggest that SSFRs
cease to grow further at the high-mass end. While in this redshift range our radio-derived
SSFRs agree with the far-IR based ones at the lowest masses probed, the radio measurement yields about 0.4 dex (i.e. significantly) higher SSFRs at the high-mass end as they do
not show a different redshift trend than at lower z . As our highest redshift bin is centered
at a slightly higher z compared to the corresponding one of Rodighiero et al. (2010a) the
63
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
difference might be slightly lower if the bins were perfectly matched and given the highmass SSFR-evolution for SF galaxies is continuing at z > 1.5. We therefore see no clear
evidence for strong discrepancies of radio- and far-IR stacking derived SSFRs at high z as
speculated by Rodighiero et al. (2010a) when comparing their results to those of Pannella
et al. (2009) and especially those of Dunne et al. (2009). We emphasize, however, that future far-IR studies could test potential mass-dependent changes in the radio-IR correlation
at z > 1.5 responsible for the slight differences reported here.37 Based on power-law fits to
their data Rodighiero et al. (2010a) infer a steepening of βSFG towards higher z , an effect
they consequently term ‘upsizing’. Note, however, that our measurements of βSFG agree
with those of Rodighiero et al. (2010a) within the uncertainties. Tentative evidence for upsizing is also reported by Oliver et al. (2010) who use Spitzer/MIPS stacking of late-type
galaxies at 70 and 160 µm (see right panel of Figure 4.7). In the following Section we show
that we can mimic an upsizing trend, as well as the somewhat flatter evolution of the SSFR
out to z ≈ 2 reported by, e.g., Rodighiero et al. (2010a) if we restrict our SF sample to those
sources with the most active star formation.
4.5. A note on the selection of star forming galaxies
Because we cannot measure radio-based SSFRs for individual galaxies, selecting the SF
population directly in the SSFR-M∗ plane is impossible. In Section 4.2.4 we argue that the
intrinsic (dust-extinction corrected) rest-frame NUV-r color is a reliable way to select SF
galaxies (see also I10). In this section, we test our color selection in two ways in order to
demonstrate its fidelity and to assess how our findings relate to previous measurements in
the literature: we (1) choose a bluer color-cut to study the ensuing changes in the evolution
of the SSFR-M∗ relation, and we (2) compare both – the bluer and the previously used –
color cuts to the BzK-selection of SF galaxies at high redshifts (Daddi et al. 2004).
4.5.1. Highly active star forming galaxies
I10 have shown that the color selection criterion (NUV − r + )temp < 1.2 leads to a morphologically clean sample of late-type spiral and irregular galaxies with template SED-based
SSFRs that are clearly separated from the passive population (see Section 4.2.4). This
color threshold is somewhat arbitrary (as it is less well motivated than the cut we applied
to select SF systems) but by virtue of being substantially bluer than our original choice it
minimizes contamination by passive galaxies.
We derived SSFRs as a function of redshift and mass in the same way as before for
galaxies with (NUV − r + )temp < 1.2. Although the exclusion of systems with intermediate
star forming activity has reduced the sample size considerably, it was still possible to cover
the same dynamic ranges. Only the binning scheme has been slightly modified for this
strongly star formation population (see Figure 4.8). Its SSFRs usually are significantly
higher compared to our original choice of SF galaxies, the slope β of the SSFR-M∗ relation
37
Herschel/PACS observations of the GOODS-North field (Elbaz et al. 2010) revealed that in the same redshift
regime the total (8 − 1000 µm) IR luminosity appears to be overestimated when the IR template-SED fit
is constrained by a single 24 µm measurement. The deviation starts at LIR ∼ 1012 L⊙ and grows with
increasing LIR , SFR and consequently mass as these quantities are correlated. It is therefore necessary to
test the radio-IR correlation in the proposed way using far-IR data.
64
4.5. The selection of star forming galaxies
Figure 4.8. – The SSFR-M∗ relation (upper left) and time evolution of SSFRs in various massbins (upper right) for galaxies with high star formation activity ((NUV-r+ )temp < 1.2). Dashed
β
lines (color coded by redshift) denote two-parameter fits of the form c × M∗ to the mass
complete data (filled circles). The dynamical ranges are the same as in Figure 4.5 and 4.6,
where the other quantities shown are explained. The color threshold is substantially bluer
and rather arbitrary compared to the one used for the selection of SF systems. Compared
to the results of the entire SF sample the radio stacks yield a flatter SSFR-sequence out to
z ∼ 1.5 (β ≈ −0.08 ± 0.05) and a mild ’upsizing’ trend (lower panel) while overall a shallower
evolution of the SSFR ∝ (1 + z)2.3±0.3 is found for this sample of most vigorously SF galaxies
(upper right, where fits to the mass-complete data in the different mass bins are depicted as
dashed black lines). All these trends seen for highly active SF galaxies are hence a result of a
simple selection effect. The inverse horizontal red band sketches the inverse dynamical time
as detailed in Section 4.4.1.
65
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
Figure 4.9. – BzK diagram of our sample in various redshift bins. The color coding refers to our
choice of the (NUV − r+ )temp color threshold in order to predefine systems with high (blue),
intermediate (green) and negligible (red) star formation activity. In the lowest redshift panel
the original (Daddi et al. 2004) sBzK criterion (diagonal line) does not appear to be efficient
enough in selecting all SF galaxies and is particularly missing the systems with intermediate
levels of star formation. At higher redshifts our SF sample (all green and blue sources)
overlaps very well with the sBzK population so that our color selection for the purpose of
radio stacking is appropriate to select normal SF systems at z > 1.5.
is shallower at low to intermediate redshifts and thus in excellent agreement with those
literature results for SF galaxies discussed in Section 4.4.4 that report an almost flat SSFRsequence. At the high-z end we see a steepening of the slope β (i.e. an ’upsizing’ trend),
similar or even more evident to what was found by Rodighiero et al. (2010a) and, at lower
significance, also by Oliver et al. (2010). The evolutionary exponent n is consistent with
previous measurements as well (see e.g. Pannella et al. 2009).
The bluer color threshold hence is able to reproduce most literature findings albeit with
SSFRs that tend to be comparativey high, especially at low redshift. However, it has yet to
be confirmed that the galaxy population selected in this way is representative of the entire
SF population.
66
4.6. Summary and conclusion
4.5.2. (s)BzK galaxies at z ∼ 2
We cross-matched our 3.6 µm selected catalog with the K band selected catalog for the
COSMOS field (McCracken et al. 2010) and thus obtain a magnitude calibration in the
crucial wavebands that allows us to apply the BzK selection criterion of Daddi et al. (2004).
Figure 4.9 shows the BzK diagram for our sample, with galaxies in six redshift slices color
coded according to their (NUV − r + )temp color as described in Section 4.2.4. Our ‘star
forming’ sample is the union of all galaxies plotted in blue and green.
At z > 1.5, the sBzK criterion (all galaxies to the left of the diagonal line in each panel) is
established to efficiently select normal SF systems. Figure 4.9 illustrates that the selection
window for sBzK galaxies is populated by both the most actively star formation sources
(blue dots) and the majority of the sources with intermediate star forming rates (plotted in
green; i.e. the rest of the SF sample used throughout this Chapter). Only a small number
of objects with moderate SF activity fall into the passive BzK region in the upper right of
each panel. This is the reason for the aforementioned excellent agreement of our results
with Pannella et al. (2009) at z ≈ 2.1; their and our sample are virtually indistinguishable
and both studies rely on the same radio data. More importantly, however, the BzK diagram
strongly supports our original selection of SF objects in the crucial redshift regime z > 1.5,
where we have just shown that previously reported changes in the slope β can be mimicked
by simply selecting only very blue objects, hence, most actively forming systems.
4.6. Summary and conclusion
Based on an unprecedentedly rich sample of galaxies selected at 3.6 µm with panchromatic
(FUV to mid-IR) ancillary data and mapped in 1.4 GHz radio continuum emission in the
COSMOS field we have measured stellar mass-dependent average (specific) star formation
rates ((S)SFR) in the redshift range 0.2 < z < 3. These were obtained using a median image
stacking technique that is best applied in the radio regime where the angular resolution is
high and the fraction of direct detections is comparatively low such that blending of sources
is negligible.
We individually measured integrated radio flux densities in each stacked image and
showed that a uniform (i.e. mass-independent) correction factor is inappropriate to convert between peak and total flux density when high angular resolution radio continuum
data is used. Furthermore, we applied various criteria in order to minimize the impact of
contaminating radio flux density from active galactic nuclei and discussed to which lower
mass limit at a given redshift our sample remains representative with respect to the star
formation properties of the underlying population. We emphasize that all our findings are
to be regarded as most robust at z < 1.5 while our data place valuable constraints on
evolutionary trends at the highest masses as far as z = 3.
Using the template-based, rest-frame (NUV − r + )temp color from SED-fits in the NUVmid-IR, we separate SF galaxies from quiescent systems in order to study the average mass
dependence of their SSFR at all epochs considered. We also discussed potential effects
introduced by such a color threshold, such as mimicking a potential upturn of the SSFR-M∗
relation.
67
4. Star formation at 0.2 < z < 3 in mass-selected galaxies in the COSMOS field
Our findings are summarized as follows:
1. The massive end of our global sample of mass-selected galaxies (including quiescent and SF systems) shows a power-law relation between SSFR and stellar mass
β
(SSFR ∝ M∗ ) with an index of roughly −0.7 . βALL . −0.6 and a trend towards shallower indices with increasing redshift. Towards lower masses the relation appears
to flatten, probably because quiescent galaxies with low SSFRs preferentially occupy
the massive end of the normal galaxy population.
2. For a given stellar mass we report a strong increase of the SSFR with redshift that is
best parametrized by a power-law ∝ (1 + z)4.3 .
3. The relation between SSFR and mass for star forming (SF) systems only (referred to
as the SSFR-sequence) evolves as (1 + z)3.5 and shows a shallower power-law index of
βSFG ≈ −0.4 because quiescent galaxies do not lower the observed average SSFRs at
the high-mass end anymore. The parameter βSFG does not significantly change with
cosmic time so that the average SSFR is best described by a separable function in
mass and redshift (Eq. 4.8 in Section 4.4.3).
4. Towards lower masses and z > 1.5 also the SSFR-sequence itself tends to flatten
which might be explained by an upper limiting threshold where average SF systems
already reach levels of star formation that qualify them to double their mass within
a dynamical time. It is plausible that the SSFR at a given time does not continue
to increase till the regime of dwarf galaxies at the rate predicted by our power-law
index. We, however, cannot rule out that low-mass systems with high star formation
activity but also very high dust content are missed given the limiting magnitude in our
selection band.
We firmly conclude that, out to z ∼ 1.5, our results hence neither support the so-called
’SSFR-downsizing’ nor ’-upsizing’ scenarios proposed by some earlier work while they do
confirm the downsizing scenario in the following take:
The SFR declines strongly but in a mass-independent fashion while the most massive
galaxies always show the least star formation activity and are hence the first to fall below
their past-average star formation activity.
68
5. A constant characteristic mass for star
forming galaxies since z ∼ 3 in the
COSMOS field
In this Chapter the results of the previous Chapter are used to obtain a deeper insight into
the mass-dependent cosmic star formation history. First we combine our results with recent
measurements of the galaxy (stellar) mass function in order to determine the characteristic
mass of a star forming galaxy at a given epoch: we find that since z ∼ 3 two thirds of all
new stars were always formed in galaxies of M∗ > 109.75 M⊙ with a constant peak around
M∗ = 1010.6±0.4 M⊙ . This constancy of the characteristic mass is surprising as it challenges
the often stressed ’downsizing paradigms’ in which the characteristic mass is supposed to
shift towards smaller values over time. Finally, our analysis constitutes the most extensive
SFR density determination with a single technique out to z = 3. This chapter is part of the
publication
A. Karim, E. Schinnerer, A. Martínez-Sansigre, M. T. Sargent, A. van der Wel, H.-W. Rix,
O. Ilbert, V. Smolčić, C. Carilli, M. Pannella, A. M. Koekemoer, E. F. Bell & M. Salvato, 2011,
ApJ, 730, 61, The star formation history of mass-selected galaxies in the COSMOS field
5.1. Introduction
Over the past 15 years one of the most important quantities in observational cosmology
has been the star formation rate density (hereafter SFRD), the star formation rate (SFR)
per unit comoving volume. Describing the global rate of star formation in the universe
at a given cosmic epoch, it has attracted so much interest since already initial studies
revealed its rapidly evolving character (Lilly et al. 1996; Madau et al. 1996). It substantially
declines since ∼ 10 Gyr ago following the purported maximum of star formation activity
in the universe (see also Hopkins and Beacom 2006, for a compilation). After the initial
findings many results are found in the literature that support this picture of the cosmic star
formation history (CSFH) based on ever-growing galaxy samples leading to an improving
accuracy (e.g. Chary and Elbaz 2001; Hopkins 2004; LeFloc’h et al. 2005; Smolčić et al.
2009a; Dunne et al. 2009; Rodighiero et al. 2010b; Gruppioni et al. 2010; Bouwens et al.
2011b; Rujopakarn et al. 2010).
The literature results cover a vast diversity of SFR tracers including ultraviolet (UV)
light, emission line diagnostics, (far-)infrared (IR) emission as well as synchrotron emission
from supernova remnants detected at radio continuum wavelengths. How much of the
total SFRD, i.e. the contribution of all star forming (SF) galaxies, can be observed clearly
depends on the depth of the data used. All studies therefore rely on extrapolations to
account for the contribution of faint (low-mass) systems.
The results of the previous chapter allow us to accurately constrain the CSFH even in a
69
5. A constant characteristic mass for star forming galaxies
mass-dependent fashion, a previously barely explored parameter. Based on our measurement of radio-derived SFRs as a function of mass we directly derive SFRDs for SF galaxies
above the limiting mass at z < 1.5 and further constrain the CSFH out to z = 3. We will
also introduce two alternative extrapolations to low-mass objects that we do not directly observe. Because of our generally low mass limit, the impact of the extrapolation – especially
out to z = 1.5 – to these faint galaxies is small compared to most other studies.
5.2. The mass distribution function of the SFRD at fixed
redshift
At a given redshift and stellar mass, the SFRD is computed as the product of (i) the comoving number density as inferred directly from the number of galaxies in the relevant mass
bin and (ii) their average SFR as measured in our stacking analysis.
As already pointed out, our SFRs likely represent an upper limit at the smallest masses
where the sampling of the underlying population is no longer representative. Consequently,
SFRDs at low masses are upper bounds, as we can correct the number counts in a given
low-mass bin for the lost objects. This is done by computing the expected number from
the observed mass functions derived for the same sample of SF galaxies that is used for
this study (for further details see Ilbert et al. 2010, I10 in the following). We account for
the slightly smaller portion of the COSMOS-field accessible to the radio-stack compared
to the area used for the derivation of the mass-functions. The correction for the expected
number counts is always small so that corrected and uncorrected values of SFRD(M∗ , z )
agree within the errors. Since it is a systematic correction it still needs to be taken into
account.
All number-count corrected and uncorrected data points for the SFRD(M∗ , z ) are shown in
Figure 5.1. There appears to be a characteristic mass of M∗ = 1010.6±0.4 M⊙ that contributes
most to the total SFRD at a given redshift. Up to z ∼ 1.8 our data points sample below this
characteristic mass and the peak is well constrained. At higher redshifts this is no longer
the case.
We want to motivate now that the underlying functional form for the distribution of data
points in the SFRD-M∗ plane is actually known because of two facts:
1. There is a (possibly broken) power-law relation between (S)SFR and stellar mass for
SF galaxies at all z < 3 as measured in this study.
2. The functional form of the mass function for SF objects in the same redshift range is
well determined.
Regarding the second point, the mass function of SF galaxies is commonly (e.g. Lilly et al.
1995; Bell et al. 2003, 2007; Zucca et al. 2006; Arnouts et al. 2007; Pozzetti et al. 2009;
Ilbert et al. 2005, 2010) found to be well parametrized by a power law with an exponential
cutoff at a characteristic mass M ∗ as introduced by Schechter (1976) of the form
∗
ΦSFG (M∗ )dM∗ = Φ∗SFG (M∗ /MSFG
)αSFG
∗
∗
× exp (−M∗ /MSFG
) d(M∗ /MSFG
).
70
(5.1)
5.2. The mass distribution function of the SFRD at fixed redshift
Figure 5.1. – The distribution of the SFR density (SFRD) with respect to stellar mass, as
measured at various epochs out to z ∼ 3. In each panel the data points have been derived by
multiplying the observed number densities of SF galaxies with the average (stacking-based)
radio SFRs. Below the limit where our data is regarded mass-representative (see Section
4.2.6 and Appendix A.3) – depicted by red dashed vertical lines – number densities have been
corrected using the mass functions (Ilbert et al. 2010). The uncorrected data are shown
for comparison as open circles suggesting that these corrections are generally small and no
corrections are needed at z < 1.5. For 0.8 < z < 1.2, the [OII]λ3727-derived SFRDs (from
Gilbank et al. 2010b); open diamonds, rescaled by a constant factor of two to match our data
agree well with the trends in our data. The same holds true for the UV-based results by Cowie
and Barger (2008) depicted at 1.2 < z < 1.6 for which no rescaling was necessary. Note that
their data was derived over a broader range in redshift down to z = 0.9. As our data suggest
globally only a mild evolution between 0.9 < z < 1.4 the comparison depicted is justified.
In each panel we overplot the Schechter function that results from multiplying the best-fit
radio derived SSFR-sequence at a given epoch with the corresponding mass function for SF
galaxies. The uncertainty range is obtained by choosing the two sets of Schechter parameters
within their error margins that maximize/minimize the integral. Dashed blue lines show the
distribution obtained if an upper limit to the average SSFR at lower masses (see Section 4.4.2
for details) is assumed (referred to as ‘case B’ in Section 5.2). All literature data plotted here
have been converted to our Chabrier IMF.
71
5. A constant characteristic mass for star forming galaxies
Table 5.1.
Schechter parameters for the stellar mass function of star forming galaxies
∆zphot
0.2-0.4
0.4-0.6
0.6-0.8
0.8-1.0
1.0-1.2
1.2-1.5
1.5-2.0
2.0-2.5
2.5-3.0
αSFG
−1.32+0.01
−0.01
−1.32+0.01
−0.01
−1.32+0.01
−0.01
−1.16+0.01
−0.01
−1.19+0.02
−0.02
−1.28+0.02
−0.02
−1.29+0.02
−0.02
−1.29+0.03
−0.03
−1.29+0.03
−0.03
∗
log(MSFG
)
M∗ [M⊙ ]
[10−3 Mpc−3 dex−1 ]
Φ∗SFG
11.00+0.03
−0.03
11.04+0.03
−0.03
10.95+0.02
−0.02
10.86+0.02
−0.02
10.92+0.02
−0.02
10.91+0.02
−0.02
10.96+0.02
−0.02
10.95+0.03
−0.03
10.95+0.03
−0.03
1.15+0.08
−0.07
0.70+0.05
−0.04
0.86+0.05
−0.05
1.38+0.06
−0.06
0.94+0.05
−0.05
0.68+0.03
−0.03
0.46+0.02
−0.02
0.32+0.06
−0.06
0.27+0.05
−0.05
Note. — At z < 2 all parameters have been derived by I10.
At z > 2 we assume a non-evolving shape so that αSFG and
∗
MSFG
are taken to be the average of the respective lower z
values. Φ∗SFG was then derived by matching the number densities to those observed in the mass-representative regime of
our data.
This Schechter function has recently been qualitatively as well as quantitatively been modeled to be the natural consequence of essentially two types of cessation of star formation
(Peng et al. 2010).1
Multiplying ΦSFG (M∗ ) by the SFR-sequence, i.e. another power-law in mass, again produces a Schechter function. Hence we can write
SFRD(M∗ , z)dM∗ = ΦSFRD (Φ∗SFRD , α̃, M ∗ ) dM∗ ,
(5.2)
i.e. a distribution (SFRD function hereafter) of the same functional form as Eq. (5.1) with
the three parameters Φ∗SFRD , α̃ and M ∗ . While the exponential cutoff mass M ∗ is the same
∗ ), α̃ = α
as the one in the mass function (defined above as MSFG
SFG + β̃SFG is the sum of
the low-mass slope of the mass function of SF galaxies and the slope2 of the SFR-sequence
(see also Santini et al. 2009, for a similar parameterization). The parameter Φ∗SFRD acts as
a normalization and its role in the global evolutionary picture will be discussed in Section
5.3.
The index αSFG and also the cutoff mass M ∗ for SF galaxies are constant in the redshift
regime considered (e.g. Bell et al. 2003, 2007; Arnouts et al. 2007; Pérez-González et al.
1
Peng et al. (2010) refer to these two processes as ’environment-’ and ’mass-quenching’. The former one
is likely to be explained by star formation being shut off in satellite systems as soon as galaxies fall into
larger dark matter halos while the latter one is a continuous process stopping star formation within galaxies
∗
above the characteristic mass MSFG
at a rate proportional to their SFR. In the following we will make use of
∗
evolutionary constraints on the mass function parameters αSFG , Φ∗SFG and MSFG
for SF galaxies in particular.
Their trends are not only supported by recent literature (see the further discussion in this Section) but also
naturally contained in the empirical Peng et al. (2010) model.
2
Please note that β̃SFG denotes the slope of the SFR-M∗ relation for SF galaxies which is connected to the
slope βSFG of the SSFR-sequence (see Section 4.4.1 and Table 4.4) by β̃SFG = βSFG + 1.
72
5.2. The mass distribution function of the SFRD at fixed redshift
2008; Pozzetti et al. 2009 as well as Table 5.1 which is based on the results of Ilbert et al.
∗
stay constant also at z > 2. These assumptions
2010). We assume here that αSFG and MSFG
are tentatively supported by the few observational constraints reported for these high redshifts as detailed in Section 5.3. As detailed in Section 4.4.1, the power-law index βSFG –
that enters the parameter α̃ = αSFG + βSFG + 1 in Eq. 5.2 – is also found to be a constant.
However, we explained in Section 4.4.2 that at masses lower than the crossing mass between the SSFR-sequence and a possible SSFR-threshold βSFG = 0 should be assumed. In
the following we will hence consider two possible scenarios below the suggested crossing
mass at a given redshift:
Case A :
α̃ = αSFG + βSFG + 1
Case B :
α̃ = αSFG + 1.
Figure 5.1 shows that at z < 1.5 the parameterization of the SFRD function in Eq. (5.2)
can reproduce our data at all masses sampled and irrespective of the exact value of α̃.
For this redshift range Figure 5.1 also includes results of two other studies that rely on
different SFR tracers. At z ∼ 1 the dependence of the SFRD on stellar mass has recently
been measured using the [OII]λ3727 line to trace star formation (Gilbank et al. 2010b). We
over-plot these data points in the corresponding redshift bins in Figure 5.1 and find that
our SFRD function accurately fits these measurements as well.3 The same holds for the
UV-derived results based on a Salpeter IMF by Cowie and Barger (2008) in the GOODSNorth field at 0.9 < z < 1.5. Given our results, the global evolution of the SFRD-function
between 0.9 < z < 1.4 is mild such that we can plot these data in Figure 5.1 in the bin
1.2 < z < 1.6. It is worth noting that the Cowie and Barger (2008) measurements at z < 0.9
equally support our finding that the peak of the SFRD does not shift with redshift to higher
values.
Below the limiting stellar mass (dashed red lines in Figure 5.1) our data points are lower
than the prediction of Eq. 5.2 if we assume case A for α̃ (even though we have applied a
number density correction). Moreover, we remind the reader that – in keeping with our previous discussion – these data points are likely upper limits. Given the comparatively large
uncertainties of our SFRD functions at high z these deviations are not highly significant but
the trend is systematic and suggests a steepening of the low-mass slope of the SFRD function. It is directly related to the fact that the corresponding data points deviate from the
best-fit (S)SFR-M∗ relation at lower mass. In Section 4.4.2 we proposed an upper limit to
the average SSFR due to dynamical reasons as a possible explanation for the trends. Taking
into account this limit of SSFR = 1/τdyn ∼ 2.7 Gyr−1 yields an index βSFG = 0 below the
mass at which our fitted high-mass SSFR-M∗ relation crosses the supposed SSFR limit at a
given epoch. We plot the SFRD function for α̃ = αSFG + 1 as dashed blue lines in Figure 5.1.
As the crossing mass increases with redshift and lies below the mass-representativeness
threshold at z < 1 it has little impact on the mass-integrated SFRD. The reason is that
the mass-dependent SFRD has declined already by at least an order of magnitude from the
3
These data are based on a Baldry & Glazebrook IMF and have been converted to the Chabrier scale. An
additional rescaling by a constant factor of two was necessary in order to match our calibration. This is
in agreement with the results by Gilbank et al. (2010b) that show SFRs based on practically all probed
alternative tracers to be in excess of the [OII]-derived ones. They discuss possible explanations for this
deviation. Given the well known global uncertainty in the absolute calibration of SFR tracers this deviation
is, however, not significant.
73
5. A constant characteristic mass for star forming galaxies
Figure 5.2. – The Schechter-function description of the SFRD (referred to as SFRD function)
for z < 2.5, with color denoting the redshift range. This plot combines the information in the
preceding Figure, now displayed with a linear scaling of the y-axis. The dashed vertical lines
∗
of different colors show the Schechter parameter MSFG
(from Ilbert et al. 2010) for different
redshifts. It is found to be nearly redshift-independent for SF galaxies. The representative∗
ness limit of our SF sample is below MSFG
at all epochs as indicated for the highest redshift
bin (2 < z < 2.5; dash-dotted vertical line). Thick dashed lines of different colors depict the
modified low-mass end trends for our SFRD functions (referred to as ‘case B’) that result from
assuming an upper limit to the average SSFR of SSFR ∼ 1/τdyn . Here, τdyn ∼ 0.37 Gyr is the
dynamical timescale for normal SF galaxies (see Section 4.4.2 for details). This plot clearly
∗
shows that the characteristic mass of SF galaxies – which always lies below MSFG
– does not
evolve over time. This conclusion holds regardless of the exact shape of the SSFR-sequence at
lower masses. Therefore, our data exclude a scenario in which the peak of the SFRD function
has shifted to lower masses at later epochs.
peak value before reaching the crossing mass. The changes are largest at z > 1.8 where
the dashed SFRD function (case B) drops quickly towards lower masses right after the peak
and, in doing so, traces our data points better than before for α̃ = αSFG + βSFG (case A).
However, we emphasize that our data cannot clearly favor case A or B proposed given the
large uncertainties of the Schechter parameters and the lack of representativeness of our
data at such low masses at high z . Any scenario suggested, hence, awaits confirmation
based on deeper data in the selection band once they are available. We robustly conclude
that a single Schechter function is a good model for the SFRD-function over all masses at
least out to z ∼ 1 and that the distribution of SFRDs peaks in the same mass-range at all z
probed in both case A and B.
Figure 5.2 shows the time evolution of our above constructed SFRD function. This nonlogarithmic plot clearly illustrates the existence of a characteristic mass of star formation
at all epochs although it should be kept in mind that our results are most robust at z < 1.5.
74
5.2. The mass distribution function of the SFRD at fixed redshift
Our findings exclude an evolution of this characteristic mass towards lower values with
cosmic time. At z < 1.5 this important result is supported by independent observations
at different wavelengths (Cowie and Barger 2008; Gilbank et al. 2010a,b) and, towards
z ≈ 2, also by empirical arguments (Peng et al. 2010) while the recent model of Boissier
et al. (2010) predicts a mild evolution of this characteristic mass by about 0.3 dex. In
Figure 5.2 again dashed lines of corresponding color denote the low-mass trends of the
SFRD functions once we assume the SSFR-limit discussed. As pointed out above, within
the important mass-range above 1010 M⊙ – at which the SFRD function peaks at any epoch
– a mass-independent proportional increase is apparent even out to z > 2. In contrast
to that, the mass-dependent SFRD appears to evolve mildly below 109 M⊙ . As a result
galaxies in the stellar mass range between 1010 −1011 M⊙ contribute most to the global – i.e.
mass-integrated – SFRD at any epoch but low-mass systems gain more relative importance
towards low redshifts. Evidently, low-mass systems show the same evolutionary trends as
those of higher mass if case A is assumed.
Earlier observational findings appear to be at odds with the existence of a characteristic
stellar mass for star formation we measure. While they are all based on shallower survey
data compared to our COSMOS imaging, the limiting magnitude of these samples is not
necessarily the reason for the different conclusions. Juneau et al. (2005) – using a massindependent extinction correction and hence a linear conversion from [OII] luminosity to
SFR – report that out to z ∼ 2 the contribution to the increase of the global SFRD is more
rapid, the more massive the galaxies are. While this is a similar trend we find if we assume
an upper limit in SSFR (case B), their lowest stellar mass-bin – centered at 109.6 M⊙ –
always appears to contribute most to the SFRD integrated over all masses. Hence, there
is no clear evidence for a peak in the SFRD mass-distribution function and certainly not
in the higher mass-range our data supports. However, based on their findings in the local
universe (Gilbank et al. 2010a), Gilbank et al. (2010b) empirically showed that a massdependent calibration between [OII] luminosity and SFR is more appropriate. If true, this
would modify the low the low-mass dominance in the derived SFRDs of Juneau et al. (2005)
to correspond more closely to our result.4
Independently, also the radio-stacking based study by Pannella et al. (2009) suggests a
strong dependence of the dust-attenuation correction on stellar mass at higher (z > 1.5)
redshifts. Similarly to Juneau et al. (2005), Bauer et al. (2005) derive their [OII]-based
(S)SFRs from a mass-independent calibration albeit neglecting extinction corrections.5 Finally, Bundy et al. (2006), who favor a shift of the characteristic mass towards lower values
with cosmic time, entirely base their conclusion on the stellar mass functions they derive
for SF galaxies (selected by rest-frame (U-B) color and [OII] equivalent line width) within
the DEEP2 survey sample. At z . 1.4 these mass functions do not show an evolution of
∗
the faint-end slope, but the Schechter parameter MSFG
appears to decrease with cosmic
time, in contrast to the already discussed broad agreement in the more recent literature
∗
according to which neither αSFG nor MSFG
change in this redshift range.
To conclude, we summarize our findings as follows.
4
Indeed, as Gilbank et al. (2010b) point out, the mass-dependence here is not only introduced by dust extinction but results from an interplay of various additional factors, e.g. the metallicity or the ionisation
parameter.
5
In the context of mass-dependent evolutionary effects not considering any extinction correction is equivalent
to considering a mass-uniform one.
75
5. A constant characteristic mass for star forming galaxies
1. Up to normalization, the mass distribution function of the SFRD at z < 1 is a universal
Schechter function with possible deviations only below 108 M⊙ .
2. We explain this surprising constancy in shape of this SFRD-function by the nonevolving slope of the SFR-sequence and the constant shape of the mass function for
SF galaxies.
3. Our data at z < 1.5 clearly disfavors a strong ’downsizing’ scenario in which the characteristic mass of SF galaxies that contribute most to the overall SFRD – integrated
over all masses at a given time – shifts towards lower values over cosmic time. The
situation does not appear to change even at z > 1.5 where, however, deeper data is
needed to confirm our results. The characteristic mass is M∗ = 1010.6±0.4 M⊙ .
4. If we assume an upper limit to the average SSFR of the order of the inverse dynamical
scale (τdyn ∼ 0.37 Gyr) the SFRD of galaxies less massive than 109 M⊙ evolves less
rapidly than the one of the dominant higher mass range above 1010 M⊙ .
5.3. The evolution of the SFRD
As all introduced parameters show this remarkable constancy throughout the redshift range
probed (at least out to z ≈ 1) the redshift dependence of Eq. (5.2) is entirely contained in
the normalization Φ∗SFRD . Eq. (5.2) becomes a separable function so that we rewrite:
SFRD(M∗ , z)dM∗ = Φ∗SFRD (z) ϕ (α̃, M ∗ ) dM∗ ,
(5.3)
where mass-dependence consequently is solely contained in the universal SFRD function ϕ.
The global SFRD at a given redshift, integrated over all masses, is simply given by
SFRD(z) =
Φ∗SFRD (z)
Z
ϕ (α̃, M ∗ ) dM∗ .
(5.4)
In the following we will motivate that the evolution of the integrated SFRD follows a simple
power-law of the form
n ∗ +n
Φ∗SFRD (z) M⊙ /yr/Mpc3 ∝ (1 + z) ΦSFG SSFR ,
(5.5)
where the two power-law indices result from the change in stellar mass density contained
in SF galaxies and the increase of the (S)SFR-sequence with redshift.
As detailed in I10 and previously also found by other studies (e.g. Bell et al. 2003, 2007;
Arnouts et al. 2007; Pozzetti et al. 2009) the stellar mass density of SF galaxies grows
after the Big Bang only until z ∼ 1. At lower redshifts it stays constant. Consequently,
as the shape of the mass functions does not evolve, also the Schechter parameter Φ∗SFG in
the mass function is constant in this redshift regime, apart from fluctuations due to large
scale density fluctuations. As shown in Figure 5.3, these fluctuations are consistent with
cosmic variance as estimated by Scoville et al. (2007c) and detailed in I10.6 It is clear that
cosmic variance effects are strongest at low redshifts as the effective volume sampled in a
redshift bin with ∆z = 0.2 increases with redshift. In the interest of simplicity and to avoid
systematic errors caused by cosmic sampling variance we adopt a constant Φ∗SFG at z < 1.
6
For a detailed discussion on cosmic variance in the COSMOS field we refer to Meneux et al. (2009).
76
5.3. The evolution of the SFRD
Figure 5.3. – The redshift dependence of the Schechter parameter Φ∗SFG of the mass functions
for SF galaxies as derived in the COSMOS field (I10). At z < 1 the normalization Φ∗SFG
behaves like the other Schechter parameters and stays constant except for fluctuations very
likely caused by cosmic variance. An estimate of the cosmic variance error (see Scoville
et al. 2007c, for further details) is added in quadrature to the error of the Schechter fit at
these redshifts, as indicated by dotted error bars. At earlier epochs the mass build-up is
reasonably well characterized by a power law in (1 + z). This trend is consequently also
seen in the evolution of the stellar mass density of SF galaxies (I10). The two highest redshift
points (open symbols) were obtained under the assumption that the mass functions keep their
shapes also at earlier cosmic times by matching the normalization to the numbers of galaxies
observed in our mass-representative bins at the high-mass end. This assumption is supported
by the direct observational constraint of Φ∗ALL from the best-fit Schechter-parameterization of
the total mass-function measured by Marchesini et al. (2009) which – at these high redshifts
– should be representative for the SF population; red diamonds.
If we therefore set nΦ∗SFG (z < 1) = 0 in Eq. (5.5) the evolution of the integrated SFRD
in the range 0 < z < 1 is entirely described by the global, i.e. mass-uniform, decline of
the average SFR of SF galaxies with cosmic time. It is important to emphasize once again
that this strong decline is definitely not caused by a decreasing number of SF galaxies, in
particular not at all at the high-mass end. As the efficiency of star formation within SF
systems appears not to change over cosmic time (Daddi et al. 2010a; Tacconi et al. 2010),
we conclude that below z ∼ 1 the strongly evolving integrated SFRD must be exclusively
caused by a strongly declining mass density of cold molecular gas available for star formation towards the local universe. Recent theoretical model predictions (Obreschkow and
Rawlings 2009; Dutton et al. 2010) indeed support such an evolutionary behavior of the
cosmic mass density of molecular hydrogen. As we already explained in Section 4.4.3, systematic redshift uncertainties will not influence our conclusions either as they would only
be propagated along the redshift trend inferred.
77
5. A constant characteristic mass for star forming galaxies
At earlier epochs (i.e. z > 1) we monitor the redshift dependence of the parameter Φ∗SFG
as measured by I10 (Table 5.1). Figure 5.3 shows that the above choice of a power law
at z > 1 is a reasonable assumption and we find nΦ∗SFG (z > 1) = −2.38 ± 0.02 from a fit
to our COSMOS data points at 1 < z < 3. It should be mentioned that the two highest
∗
redshift points in Figure 5.3 (open circles) were obtained by assuming that αSFG and MSFG
stay constant also at z > 2 where I10 did not directly measure the mass function. The
normalization Φ∗SFG (z > 2) was therefore obtained by matching the number densities to
those observed in the mass-complete regime of our data when fixing the parameters αSFG
∗
and MSFG
to their average values at z < 2. This extrapolation is supported by the total mass
function at z > 2 measured by Marchesini et al. (2009). At these high redshifts we assume
the total mass function to be representative for the SF population as quiescent galaxies are
not expected to significantly contribute to the number density. The study by Marchesini
et al. (2009) was carried out based on data taken in various survey fields for which deep
NIR imaging is available allowing them to estimate Schechter parameters for the total mass
function also in two high-z bins in the ranges 2 < z < 3 and 3 < z < 4. Within the errors
all our extrapolated Schechter parameters at 2 < z < 3 are in good agreement with their
∗
∗
results. In particular the exponential cutoff mass at 2 < z < 3, MALL
≡ MSFG
= 1010.96 ,
7
they find agrees remarkably well with our assumption (see Table 5.1). Their normalization
Φ∗ALL ≡ Φ∗SFG does not deviate significantly from our prediction and the evolutionary trend
we suggest is also supported by their data (see Figure 5.3). It is clear, however, that future
measurements of the stellar mass function at z > 1.5 – based on deeper NIR or mid-IR data
– are critical to confirm the validity of our assumptions. Based on the currently available
data we conclude that the stellar mass build-up in the SF galaxy population inevitably leads
to a shallower decline of the integrated SFRD between 3 > z > 1 compared to the steep
decline between 1 > z > 0.
In order to validate our parameterization of the evolution of the integrated SFRD we proceed as follows. First, we simply add up all SFRDs measured in different mass bins in a
given redshift bin (all data points shown in the corresponding panels in Figure 5.1) obtaining a lower limit to the integrated SFRD at that epoch. Second, in order to account for the
contribution of the low-mass (log(M∗ ) < 9.5) SF population that we cannot directly measure,
we integrate Eq. (5.2) from our mass-limit down to 105 M⊙ . As we discuss in Section 5.2 a
single value of the index α̃ in Eq. (5.2) might not be valid over the entire low-mass range as
the SSFR-M∗ relation might flatten as soon as an upper limiting SSFR is reached. The upper left panel in Figure 5.4 hence shows the two alternative extrapolations and all obtained
data are given in Table 5.2. The contribution of the integral generally lifts the SFRD at a
given redshift by a linear factor of ∼ 1.4 if we assume an SSFR-limit (red filled circles) and
∼ 1.7 if a single low-mass end slope α̃ is used (red open circles), suggesting the stacking
analysis missed ∼ 30 % or ∼ 40 % respectively of the integrated SFRD. The differences between both extrapolations are largest at z > 1 below which either method yields practically
the same results. As pointed out in Section 5.2 our data cannot clearly rule out any of the
two alternative low-mass Schechter functions proposed. Consequently, our extrapolations
overlap within their individual uncertainty ranges at all redshifts. In the following we favor,
however, the extrapolation that includes the SSFR-limit as it assures a more conservative
approach compared to the generally larger values the alternative extrapolation yields.
7
As Marchesini et al. (2009) estimate the mass function based on a Kroupa IMF, masses are directly comparable to ours.
78
5.3. The evolution of the SFRD
Table 5.2.
The total SFR density as a function of redshift (cosmic star formation history)
z
0.30
0.50
0.70
0.90
1.10
1.40
1.80
2.25
2.75
SFRDobs (z)
[M⊙ yr−1 Mpc−3 ]
0.011
0.015
0.025
0.043
0.048
0.048
0.070
0.066
0.077
(0.011)+0.001
−0.001
(0.015)+0.001
−0.001
(0.025)+0.002
−0.002
(0.043)+0.003
−0.003
(0.047)+0.004
−0.003
(0.048)+0.004
−0.004
(0.069)+0.007
−0.008
(0.062)+0.007
−0.006
(0.077)+0.009
−0.011
SFRDint (z)
[M⊙ yr−1 Mpc−3 ]
0.018+0.002
−0.006
0.023+0.002
−0.006
0.039+0.003
−0.009
0.055+0.002
−0.008
0.061+0.003
−0.005
0.063+0.004
−0.007
0.095+0.014
−0.014
0.098+0.011
−0.009
0.121+0.017
−0.017
´
`
+0.004
´
`0.019−0.007
+0.004
´
`0.025−0.008
+0.007
´
`0.043−0.015
+0.005
´
`0.058−0.010
+0.010
`0.073−0.016
´
+0.008
`0.070−0.018
´
+0.040
`0.119−0.048
´
+0.043
´
`0.115−0.046
0.175+0.236
−0.099
Note. — The central column states the number density
corrected (raw) sum over all mass bins at a given redshift
of the product of the average SFR and the total number
of galaxies contained in the corresponding bin down to the
redshift-dependent limiting masses of this study. It is hence
the sum of the data points within each panel of Figure 5.1
and – at least out to z = 1.5 a robust direct measurement
of the total dust unbiased SFRD for galaxies more massive
than ∼ 3.2 × 109 M⊙ . The values in the right column additionally take into account the not directly measured lowmass end where we integrate over the SFRD-function at
a given redshift as introduced in Section 5.2 while we assume a potential upper SSFR limit (see Section 4.4.1 for details). The values in brackets result from deriving the lowmass end contribution by integrating the single Schechtermodels of the SFRD-functions and hence assuming no upper limit in SSFR. Like all other results presented in this
work all values are based on a Chabrier (2003) IMF.
79
5. A constant characteristic mass for star forming galaxies
Figure 5.4. – Upper left: The cosmic star formation history (CSFH) out to z = 3 from the
VLA-COSMOS survey. Black circles (raw and number density-corrected) represent the sum
of the data points in all redshift-bin panels of Figure 5.1 and hence a direct – stacking-based
– measurement of the SFRD down to the limiting mass at each epoch. Evidently, the number
density corrections are always small and no corrections are necessary at z < 1.5 where our
results are most robust. Red filled circles correspond to the ’total’ SFRD at each epoch,
obtained by integrating the Schechter-function fit (Figure 5.1) down to M∗ = 105 M⊙ and
assuming an upper limit to the average SSFR (case B in Section 5.2; see also Section 4.4.1
for details). Red open circles are obtained by the same method assuming no upper SSFRlimit (case A in Section 5.2). The redshift evolution can be described by a broken powerlaw (dashed lines) that results from the joint (non-)evolution of the SF stellar mass density
and the evolution of the (S)SFR-sequence. Down- and upward-facing triangles depict the
results by Smolčić et al. (2009a) based on VLA-COSMOS radio detections extrapolated by two
distinct radio luminosity functions (LF). Upper right: Compilation of radio-based literature
estimates of the integrated CSFH between 0 < z < 4, compared to our results. The radiostacking based results by Dunne et al. (2009) are depicted in grey and suggest a clear peak
of the CSFH at z ∼ 1.5 (see Section 5.3 for a full list of references and discussion). Bottom:
Mid- to far-IR measurements of SFRDs between 0 < z < 2.5 along with our data and the
3σ envelope from the Hopkins and Beacom (2006) compilation. The Herschel/PACS-based
results (Gruppioni et al. 2010) are lower limits at z & 1.2 and should be compared to our non
integrated measurements (filled black circles). Note the remarkable agreement of the IR- and
radio-based data at all z .
80
5.3. The evolution of the SFRD
It is evident that the number density corrections at our low-mass end discussed in Section
5.2 have almost no impact on our direct measurements (depicted as black open circles in
the upper left panel of Figure 5.4) of the SFRDs. Even more, at z < 1.5 practically no corrections were necessary which highlights again that our inferences are most robust at these
redshifts. It is therefore justified to regard the corrected values (depicted as black filled circles in the upper left and lower panel of Figure 5.4) as a direct and dust unaffected average
measurement of the SFRD for SF galaxies to a lower mass limit of M∗ ∼ 3.2 × 109 M⊙ . The
evolutionary power-law, scaled to our data points and with the indices in the two redshift
regimes, matches well the observed cosmic star formation history (CSFH) with respect to
our measured data points presenting lower limits as well as to the integrated ones. This may
seem surprising as our evolutionary model does not take into account differential effects
with mass as introduced by assuming an SSFR limit (case B in Section 5.2). However, since
the bulk of the mass-integrated SFRD is contained in our direct stacking based measurements even at high z – which show a mass-independent evolution – the model represents a
good approximation.
In Figure 5.4 we also compare8 our data to the CSFH derived from confirmed SF radio
sources within the COSMOS field in conjunction with extrapolations based on two distinct
evolved local radio luminosity functions (see Smolčić et al. 2009a, for details). This comparison shows how good a deep radio survey constrains the CSFH and leads us to slightly favor
the extrapolations based on the Condon (1989) radio luminosity function in the Smolčić
et al. (2009a) study as already our mass-limited, direct, stacking-based measurements of
the SFRD on their own already reach the values which they inferred using the Sadler et al.
(2002) radio luminosity function at any z < 1.
The upper right panel of Figure 5.4 shows our data along with other radio-based measurements (Haarsma et al. 2000; Machalski and Godlowski 2000; Condon et al. 2002; Sadler
et al. 2002; Serjeant et al. 2002; Smolčić et al. 2009a) and the radio-stacking derived CSFH
by Dunne et al. (2009). Since the referenced measurements based on radio detections have
been extensively discussed in Smolčić et al. (2009a), we will focus our comparison on the
study of Dunne et al. (2009) as it is methodologically closest to our study. Here the extrapolations towards faint sources are based on the evolving K-band luminosity function with the
fixed faint-end slope presented by Cirasuolo et al. (2010). As we previously pointed out, the
evolutionary trends Dunne et al. (2009) find are in good agreement with our results. Also
on absolute scales the results of both studies are basically indistinguishable with significant9 deviations only at the highest redshifts probed in our study. However, at z > 1.5 the
trends observed tend to suggest different conclusions as Dunne et al. (2009) find a clear
peak of the CSFH around z = 1.5 − 2 followed by a strong decline of the SFRD with redshift.
Indeed, at the highest redshifts probed in our study the SFRD extrapolated by Dunne et al.
(2009) does not exceed our direct measurement (without extrapolations, see the top left
panel in Figure 5.4). Hence, one would have to assume that galaxies below ∼ 1010 M⊙ do
8
All literature data mentioned within the remainder of this Section are based on a Salpeter IMF and have been
converted to the Chabrier scale.
9
The error bars to the data points shown here – for which we assume an upper SSFR limit – are smaller at high
redshifts compared to those of the corresponding ones if no limit is assumed. We might have underestimated
the uncertainty introduced by the extrapolations in the former case because of the assumed error to the
dynamical timescale (370 ± 50 Myr) which is the purported limit to the inverse SSFR. However, it should be
noted that Dunne et al. (2009) do not include any uncertainty caused by their extrapolation into their error
budget.
81
5. A constant characteristic mass for star forming galaxies
not contribute at all to the mass-integrated SFRD at z > 2 in order to support this peak
based on our data.
Especially when compared to dust extinction corrected UV-based studies the existence
and location of the CSFH peak as measured by a dust-unbiased star formation tracer is important. Recent UV-based measurements (Reddy and Steidel 2009; Bouwens et al. 2011b)
suggest a peak of the CSFH at around z = 2 − 2.5 and assume that the dust obscuration
for the bulk of SF galaxies does not dramatically change out to z ∼ 4 (as shown by e.g.
Bouwens et al. 2009; Finkelstein et al. 2009; McLure et al. 2010; Wilkins et al. 2010). Our
rising SFRD at z > 2 suggest that SF galaxies at these redshifts have a somewhat higher
dust content or obey a different reddening law than the corresponding sources at lower
redshifts. Whether dust-obscured sources at z > 2 are lost in optical/UV based measurements of the CSFH cannot be definitely answered given the mentioned large error bars our
data show. Future Herschel studies of the total IR luminosity evolution at z > 2 should
reveal potentially larger dust reservoirs in these systems. The even more rapid decline of
the radio-based SFRD as derived by Dunne et al. (2009) appears to support the picture
drawn by e.g. Bouwens et al. (2011b) that obscured star formation does not significantly
contribute to the global SFRD at z ≫ 4. Such conclusions should, however, be treated
with caution as it is highly unclear at such early cosmic times what extrapolation to the
directly measured radio derived SFRDs are needed given the high stellar mass limits (see
also Gallerani et al. 2010).
Our integrated CSFH is also supported by recent studies carried out at mid-IR (Rodighiero
et al. 2010b) and far-IR (Gruppioni et al. 2010) wavelengths. The latter study is based on
∼ 210−240 Herschel/PACS detections at 100 and 160 µm in 150 arcmin2 within the GOODSN field and provides us with a deep view of the dust-unbiased CSFH. The lower panel in
Figure 5.4 shows that the agreement of the Herschel-based results presented by Gruppioni
et al. (2010) with our radio-stacking derived mass-integrated CSFH is striking. Out to z ∼ 1
we also find a broad agreement with the measurements of Rodighiero et al. (2010b). While
Gruppioni et al. (2010) show only lower limits at z & 1 below this redshift both studies
measure an evolution of (1 + z)n with n = 3.8 ± 0.3 (0.4). A recent 24 µm based study by
Rujopakarn et al. (2010) confirms this result measuring n = 3.4 ± 0.2. All these values are
in remarkable agreement with our average measured evolution of the SSFR-sequence of
hnSFG i = 3.5 ± 0.02 (see Section 4.4 and Table 4.5)10 and hence a strong support for both
our measurement as well as our parameterization given in Eq. (5.5), especially out to z = 1.
It is, however, worth mentioning that our work, compared to the other studies mentioned,
draws on a far larger sample.
Finally we want to stress the fact that any shallower high redshift trend in the evolution
of the SSFR-sequence also at the high-mass end would indeed lead to a decline in the
evolution of the SFRD as Eq. (5.5) suggests. This scenario cannot be ruled out given our
data as the SSFR at the low-mass end of our sample tends to flatten and the high-mass end
might follow at slightly higher redshifts based on the dynamical time arguments presented
in Section 4.4.2 that result in a global upper limit to the average SSFR. Hence, again, a
deeper mid-IR selected sample of SF galaxies is needed to accurately probe the regime
above z = 1.5 where the CSFH is supposed to peak.
10
Note that the scatter of the individual measurements at different redshifts of βSFG stated in Table 4.5 is
actually a more realistic uncertainty range than the formal error to their weighted mean.
82
5.4. Summary and conclusion
5.4. Summary and conclusion
Building on the results of the previous chapter we explored the cosmic star formation history (CSFH) in a mass-dependent fashion. By taking advantage of the simple functional
form of both the (S)SFR-sequence and the mass function of SF galaxies in the redshift
range we study we have shown that
• the mass distribution function of the comoving SFR density (SFRD) at any redshift
below z = 1 is well parameterized by a single Schechter function with a possible
low-mass modification at higher z .
• the typical mass of a SF galaxy contributing most to the total (stellar mass integrated)
SFRD is 1010.6±0.4 M⊙ , with no evidence for evolution out to z = 3.
Out to z ≈ 1 the evolution of the integrated SFRD, in turn, is entirely controlled by
the mass-uniform evolution of the SSFR-sequence as the number of SF galaxies in a given
comoving volume does not change anymore. A strong and global decline in the mass density
of molecular gas, i.e. the reservoir out of which stars are formed, appears therefore to be
the only driver of the observed decrease of the integrated SFRD with cosmic time. The rate
at which the SFRD declines is in excellent agreement with the most recent other studies
that use mid- to far-IR emission as an alternative dust-unbiased tracer for star formation.
Towards earlier epochs this steep trend becomes shallower as the comoving stellar mass
density of SF systems decreases. In other words, there are simply less (SF) galaxies at
z > 1 while their individual SFRs further increase with redshift. This statement is certainly
valid for galaxies more massive than 1010 M⊙ which dominate the CSFH at all epochs out
to z = 3. Our results do not suggest any change of this trend towards the highest redshifts
probed but it should be emphasized again that our data cannot constrain the situation as
strongly as at z < 1.5. Hence, we do not rule out that the CSFH peaks in this redshift range.
Indeed, the constancy of the SSFR at z ≫ 2 suggested by other studies and motivated by
the dynamical time threshold we discuss would give rise to a decline of the global SFRD at
such high redshifts.
83
5. A constant characteristic mass for star forming galaxies
84
6. Extreme star formation within 1.5 Gyr
after the Big Bang: a case study
Only recently, i.e. around the start of this PhD thesis, spectroscopic observations of millimeter (mm) sources revealed that objects with extreme star formation activity exist already
in the very early universe (at redshifts z > 4). The star formation rates (SFRs) measured
in these few sources known to-date reach the equivalent of at least several hundreds of
solar masses per year. This gives rise to refer to them as the most vigorously star forming
environments in the universe. Previously, similar SFRs have only been measured in the
rare high redshift hosts of bright quasi stellar objects (QSOs) while the newly discovered
massive starbursts are typically selected as (optically faint) star forming sources.
Massive starbursts at such early times bear the potential to substantially boost our understanding of cosmological structure formation and the build-up of the massive end of
the z & 2 galaxy population. It is likely that the high star formation rates are triggered
by (major) galaxy mergers within early mass overdensities (so-called proto-clusters) predicted by cosmological simulations. Extreme starbursts can therefore be regarded as the
lighthouses of proto-clusters which – in a hierarchical universe – are the seeds of the most
massive galaxy clusters observed to-date. Recent observational results confirm this to be a
promising road and highlight the special importance of high redshift massive starbursts for
constraining models of cosmic structure formation. Only eight extreme starbursts at z > 4
have been detected in carbon monoxide (12 CO) emission, two of which are gravitationally
lensed. These observations reveal large reservoirs of molecular gas which – combined with
the high star formation rates – suffice to build up very massive galaxies in short time. There
is growing observational evidence that massive quiescent galaxies (i.e. objects with little
ongoing star formation) exist already at z > 2 and the z > 4 extreme starbursts are hence
good candidates to be their progenitors. Moreover, the elliptical morphologies of the quiescent sources have likely been shaped by major mergers.
The connection to the earliest quiescent galaxies is not the only motivation to assemble a
representative sample of these early massive starbursts. It is also important to shed light on
the importance of extreme star formation for the global cosmic star formation activity at the
highest redshifts. The massive starbursts unveiled to-date are known to be dust-rich and
might hence represent an important fraction of dust-obscured star formation in the early
universe. While ultra-deep surveys suggest that dust-enshrouded star formation drastically
ceases its importance at redshifts beyond z ∼ 4, they might underscore the massive end due
to the small area covered and a potentially incomplete selection strategy for high redshift
star forming sources.
It is an ongoing effort (see Section 7.4.2) of this PhD project to construct a comprehensive sample of z > 4 extreme starbursts based on the identification of radio continuum
counterparts to distant Lyman-break galaxies (LBGs), i.e. star forming systems which are
selected via the broad-band dropout technique in the B or V band. With its deep (in par-
85
6. Extreme star formation within 1.5 Gyr after the Big Bang: a case study
ticular at radio wavelengths) and extensive observational coverage and large contiguous
area, the COSMOS field is the ideal celestial area for this effort. The discovery of three
spectroscopically confirmed z > 4 massive starbursts during this thesis has proven the
success of our radio-based approach. Based on time-consuming follow-up observations at
mm-wavelengths in continuum and spectroscopy one of these new sources could already
be studied in detail as presented in this Chapter. This analysis reveals an interesting composite nature of the z ∼ 4.62 massive and gas-rich starbursts Vd-17871, making it to-date
the most distant host of an obscured active galactic nucleus. This exceptional source yields
important insights into the diversity of the high redshift starburst population representing
yet another motivation for a detailed and representative ensemble study. This Chapter is
about to be submitted to The Astrophysical Journal for publication as
A. Karim, E. Schinnerer, P. L. Capak, V. Smolčić, M. T. Sargent, M. Aravena, E. Le Floc’h,
H. Aussel, A. Martínez-Sansigre, F. Bertoldi, C. L. Carilli, E. Dwek, O. Ilbert, E. van Kampen,
A. M. Koekemoer, H. J. McCracken, M. Michałowski, H.-W. Rix, M. Salvato, I. Smail & J.
Staguhn, A dark knight rises: a hidden quasar in the z ∼ 4.62 molecular gas-rich starburst
system Vd-17871
6.1. Introduction
One of the key questions in modern observational cosmology regards the importance of
galaxies showing highly elevated star formation activity (starbursts) for the total comoving
volume-averaged star formation rate (SFR) density (SFRD) and whether it changes over
cosmic time. While at low and intermediate redshifts (z < 2) the picture emerged that
(merger-driven) starburst galaxies contribute very little to the global star formation (e.g.
Robaina et al. 2009; Elbaz et al. 2011; Rodighiero et al. 2011) the situation might be drastically different at very high redshifts z > 4. At these earlier cosmic times – when the
universe was denser – it is plausible that stars mainly formed in galaxies residing in more
clustered environments where major mergers trigger a substantial amount of the starburst
activity.
Indeed, massive starbursts have been found in the rare galaxy overdensities known at
z > 4 (Daddi et al. 2009b,a; Capak et al. 2011) with growing evidence that star forming
sources at these redshifts tend to cluster around individual extreme starbursts (Capak et
al. in prep.).1 This is suggestive that extreme star formation may contribute significantly
to the cosmic SFRD in the very early universe.
Given their extreme SFRs of several hundreds to more than a thousand M⊙ /yr massive
starbursts at z > 4 are ultra luminous infrared (IR) galaxies (ULIRGs) with IR luminosities
LIR ≫ 1012 L⊙ and expected cold dust temperatures of TD ∼ 35 K similar to starbursts at
z ∼ 2 (e.g. Kovács et al. 2006). While the expected monochromatic flux densities at millimeter (mm) wavelengths are detectable with modern bolometer cameras the large beam-sizes
of & 10′′ of single-dish telescopes often lead to major problems in the association with the
correct counterparts at much shorter wavelengths. The unambiguous counterpart identification and accurate spectroscopic redshifts are, however, a prerequisite for observations
1
Observational evidence for galaxy overdensities at such high redshifts (so-called proto-clusters) has been
reported earlier (e.g. Overzier et al. 2006, 2008). Those proto-clusters have been searched for in the environments of massive high redshift radio galaxies selected as ultra steep spectrum (USS) radio sources (see
De Breuck et al. 2002, for details on the massive nature of USS radio sources and their selection).
86
6.1. Introduction
of rotational transitions of the 12 CO molecule within the relatively narrow bandwidths mmtelescopes provide.2 Measuring the 12 CO emission, in turn, is critical for key insights into
the state and distribution of the potentially large reservoirs of molecular gas fueling the
star formation activity in these objects. Blind searches for 12 CO-line emission – without
pre-determination of spectroscopic redshifts – have been extremely time consuming and
feasible to-date for only two z & 4 sources with highly boosted flux levels due to gravitational lensing (Lestrade et al. 2010; Cox et al. 2011).
As a result, single-dish blank-sky mm-surveys alone might not be the most promising
road to assemble a comprehensive sample of massive starbursts in the very early universe.
Pointed interferometric continuum observations of the brightest objects (e.g. Younger et al.
2007) help to increase the success rate (Capak et al. 2011; Smolčić et al. 2011) but they are
restricted to individual sources pre-selected solely by their emission at mm-wavelengths.
Consequently, to-date 12 CO emission has only been detected in six unlensed z > 4 sources
residing in a number of prominent deep-fields with highly different ancillary data (Schinnerer et al. 2008; Daddi et al. 2009b,a; Coppin et al. 2010; Riechers et al. 2010; Carilli
et al. 2010). Due to those often serendipitous detections in different environments important questions remain open. Especially their relation to the better-studied population of
z ∼ 2 starbursts (e.g. Chapman et al. 2005; Greve et al. 2005), typically found among the
so-called sub-millimeter galaxies (SMGs), their intrinsic diversity and nature are unclear. A
representative census of extreme star formation within the first 1.5 Gyr is, however, critical
to provide tight constraints for cosmological models (e.g. Baugh et al. 2005; Coppin et al.
2009).
Optical data in combination with radio data provide a promising road to reveal extreme
starbursts at z > 4 in their full diversity based on mm-follow-up observations (Capak et al.
2008; Schinnerer et al. 2008) and to be confirmed here.3 Modern cosmological deep field
surveys – particularly the 2 deg2 Cosmic Evolution Survey (COSMOS; see Scoville et al.
2007d, for an overview) – reach not only an adequate celestial area but also depth of their
panchromatic data to provide a comprehensive view on the z > 4 starburst population,
superior to the smaller areas and single waveband selection window current mm-surveys
provide.
At redshifts z > 4 massive star forming environments and molecular gas reservoirs have
been found also around optically luminous – typically broad line-selected – quasars (e.g.
Omont et al. 1996; Carilli et al. 2002; Walter et al. 2003; Riechers et al. 2006, 2008). At
all z > 2 the star formation properties of such quasars have not been found to differ significantly from those derived for massive starbursts (Riechers 2011; Daddi et al. 2010b).
Yet, tentative evidence for different gas excitation and spatial distribution properties might
point to an evolutionary merger sequence from an initial starburst to a far-IR bright quasar
(Riechers et al. 2010). Such an evolutionary link has been suggested also for z ∼ 2 sources
by Coppin et al. (2008) similar to the scenario proposed for a link between local ULIRGs
2
Note, however, that the Atacama Large Millimeter Array (ALMA) in full operation will drastically improve the
current situation both with respect to counterpart identification as well as to bandwidth restrictions in blind
searches for 12 CO line emission.
3
Note that also the z = 4.76 starburst J033229.4-275619 (Coppin et al. 2009) found in the LABOCA Survey
of the Extended Chadra Deep Field-South (LESS; Weiß et al. 2009b) nominally is an optical broad-band
dropout galaxy with a weak radio continuum counterpart. A deep mm-survey accompanying a panchromatic
deep field therefore provides valuable ancillary data while the actual selection function is based on much
different wavelength data.
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6. Extreme star formation within 1.5 Gyr after the Big Bang: a case study
and quasars by Sanders et al. (1988). Regardless of the validity of such an evolutionary
sequence, it is clear that intrinsically different objects comprise the population of extreme
starbursts at high redshift and it is desirable to explore the full diversity of this population.
A population largely ignored so far in this picture are (radio-quiet to radio-intermediate)
obscured quasars4 which might contain similarly large molecular gas reservoirs and reach
comparable far-IR luminosities as the massive star forming sources at high-z (MartínezSansigre et al. 2009). Obscured active galactic nuclei (AGN) are supposed to contribute
a substantial fraction to the unresolved (hard) X-ray background at energies above 1 keV
(see Comastri 2004, for a review). Globally, they might be more abundant than unobscured
quasars (e.g. Martínez-Sansigre et al. 2005, 2008) while at higher X-ray luminosities at
least a 1:1 ratio is expected (e.g. Ueda et al. 2003; Treister and Urry 2005). While obscured
AGN are found in deep hard X-ray surveys (e.g. Alexander et al. 2003) they merely trace the
lower luminosity end (i.e. Seyfert -2 objects; Martínez-Sansigre et al. 2006b). Mid-IR selection has proven to be a vital strategy for finding the intrinsically more luminous obscured
sources (e.g. Martínez-Sansigre et al. 2005). Provided deep enough optical data is available
obscured quasars could also be found in apparently star forming galaxies selected at restframe optical wavelengths where the host galaxy dominates the emission over the heavily
obscured AGN. Detailed radio continuum studies of obscured AGN (Martínez-Sansigre et al.
2006a; Klöckner et al. 2009) suggest that they resemble radio quiet rather than radio-loud
AGN while typically exhibiting higher radio luminosities compared to the radio quiet population. Therefore these sources are expected to be detectable even beyond z = 4 in deep
radio continuum surveys.
In this Chapter we report on the detection of molecular gas emission as traced by the
redshifted 12 CO(J = 5 → 4) rotational transition (CO(5-4) in the following) in the z = 4.622
starburst system Vd-17871 using the Plateau de Bure Interferometer (PdBI). Residing in
the COSMOS field for which high-quality and deep multi-wavelength (hard X-rays to radio
continuum) photometric data exist, this source has been selected as a V-band dropout –
and hence Lyman Break Galaxy (LBG) – with a weak 1.4 GHz counterpart. As we will
show, in addition to a large reservoir of molecular gas this source harbors an obscured
radio-intermediate AGN. This confirms that the optical selection of (normal) star forming
galaxies is capable of revealing extreme starbursts but also obscured composite sources
at very high redshifts. As this AGN is hidden it manifests its presence mainly through
substantial heating of the dust continuum at rest-frame mid-IR wavelengths.
Throughout this Chapter all observed magnitudes are given in the AB system. We assume
a standard cosmology with H0 = 70 (km/s)/Mpc, ΩM = 0.3 and ΩΛ = 0.7 consistent with the
latest WMAP results (Komatsu et al. 2009) as well as a radio spectral index of αrc = −0.8
(e.g. Condon 1992). A Chabrier (2003) initial mass function (IMF) is used for all stellar
mass and SFR calculations in this Chapter.
4
For an introduction and review on different types of active galactic nuclei and their unification see Antonucci
(1993); Urry and Padovani (1995).
88
6.2. Target selection and observations
6.2. Target selection and observations
From a sample of 15,000 V-band dropout galaxies (see Steidel et al. 1995, 1996, for an introduction into the broad-band dropout selection method and initial results) in the COSMOS
field we selected Vd-17871 as one of six objects with weak counterparts in the deep VLA
1.4 GHz imaging (Schinnerer et al. 2010). The similarly selected source J1000+0234 had
been previously revealed to be a z ∼ 4.5 extreme starburst with a large molecular gas content and evidence for an on-going major merger (Capak et al. 2008; Schinnerer et al. 2008).
In the following we describe key features of Vd-17871 and our follow-up observations.
6.2.1. Panchromatic COSMOS data and selection criteria
Ground-based imaging of the COSMOS field has been obtained in 23 optical to near-IR
bands at the Subaru, UKIRT and CFHT telescopes (Capak et al. 2007; Ilbert et al. 2009;
McCracken et al. 2010). The field has been surveyed by the Very Large Array (Schinnerer
et al. 2007, 2010), the Hubble and Spitzer Space Telescopes (Scoville et al. 2007b; Sanders
et al. 2007) and the XMM-Newton as well as Chandra X-ray telescopes (Hasinger et al.
2007; Elvis et al. 2009). At far-IR and sub-mm wavelengths the COSMOS field has been
observed by Herschel/PACS (Poglitsch et al. 2010) as part of the PACS Evolutionary Probe
(PEP) survey (Lutz et al. 2011) and by Herschel/SPIRE (Griffith and Stern 2010) as part of
the Herschel Multi-tiered Extra-galactic Survey (HerMES; Oliver et al. in prep.).
Vd-17871 is part of the V-band dropout sample – star forming sources at z > 4 – culled
from the latest release of the COSMOS photometric catalog. This sample has been selected
based on the broad-band color criteria described in Iwata et al. (2007) among objects with a
signal-to-noise ratio (SNR) of more than 2σ in the Subaru z + band: V − i+ > 1.55, i+ − z + >
−1, V − i+ > 7(i+ − z + ) + 0.15.
LBGs at z ∼ 3 typically have radio-derived star formation rates (SFRs) of ∼ 30 M⊙ /yr
(Carilli et al. 2008) while for massive (Spitzer/IRAC detected) LBGs in the GOODS-North
field Magdis et al. (2010) find ∼ 100 M⊙ /yr based on their radio and IR-emission. For an
individual source at a typical V-band dropout redshift of z = 4.5 to be detected at a > 3.5σ
level in the deep imaging of the VLA-COSMOS field (12 µJy average rms; Schinnerer et al.
2010) an SFR of > 2000 M⊙ /yr is required if the local calibration of the far-infrared/radio
relation by Bell (2003b) is used. As this clearly would be an extreme SFR enhancement
compared to the average LBG, we searched for weak radio continuum emission in the near
vicinity of all V-band dropouts in order to find extreme starbursts.
Vd-17871 is indeed associated with a 7.2σ source in the deep VLA-COSMOS image at
2.5" resolution. Given the high significance of the radio counterpart the above calculation
suggests a tremendous SFR of ∼ 4000 M⊙ /yr in this object. Hence, even if only 10 %
of the total radio emission were powered by star formation, Vd-17871 would still show a
significantly elevated stellar mass growth compared to the global population of massive
LBGs.
6.2.2. Keck/DEIMOS observations
Spectroscopic observations of Vd-17871 with the Deep Imaging Multi-Object Spectrograph
(DEIMOS; Faber et al. 2003) on Keck-II have been carried out in February 2009 under clear
conditions (∼ 1′′ seeing). The total observing time of 4 hr was split into blocks of 30 min
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6. Extreme star formation within 1.5 Gyr after the Big Bang: a case study
Figure 6.1. – Smoothed Keck/DEIMOS spectrum for Vd-17871 (black) showing a significant
single emission line detection but no underlying continuum. The line shape suggests it to
be Lyman-α at a redshift of z = 4.626. Tentatively, the line is double-peaked placing a lower
limit to the velocity dispersion of & 1000 km/s and at most ∼ 2170 km/s (see Section 6.3.3 for
details). Both values are compatible with line widths typical for the narrow-line region in the
vicinity of an AGN. We also show the average empirical Lyman Break Galaxy template (green)
by Shapley et al. (2003) indicating prominent absorption lines typically seen in high redshift
star forming systems by vertical dashed lines. The transmission curves for three Subaru
intermediate band filters are indicated in grey showing that filter IB679 covers the Lyman-α
line explaining the flux elevation seen in the optical to near-IR spectral energy distribution
(see Figure 6.3).
and the 830l/mm grating tilted to 7900 Å as well as the OG550 blocker were used while
ghosting was removed by dithering the targets by ±3′′ along the slit.
For data reduction we used the modified DEEP2 DEIMOS pipeline (see Capak et al. 2008)
and we determined the total instrumental throughput using the standard stars HZ-44 and
GD-71. Using bright stars in the mask we estimated the amount of wavelength-dependent
slit losses from dispersion as well as extinction in the atmosphere and corrected for the A,
B, and water absorption bands.
The 1D-spectrum is shown in Figure 6.1. One emission line is clearly detected. Its
strength and shape strongly suggest it to be Lyman-α emission redshifted to z = 4.626 ±
0.001. We detect no underlying continuum emission, not surprising given the faintness of
the source at observed optical magnitudes (i+ ∼ 25.5). Due to the same reason absorp-
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6.2. Target selection and observations
tion lines typically seen in star forming sources at high z (e.g. Shapley et al. 2003) remain
invisible. No potential spectral line emission from an active galactic nucleus (AGN) are
seen.
6.2.3. Millimeter continuum and CO-line observations
We observed Vd-17871 with the 117 element array bolometer camera MAMBO-II (Kreysa
et al. 1998) operating at 1.2 mm (250 GHz) during pooled observations in March 2009 at
the IRAM 30 m telescope. Pointing accuray was checked every 20-40 minutes using the
nearby sources J0948+004 and J1058+016. Regularly, gain calibration was performed and
focus was checked using mm-bright sources such as Saturn. Fluxes and foci have been
always found to be accurate and stable. MAMBO-II was used in on-off mode with one scan
consisting of two off-source positions in between two on-source position and an integration
time of one minute per position resulting in a total of four minutes per scan. The azimuthal
wobbler throw – i.e. the on-sky angle between the off-source positions covered by the periodic movement of the secondary mirror – was chosen to be between 32 and 45 degrees.
Individual scans were obtained at different times of the day resulting in different physical
off-source positions, thereby minimizing the risk of the sky position being accidentally coincident with another astronomical source. The source elevation during the observations was
never below 45 degrees. The total integration time (using the most sensitive pixel number
20) was 2.6 hours and resulted in a significant detection of S1.2 mm = 2.5 ± 0.5 mJy/beam
under a low sky-noise level (typically . 50 mJy/beam). The atmospheric opacity was always
below τ230 GHz ≤ 0.3. We used the MOPSIC data reduction package (R. Zylka, IRAM) to
obtain the flux measurement given above and in Table 6.1.
At the IRAM Plateau de Bure Interferometer (PdBI) Vd-17871 was observed between October 2010 and March 2011 in B, C and D configuration at 3 mm with the wide-band correlator WideX (3.6 GHz of total bandwidth in dual polarization mode) tuned to 102.4476 GHz,
i.e. the redshifted frequency of the 12 CO(5-4) transition. Usually all six antennas were
available during the observations. The nearby quasar J0948+003 was used for atmospheric
amplitude and phase calibration of all observing tracks. Given the slight polarization of this
source long tracks were manually split in two parts in order to obtain similar fits to the
phase variations in both polarizations, hence improving the phase calibration compared
to the results of the automatic pipeline reduction. For tracks with sufficient SNR, bandpass calibration was performed using the same source, J0948+003. This way the effect
of ’parasites’, i.e. signal peaks in individual spectral channels artificially produced by the
electronics of the PdBI, could be reduced to a minimum. J0948+003 shows some spectral
slope, i.e. an increase in flux density with frequency in the lowest frequency quarter of the
wide-band. This slope does not affect the channels expected to cover the line emission but
might partially lower the continuum flux level in the off-line channels at the high velocity
end. A continuum level estimated from all off-line channels will, however, not significantly
suffer from this flux reduction due to the large bandwidth available. For two out of five
tracks used to obtain the final results the stronger quasars 3C84 or J1055+018 were used
as bandpass calibrators in order to obtain a sufficient signal and, hence, accuracy in the
correction. This leads to a single clearly identifiable ’parasite’ not associated with any
physical line emission. We consequently flagged the associated spectral channels for our
analysis. We reduced the data with the routines CLIC and MAPPING contained in the latest
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6. Extreme star formation within 1.5 Gyr after the Big Bang: a case study
version5 of the GILDAS software (Guilloteau and Lucas 2000). Using natural weighting, a
velocity-integrated map of the CO(5-4) emission with a restoring beam of 3.87′′ × 2.36′′ was
obtained, the resolution for the off-line continuum emission is 3.75′′ × 2.25′′ . The net onsource integration time of 13 hours gave an rms of 0.42 mJy/beam in a single 50 km/s (i.e.
17 MHz) wide channel and 0.03 mJy/beam in the 3.3 GHz wide line-free continuum. Using
the MAPPING task uv_average we averaged over the channels covering the line emission
(i.e. 850 km/s; see below) and, independently, over the same number of off-line channels.
We subsequently subtracted the latter average from the former via the task uv_subtract
in order to image the net line emission. We also used the task uv_average for imaging
the continuum emission using all off-line channels. Finally, we separately imaged the line
and the continuum emission with a cell size of 0.4"/pixel and used the clean task to obtain
beam-deconvolved maps. For both images CLEANing was performed down to 1σ within a
box around the source. Using a threshold of 2σ does not alter the results. The resulting
maps are shown in Figure 6.7.
6.3. Source properties of Vd-17871
6.3.1. The molecular gas reservoir
We detect spatially unresolved CO(5-4) line emission toward Vd-17871 at a significance of
5.8σ . The MAPPING task uv_fit was used to confirm that the emission is unresolved. A
Gaussian fit to the line profile (Figure 6.2) yields a peak line strength of (1.3±0.2) mJy/beam
and a full width at half maximum (FWHM) of (397 ± 82) km s−1 . This results in a velocityintegrated line intensity of (0.56±0.15) Jy km s−1 . The line is centered at (102.508±0.009) GHz
(i.e. zCO = 4.622 ± 0.001) and hence blue-shifted by (279 ± 33) km/s with respect to the
Ly-α emission, a typical offset commonly found in z ≫ 1 starbursts (e.g. Greve et al.
2005). We marginally detect the 3 mm dust continuum emission in Vd-17871 at a 4.3σ
level (0.13 mJy/beam) in the line-free channels.
Following Solomon and Vanden Bout (2005) we derive a line luminosity of L′CO(5−4) =
(1.8 ± 0.4) × 1010 K km s−1 pc−2 (LCO(5−4) = (1.1 ± 0.3) × 108 L⊙ ) from the velocity-integrated
CO(5-4) line-flux. To convert this luminosity into a total molecular gas mass we assume –
in absence of lower-J CO observations – that a single molecular gas phase is thermalized
up to the J = 5 level. In this case L′CO(5−4) = L′CO(1−0) and a typical conversion factor
of αCO = 0.8 found for local ULIRGs (Downes and Solomon 1998) and commonly used for
high-z starbursts (Solomon and Vanden Bout 2005) leads to a total molecular (H2 +He) gas
mass of (1.4 ± 0.4) × 1010 M⊙ .
6.3.2. Panchromatic morphology and ultraviolet to mid-IR photometry
The rest-frame ultraviolet (UV) morphology of Vd-17871 is fairly complex with two main
emission knots being separated by 1.5" (i.e. ∼ 10 kpc at z = 4.662) with a position angle of
∼ 45 degrees (east of north; Figure 6.7). A priori it is not clear if both knots belong to the
same astronomical system. As the Keck/DEIMOS observations only targeted the northern
knot (source A in the following) with an east-west slit orientation no spectroscopic redshift
5
We used the GILDAS release from April 2011, the latest public version available at the time of data calibration
and reduction.
92
6.3. Source properties of Vd-17871
Figure 6.2. – Redshifted 12 CO(5-4) spectrum from IRAM/Plateau de Bure Interferometer observations towards Vd-17871 in the 3 mm atmospheric window. The full 3.6 GHz bandwidth
provided by the WideX correlator translates into a 10,000 km s−1 velocity coverage. We significantly detect the ∼ 400 km s−1 wide (FWHM) 12 CO(5-4) line blue-shifted by (280 ± 34) km s−1
with respect to the Lyman-α line as indicated by the vertical dashed lines resulting in a redshift of zCO = 4.622. The spectrum has been re-binned to a velocity resolution of 50 km s−1
and the line profile has been fit by a single Gaussian. The channel rms is indicated by gray
horizontal lines in steps of 1σ . The underlying 102 GHz continuum is detected at a ∼ 4 σ level
in the combined off-line channels.
information has been retrieved for the southern one (source B). We therefore separately
extracted the photometry at both positions, as verified and described in detail by Smolčić
et al. (in prep.). As the sources are separated by 1.5”, which is smaller than the aperture
used to extract the photometry a deblending strategy was required in the bands where
both sources are detected. At optical wavelengths, where the sources are well separated
we have simply subtracted the interfering source from the image, while in the IRAC (3.6
and 4.5 µm) bands we have modeled the interfering source as a point source before subtraction. In Figure 6.3 we show the spectral energy distributions (SEDs) of both sources
which appear very similar. The observed optical photometry therefore indeed supports a
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6. Extreme star formation within 1.5 Gyr after the Big Bang: a case study
Figure 6.3. – The rest-frame UV-to-near-IR spectral energy distributions (SEDs) of both components that are likely part of the system Vd-17871 (see Figure 6.7). The photometric data
(black filled circles) are obtained from ground- and space-based observations in 37 broad and
intermediate bands in the COSMOS field. We used a deblending strategy (see descriptions
in the text) in order to separately extract the photometry at the positions of the rest-frame
UV sources A (left panel) and B (right panel) seen in the ACS imaging (Figure 6.7). While
only the redshift of source A has been determined spectroscopically (see Figure 6.1), both
sources are optically faint and appear photometrically very similar, suggesting both to reside
at a similar (high) redshift. The best fit Bruzual and Charlot (2003) templates (BCO3, blue
solid curves) to the photometry of both sources suggest the emission to be of stellar origin
in each case (the best fit parameters are stated in the text). In contrast, the AGN-dominated
(power-law) spectrum of the local ULIRG/Seyfert-1 Mrk 231 (red solid curves;Polletta et al.
2007) – using the scaling to the far-IR emission for source A (see Figure 6.5) – poorly fits the
observed data. Also source B is not well fit by this template (see Section 6.3.3 for details and
further implications). Source A shows a flux elevation in the intermediate band centered at
0.679 µm due to Lyman-α emission (see Figure 6.1) which is strongest at the position of this
source.
high redshift nature of source B. Using the latest version of the publicly available hyper-z
code (Bolzonella et al. 2000) and a library of observed and synthetic templates we fit the
observed stellar SEDs separately for both sources while fixing the redshift to the spectroscopically measured value. All 37 filters available have been used in both cases. In the
models used we force the derived galaxy age to be less than the difference between the age
of the universe at a given redshift and a fixed formation redshift of z = 8. We assumed a constant and, alternatively, exponentially declining star formation histories (SFHs) ∝ exp −t/τ∗
with τ∗ = (0.1, 0.2, 0.3, 0.6, 2, 5, 15) Gyr. Furthermore assuming a Calzetti et al. (2000) extinction law we varied AV from 0-4 in steps of 0.2. Both sources are best fit with templates
from the Bruzual and Charlot (2003) stellar population synthesis library, exponentially declining SFHs (τ∗ (A) = 0.1, τ∗ (B) = 0.3 Gyr) and AV = 0. While both sources are found to
be young the fits suggest a somewhat lower age of 0.45 Gyr for source A compared to the
0.72 Gyr found for source B. Indeed, the parameters found for source A are reminiscent of
a starburst or single burst model. Within the error margins the individual stellar masses
for both sources are very similar with M∗ (A) = 1010.45±0.2 M⊙ and M∗ (B) = 1010.35±0.2 M⊙
94
6.3. Source properties of Vd-17871
leading to a total stellar mass content of ∼ 5 × 1010 M⊙ in this system. Nominally, the total
baryonic mass budget in the system Vd-17871 (source A and B) is dominated by stars by
80 % and by 66 % if we underestimated the gas mass by 50 % (see below). If we consider
only the spectroscopically confirmed source A, however, and assume that all the gas is concentrated in this source, the molecular gas fraction is between one third to one half of all
baryons.
Figure 6.4. – Redshift probability distribution functions for the two neighboring sources seen
in the ACS imaging (see Figure 6.7). The photometric redshift (photo-z) estimation is based
on the observed, deblended photometry for both sources (see Figure 6.3) using a variety of
template libraries, star formation histories and dust extinction parameters and the hyperz code provided by Bolzonella et al. (2000) (see text for details). Source B shows a clear
probability maximum at z ∼ 4.2 while for source A a similarly high redshift is favored. Within
the uncertainties both values are consistent with the spectroscopic redshift determination of
source A (see Figure 6.1).
The absolute V-band magnitudes found from the best-fit templates are equally faint for
both sources (MV (A) = −23.05, MV (B) = −22.66) and compatible with the purported high
redshift nature. Moreover, if we treat the redshift as a a free parameter in our fits we obtain
very similar photometric redshifts of ∼4.1 (∼4.2) for source A (B), close to the spectroscopic
determination (see Figure 6.4). Moreover, in the deep KS -band imaging of the COSMOS
field from the UltraVISTA survey (McCracken et al. in prep.) source A is detected at a
level consistent with the rest-frame U-band emission expected for a high redshift galaxy
while there is no evidence for a foreground object at the position of source B or elsewhere.
Instead, at the position of source B only a tentative detection is found in the UltraVISTA KS band image. An interesting photometric feature is clearly seen in source A where the flux in
95
6. Extreme star formation within 1.5 Gyr after the Big Bang: a case study
the Subaru intermediate band IB679 is substantially boosted as it covers the Ly-α line at the
observed redshift (see Figure 6.1). The emission in the intermediate band filter is overall
diffuse and extends towards source B. Moreover, in the two-dimensional Keck/DEIMOS
spectrum the Ly-α line shows multiple components both spatially and in redshift.
Within the positional uncertainty both the CO and the dust continuum emission are centered at the position of source A while the radio continuum – detected at higher significance
compared to the mm-data – peaks right between both UV emission knots at a distance of
0.6" (corresponding to 4 kpc at z = 4.662). The comparatively strong Spitzer/IRAC 3.6 µm
emission is centered at the position of source A, suggesting substantial flux contribution
from the redshifted Hα line compatible with the massive star forming nature of this object.
Higher signal-to-noise mm-data are required to clarify whether all interferometric data spatially coincide at the 1.4 GHz position or if rather the radio continuum is offset to all other
emission sources including the Ly-α and Hα lines.
We conclude that both emission knots seen in the ACS imaging are most likely part of
the same astrophysical system while the bulk of star formation activity is probably concentrated in the northern part (A). This source geometry and the spectral information is
overall reminiscent of an early-stage major galaxy merger and very similar to the previously spectroscopically confirmed source J1000+0234 (Capak et al. 2008) that has been
selected using the exact same criteria.
6.3.3. The thermal dust to radio continuum emission properties and
indications for nuclear activity
Space-based mid- to far-IR data (from Spitzer/MIPS, Herschel/PACS&SPIRE) are available
for Vd-17871. These are complemented by the continuum photometry obtained at 1.2 mm
and 3 mm to provide insights into the amount, temperature and state of its dust emission.
A single modified black body (gray body; e.g. Beelen et al. 2006) with a dust temperature
TD = (42 ± 1) K at an emissivity of β = 1.5 ± 0.1 provides a good description of the farIR emission, particularly tracing well the cool dust peak in Vd-17871. Trying to fit all
IR data with the prototypical starburst IR-SED by Elbaz et al. (2011) significantly fails
to reproduce the mid- to far-IR emission observed if scaled to match the single dish and
interferometric cool dust continuum data (Figure 6.5). This template would likewise overpredict the mm-emission and the SPIRE photometry if scaled to the MIPS datum unless we
were to significantly vary its cool dust emission properties. At the redshift of the source
the 24 µm band falls right between the prominent rest-frame 3.3 µm and 6.6 µm polycyclic
aromatic hydrocarbon (PAH) features which hence cannot have boosted the mid-IR emission
observed. The global IR-emission in Vd-17871 is in better agreement with the redshifted
and properly scaled IR SED of the local composite starburst and Seyfert-1 ULIRG Mrk 231
(Polletta et al. 2007), leading to a total (8 − 1000) µm far-IR luminosity of ∼ 8 × 1012 L⊙ for
Vd-17871 that would hence be partially powered by an AGN. On the other hand, the optical
spectrum and the deep Chandra imaging do not yield evidence for the presence of an AGN
in Vd-17871. No prominent spectral lines (such as CIV λ1540) and no X-ray emission are
detected but the absence of such features could also point to a high level of obscuration in
our line of sight. While the slit orientation might have prevented us from observing further
spectral line emission the Lyman-α line width of . 50 Å (i.e. . 2170 km/s) suggests that
the slit covers the central (narrow-line) region since it is broad compared to typical values
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6.3. Source properties of Vd-17871
found in pure star forming sources.6 Yet, it is too narrow for being consistent with line
emission originating from the broad-line region. This suggests that the AGN in our line
of sight is covered by a central dust screen, compatible with the obscuring torus scenario
around the accreting black hole suggested for type-2 AGN sources (e.g. Urry and Padovani
1995). Consequently, the host galaxy dominates the rest-frame UV-optical emission.
This explains why a normal galaxy template provides the best fit to the rest-frame UVto-optical SED of Vd-17871. This holds true in particular in comparison to the Mrk 231
template. In Figure 6.3 we show the redshifted UV-to-near-IR part of the Mrk 231 template in addition to the best-fit stellar population synthesis models. Since the 3 mm dust
continuum appears to coincide with source A (as well as the CO emission; see Figure 6.7)
we chose for this source the same scaling of the template as used at far-IR wavelengths
(see Figure 6.5). The short wavelength SED of source B is shown along with the redshifted
Mrk 231 template where no scaling is applied in order to reflect the purported lower contribution of this source. Figure 6.3 shows that the so-scaled Mrk 231 template is clearly
disfavored for source A and it is also ruled out for source B at optical wavelengths. If we
rescaled the Mrk 231 template – assuming that both source A and source B contribute to
the far-IR emission in equal parts – it would provide a better but still poor match to the
observed photometry, significantly over-predicting the near-IR data of both sources.
The obscured AGN hypothesis is favored further because the Mrk 231 template also
significantly under-predicts the 160 µm emission observed that is marginally detected at a
∼ 3 σ level. It hence under-predicts the total IR luminosity. It is unlikely that redshifted
strong AGN ionization lines (mainly [O IV] and [Si III]; Weedman et al. 2005) are responsible
for this substantial flux elevation as the inferred line-widths would be unusually broad. As
Martínez-Sansigre et al. (2009) point out, a typical obscured quasar has a composite midto-far-IR SED consisting of a dominant cool dust component at far-IR wavelengths as well
as deep silicate absorption in the mid-IR (see also Martínez-Sansigre et al. 2008, for results
on the mid-IR spectra of obscured quasars at high-z ). They show that clumpy torus models
(Nenkova et al. 2008a,b, e.g.) do not provide a reasonable fit of the global dust emission
unless additional extinction from cool dust – distributed on kpc scales within the host galaxy
– is assumed. Martínez-Sansigre et al. (2009) suggest two distinct gray bodies to represent
the far-IR emission of a typical obscured quasar. The cool dust emission we find is thereby
in reasonable agreement with the warmer gray body option (TD = 47 K, β = 1.6). The
differences are, however, marginal given that our single component gray body fit yields an
emissivity value consistent with that of the Martínez-Sansigre et al. (2009) component fit.
While our data do not constrain the rest-frame mid-IR portion covered by the MartínezSansigre et al. (2009) SED it is reasonable to adopt this model for our data given the strong
indications for an obscured AGN in our source.
We still need to bridge the spectral gap blueward of the cool dust emission peak. While
emission from a (clumpy) dust torus is typically represented by a continuum of hot gray
bodies (e.g. Nenkova et al. 2008a,b) the best approach in our case of sparse data coverage
6
Since the Lyman-α emission appears to be extended (see Section 6.3.2) it might at least partially originate
from distances larger than the extent of the narrow-line region. Given the tentative evidence for two distinct
line components at the spectral resolution available it is challenging to determine the line profile and hence
to derive an accurate width of the Lyman-α line. We therefore assume a single component and take its
FWHM as an upper limit to the line width. Note, however, that half the full width – in case of two line
components – would suggest a velocity dispersion of & 1000 km/s, still compatible with that expected in the
narrow-line region.
97
6. Extreme star formation within 1.5 Gyr after the Big Bang: a case study
is a simpler model. We therefore follow the descriptions in Weiß et al. (2007); Aravena
et al. (2008) and fit an alternative two-component gray body spectrum to the IR data points
excluding the observed 24 µm datum and assuming that the dust emission can be optically
thick with an optical depth τν > 1:
Sν =
Ω
[Bν (TD ) − Bν (TBG )] (1 − e−τν ),
(1 + z)3
(6.1)
thereby introducing the Planck function Bν (T ), the redshifted cosmic microwave background temperature TBG (TBG = 2.73 × (1 + z) K) and the source’s apparent solid angle
Ω (assuming a source extent of 1"). We adopt an emissivity index β = 2.0 and κ0 = 0.4
cm2 g−1 at ν0 = 250 GHz (Kruegel and Siebenmorgen 1994) in the frequency-dependent
description for the dust absorption coefficient κ(ν) = κ0 (ν/ν0 )β .
This fit yields a cool component with a temperature of TDC = 42 K – as found for the single
C = 3.98 × 108 M dominating the total dust-mass
component gray body – and mass MD
⊙
H = 1.56×106 M contribution of the bolometrically dominant hot-dust
budget against the MD
⊙
component found at a temperature of TDH = 102 K. Overall, these dust characteristics are
reminiscent of those found in unobscured mm-bright (typically broad-line selected) z ∼ 2
QSOs such as the Cloverleaf (Beelen et al. 2006) or the mm-bright X-ray absorbed broadline QSO J100038+020822 in the COSMOS field (Aravena et al. 2008). However, it should
be noted again that Vd-17871 does not belong to this class of objects but corresponds best
to the mid-IR selected radio-intermediate obscured quasars at z ∼ 2 presented by MartínezSansigre et al. (2009). The inferred total (8 − 1000) µm luminosity of the two components
is 1.48 × 1013 L⊙ to which the cool component contributes ∼ 30 %. From the average
result of our single and double component fits we conclude that the cool dust luminosity
amounts to (4.75 ± 0.75) × 1012 L⊙ which - if powered solely by star formation – suggests
an SFR of (475 ± 75) M⊙ yr−1 . Note that AGN heating of the dust might also occur on
the larger (kpc) scales the cool dust is expected to occupy (e.g. Martínez-Sansigre et al.
2009, and references therein). Therefore, strictly, also the cool dust derived SFR should
be considered an upper limit. Overall, our double gray body model in combination with
the mean obscured quasar SED from Martínez-Sansigre et al. (2009) at rest-frame mid-IR
wavelengths and a normal galaxy template (Bruzual and Charlot 2003; see above) provides
a good fit to the entire SED of Vd-17871.
The radio continuum emission yields further evidence for an AGN in Vd-17871. The total
1.4 GHz flux density of (79 ± 11) µJy beam−1 suggests a 1.4 GHz luminosity7 of (1.2 ± 0.2) ×
1025 W Hz−1 at the CO-redshift of the source which is well below the limit for a Fanaroff
and Riley (1974) class II (FRII) source8 of L1.4 GHz ∼ 5 × 1025 W Hz−1 but nominally at the
edge to be considered a radio-loud object (see Urry and Padovani 1995, for a review on the
classification of AGN).9 This flux density is consistent with the total flux density derived
if the higher resolution (1.5 × 1.4”) VLA-COSMOS image is used. Also the position of the
7
We assume a radio continuum spectrum Fν ∝ ν αrc with αrc = −0.8 (e.g. Condon 1992).
The FRI/FRII break occurs at L0.178 GHz = 2.5 × 1026 W Hz−1 which we scale to a 1.4 GHz luminosity limit
assuming again a radio continuum spectral index of αrc = −0.8.
9
Due to its clearly composite nature this source is, however, likely more similar to the radio-quiet population in
the typical quasar terminology. The bulk of the sources in the obscured quasar sample of Martínez-Sansigre
et al. (2006a) shows the same intermediate radio luminosity as Vd-17871 and a detailed high resolution
radio interferometric follow-up study by Klöckner et al. (2009) suggests that these sources are geometrically
reminiscent of the radio-quiet population.
8
98
6.3. Source properties of Vd-17871
Figure 6.5. – The rest-frame near-to-far-IR spectral energy distribution (SED) of Vd-17871 observed at mid-IR (SPITZER/MIPS), far-IR(Herschel/PACS & SPIRE) as well as mm (MAMBOII & PdBI) wavelengths (black filled circles). A clear peak in the cool dust continuum is
seen around 500 µm (rest-frame ∼ 90 µm). The redshifted templates of the local composite
Seyfert-1 ULIRG Mrk 231 (red; Polletta et al. 2007) and of the prototypical starburst SED
(blue) suggested by Elbaz et al. (2011) are overplotted as scaled to the observed photometry.
The expected template flux densities are depicted as horizontal bars in each case and have
been obtained by convolution of the spectral response of each individual instrument using
appropriate color corrections. While the starburst template poorly fits the global IR photometry if fixed to the 1 mm emission observed, the Mrk 231 model underscores the 160 µm hot
dust emission. The redshifted mean obscured quasar SED of Martínez-Sansigre et al. (2009)
(green) provides a good fit to the observed data without rescaling if we adopt the warmer
of the two alternative gray bodies (TD = 35/47 K, β = 1.6) they suggest to model the cool
dust emission. A single component gray body fit to our (sub-)mm data observed yields similar
parameters (TD = 42 K, β = 1.5; dashed black curve). Our data, however, cannot constrain
the rest-frame mid-IR portion of this model that shows the typical deep silicate absorption
features. Given our few photometric data points a simple double component gray body fit
(TD = 102/42 K, β = 2.0; solid black curve) represents best the hot and cool components of
the dust continuum emission.
radio source is found to be the same at both resolutions while the radio source is nominally
unresolved either way. However, the emission appears slightly extended given that the
higher resolution map reveals a difference in peak and total flux density. We find that the
1.4 GHz peak flux density corresponds to 65 % of the total 1.4 GHz emission (see Table 6.1).
For a point source we should see no difference between peak and total flux emission. This
difference might not be entirely explicable by the effect of bandwidth smearing (chromatic
99
6. Extreme star formation within 1.5 Gyr after the Big Bang: a case study
abberation due to the finite bandwidth) but rather by a central point source embedded in a
diffuser component.10 Consequently, we need to quantify the amount of radio flux that can
be attributed to star formation. Assuming that the local far-IR radio ratio for star forming
systems is not evolving from its local value of q = 2.64 ± 0.26 (e.g. Sargent et al. 2010a,b)
we can estimate an upper limit to the radio emission powered by star formation from its
lower bound. We follow the definition of Kovács et al. (2006),
q = log
LIR [W]
4.52 × 1012 Hz
− log(L1.4 GHz [W Hz−1 ]),
(6.2)
which is best suited given the dust properties of Vd-17871. The IR luminosity inferred
from our single component gray body is 5.5 × 1012 L⊙ and leads to F1.4 GHz . 20 µJy which
is indeed roughly consistent with the difference between total and peak radio continuum
flux density observed, suggesting this more extended radio continuum component to trace
the SFR of Vd-17871. In turn, using the total radio flux observed the q−value is 1.9 (1.7) if
the rest-frame (8 − 1000) µm luminosity is derived from the Mrk 231 template (the single
component gray body). Both results are clearly too low to be consistent with pure star
formation activity. For the sake of completeness we derive the SFR from the total radio
flux density. The corresponding radio luminosity suggests an SFR of ∼ 3800 M⊙ /yr (using
the Bell 2003b calibration) if – unrealistically – all the radio emission were powered by star
formation.
As a caveat to the above interpretation of compact and diffuse radio component we should
once again come back to the geometric situation (see Figure 6.7). Given the significant
spatial offset of the 1.4 GHz peak – coincident only with the warm dust emission as traced,
e.g., at 24 µm – it is plausible that the hot dust and major parts of the radio continuum
emission themselves originate from a spatially distinct component, possibly the southern
UV-source B in Figure 6.7. In this scenario the AGN host would be distinct from the object
harboring the bulk of the molecular gas as well as cool dust and the potentially large amount
of AGN-powered 1.4 GHz emission would have shifted the radio centroid away from the
main star forming source A. However, as outlined above, the Lyman-α line width suggests
source A to be an AGN host. Hence, it appears more likely that both source A and B are
radio continuum emitters and, possibly, both AGN hosts. Deeper mm-continuum and COdata but also higher resolution radio continuum data are required to clarify the geometric
situation and to ultimately rule out AGN ionization lines as a cause of the elevated 160 µm
flux. Additionally, deep optical spectroscopy at the position of source B might shed light on
the existence of an AGN in source B.
6.4. The diversity of extreme starbursts at high redshift
Among the very limited number of z > 4 extreme starbursts in the literature for which
CO data are available, Vd-17871 is not only at the very high redshift but also at the low
luminosity end both with respect to its far-IR as well as its CO emission. It provides the only
example known to-date for substantial dust heating by an AGN in a z > 4 massive starburst.
A criterion to classify a source as a starburst is to compare its specific SFR (SSFR) with the
10
This is also consistent with the results of Klöckner et al. (2009) who find that – on average – the radio
continuum emission of radio-intermediate obscured quasars is core-dominated to a similar level as our
source.
100
6.4. The diversity of extreme starbursts at high redshift
average trend for star forming sources. The SSFR of Vd-17871 shows a clear elevation (a
factor of 3.5-6.2; see Table 6.1) compared to the suggested limit of ∼2.7 Gyr−1 for average
star forming sources at high-z (Karim et al. 2011a) that is observationally supported (Daddi
et al. 2009b; McLure et al. 2011). It is hence valid to call Vd-17871 a massive starburst.
While a major part of the bolometric luminosity emitted by sub-mm bright sources at z ∼ 2
originates in the far-IR as a consequence of dust heated by recently formed stars, typically
30 % is powered by an AGN (e.g. Pope et al. 2008; Meneux et al. 2009) that substantially
contributes at shorter IR wavelengths. Already Coppin et al. (2009) reported that at z > 4
a massive starburst might exhibit such a composite nature but they did not find evidence
for influence of the potential AGN on the thermal dust. Daddi et al. (2009b) serendipitously
detected CO-emission from two z ∼ 4 starburst of which one is supposed to host an AGN
due to its comparatively high radio luminosity. As the example of Vd-17871 now shows it
is possible that the composition of the extreme starburst population at all z > 1 shows a
similar diversity.
More insights in the nature of extreme starbursts at high z compared to the z ∼ 2 SMG
population can be gained from their distribution in the L′CO /LIR plane which is a proxy for
the star formation efficiency. Recent results suggest the existence of two modes of star
formation (Daddi et al. 2010b; Genzel et al. 2010) that separates starbursts from the global
population of normal star forming systems with respect to their star formation efficiency.
Typically, these studies suggest that SMGs and mm-bright quasars are simply "scaled-up
and more gas-rich" versions of local starbursts (also Tacconi et al. 2006). Already well before their actual discovery it has been suggested that z > 4 starbursts should be considered
a "high redshift tail" of the typical SMG population (Dannerbauer et al. 2002, e.g.) instead
of forming a distinct population. However, no attempt has been made so far to find conclusive insights into the distribution of their star formation efficiencies compared to the z ∼ 2
sources.
We therefore compiled all available z > 4 literature sources and a representative census
of 1 < z < 3 SMGs from the literature (Figure 6.6).11 At both redshift ranges we also include
gravitationally lensed sources and consider the lowest rotational CO-transition published
for each source. The rare observational data of low-J CO transitions in high-z starbursts
suggest that the use of higher transitions might under-estimate the molecular gas mass by
up to a factor of two: Based on observations of the CO(2-1) line with the Expanded VLA
in combination with higher-J CO data Carilli et al. (2010); Riechers et al. (2010) find for
the sources GN20 (z = 4.05) and AzTEC-3 (z = 5.3) that the CO-excitation of these extreme
starbursts is only poorly fit by a single thermalized molecular gas component. These data
suggest that about half of the total gas mass is in a diffuse low-excitation phase, not directly
traced by J > 3 CO lines. Initial observational results suggest similar trends for sub-mm
selected sources at lower-z (Ivison et al. 2011). We therefore indicate in Figure 6.6 how the
sources shift if we were to apply this correction.12 In order to compare like with like we
11
The data for z ∼ 2 sources used here are taken from Frayer et al. (1998, 1999); Andreani et al. (2000); Neri
et al. (2003); Greve et al. (2003); Genzel et al. (2003); Downes and Solomon (2003); Sheth et al. (2004); Weiß
et al. (2005); Greve et al. (2005); Kneib et al. (2005); Hainline et al. (2006); Tacconi et al. (2006); MartínezSansigre et al. (2009). Data for z > 4 sources have been presented by Schinnerer et al. (2008); Daddi et al.
(2009b,a); Coppin et al. (2010); Knudsen et al. (2010); Lestrade et al. (2010); Carilli et al. (2010); Riechers
et al. (2010); Cox et al. (2011) as well as in this work.
12
Note, however, that luminous quasars hosts at high z appear to have no extended molecular gas reservoir
but solely a single, highly excited gas component (e.g. Riechers et al. 2006). If an obscured quasar like Vd-
101
6. Extreme star formation within 1.5 Gyr after the Big Bang: a case study
Figure 6.6. – The distribution of z ∼ 2 sub-millimeter galaxies (SMGs) and z > 4 starbursts
in the L′CO /LIR plane. The data have been compiled using a representative census of z ∼ 2
SMGs (filled circles) and all z > 4 extreme starbursts (filled circles with crosses) currently
available in the literature, both including gravitationally lensed objects. The data points are
color coded by their CO-redshift and lensed objects are indicated by an additional black open
circle. Symbol sizes scale with the velocity dispersion measured from the FWHM of the CO
line emission. In this compilation we always used the lowest rotational CO-transition available
for any object. For those sources for which only higher transitions (J > 3) have been observed
we indicate how they would be shifted along the L′CO axis if a low excitation gas phase were
present that contributes 50 % to the total L′CO at the (1-0) transition (gray filled circles;
see text for details). Infrared luminosities have been consistently estimated based on the
(sub-)mm data published for all objects using a typical dust temperature of 35 K. Black solid
lines denote the two sequences for local ULIRGs/distant starbursts/QSOs as well as local disk
galaxies/higher z normal star forming sources suggested by Daddi et al. (2010b). Asides rare
outliers all sources shown roughly follow the starburst sequence. The obscured quasars Vd17871 (this work) and AMS12 (Martínez-Sansigre et al. 2009) are labeled by their names
and also follow this general trend. No clear redshift trends are apparent, suggesting that
starbursts at all z > 1 are similar with respect to their star formation efficiency while the
population is comprised of intrinsically different objects.
furthermore derive IR luminosities for all sources based on the monochromatic (sub-)mm
literature data assuming a single component gray body to be a good model for the cool
dust emission heated by star formation. For this we chose a fixed emissivity β = 1.5 and
typical dust temperature of 35 K, a realistic value for the bulk of high z starbursts (e.g.
17871 mainly differs from these sources in orientation with respect to the observers line of sight a different
molecular gas excitation is not expected.
102
6.4. The diversity of extreme starbursts at high redshift
Kovács et al. 2006). For the obscured quasars Vd-17871 and AMS12 we adopt the far-IR
luminosities reported in this work and by Martínez-Sansigre et al. (2009), respectively.
As apparent from Figure 6.6 both the low- as well as the high-z samples show a wide (1
order of magnitude) spread both in L′CO as well as LIR . While for some sources the gravitational lensing magnification factors are uncertain there is a clear trend that all galaxies
shown follow the starburst sequence suggested by Daddi et al. (2010b). There are rare
outliers that tend to be closer to the "normal" star formation mode with no significant
trend. Most interestingly, the distribution of sources in the L′CO /LIR shows no redshift
trend suggesting the same principles that underlie the star formation process in starburst
environments at all z > 1.
As Riechers et al. (2010) argue the different CO-excitation laws observed in high-z quasars
(one molecular gas phase) compared to the z > 4 starbursts with confirmed two molecular
gas phases might point to different evolutionary stages influencing the molecular gas/ISM
properties. Assuming that extreme starbursts are mostly triggered by (major) mergers (e.g.
Engel et al. 2010) the different states and distribution of the molecular gas could be due
to different merger stages observed, thereby explaining the general intrinsic diversity of
this source population. This diversity might furthermore be enhanced whenever blending
of close pairs of gas-rich13 but not (yet) merging normal star forming sources occurs due to
insufficient spatial resolution in the observations (Hayward et al. 2011a). This would also
explain why some sources are closer to the normal star forming sequence of Daddi et al.
(2010b). In order to investigate if there is a true star formation bimodality blended normal
star forming sources need to be identified among those systems currently classified as starbursts. Initial high resolution studies of CO as well as dust continuum emission at 1 < z < 3
support these arguments (Engel et al. 2010; Bothwell et al. 2010). It is clear that more
high resolution data observations of the molecular gas and dust also in z > 4 starbursts are
needed to clarify the situation and will be feasible soon with the Atacama Large Millimeter
Array.
To summarize, our results – based on global far-IR and CO emission properties – suggest
no clear evidence for z > 4 massive starbursts to form a distinct population from the wellknown z ∼ 2 SMGs. However, a rich diversity of intrinsically different sources likely comprises the entire population of z ≫ 1 starbursts. As we showed in this work, in addition
to pure starbursts and gas-rich luminous QSOs also obscured quasars can be found in this
population even at z > 4. Besides J1000+0234 (Capak et al. 2008; Schinnerer et al. 2008)
and Vd-17871 we found four more dropout sources with weak radio counterparts in the
COSMOS field that qualify as extreme starbursts at z & 4. Comparing their observed
1.4 GHz and 24 µm flux densities to Vd-17871 suggests at least one object to be of a similar
composite nature as this source. For two of them – GISMO-AK03 at z = 4.757 as well as
the z = 3.9 mm-bright source SMA/AzTEC-5 (Scott et al. 2008; Younger et al. 2007) – Keck/DEIMOS observations confirmed their high redshift nature while only recently (additional)
2 mm continuum observations constrained their cool dust properties. For these sources,
however, no CO line are available yet and they will hence be discussed in follow-up work.
13
Average star forming galaxies at high redshifts are expected to contain large molecular gas fractions (Daddi
et al. 2010a; Tacconi et al. 2010).
103
6. Extreme star formation within 1.5 Gyr after the Big Bang: a case study
Table 6.1. Mid-IR-to-millimeter flux densities and derived quantities of Vd-17871
Quantity
Value
S24 µm [µJy]
S100 µm [µJy]
S160 µm [µJy]
S250 µm [µJy]
S350 µm [µJy]
S500 µm [µJy]
S250 GHz [mJy/beam]
S102 GHz [mJy/beam]
S1.4 GHz (Peak) [µJy]
S1.4 GHz (Total) [µJy]
R.A.CO(5−4) (J2000)
Dec.CO(5−4) (J2000)
R.A.102 GHz (J2000)
Dec.102 GHz (J2000)
R.A.1.4 GHz (J2000)
Dec.1.4 GHz (J2000)
LIR [L⊙ ]
108±14
<8
11.4±3.4
6.7±1.5 (±2.7)
9.1±1.7 ±3.4)
11.4±1.8 ±4.8)
2.5±0.5
0.13±0.03
57± 12
79± 11
10:01:27.080
+02:08:55.80
10:01:27.080
+02:08:55.80
10:01:27.061
+02:08:55.32
8 × 1012
1.48 × 1013
LIR [L⊙ ]
LIR [L⊙ ]
−1
SFR [M⊙ yr ]
SSFR [Gyr−1 ]
SSFR [Gyr−1 ]
zCO(5−4)
FWHMCO(5−4) [km s−1 ]
SCO(5−4) [mJy/beam]
ICO(5−4) [Jy km s−1 ]
LCO(5−4) [L⊙ ]
L′CO(5−4) [K km s−1 pc−2 ]
Mgas [M⊙ ]
(4.75 ± 0.75) × 1012
475 ± 75
9.5 ± 1.5
16.8 ± 2.6
4.622 ± 0.001
397 ± 82
1.3±0.2
0.56±0.15
(1.1 ± 0.3) × 108
(1.8 ± 0.4) × 1010
(1.4 ± 0.4) × 1010
Information
∼8σ , from S-COSMOS⋆
upper limit, from PEP‡
∼3σ , from PEP‡
> 2σ , from HerMES∐
> 2σ , from HerMES∐
> 2σ , from HerMES∐
∼8σ , from MAMBO-II
∼4σ , from PdBI off-line channels
>4σ , from VLA-COSMOS†
∼7σ , from VLA-COSMOS†
line peak
line peak
continuum peak
continuum peak
continuum peak
continuum peak
(8-1000) µm luminosity from
scaled Mrk 231 template
(8-1000) µm luminosity from
double component gray body fit
far-IR luminosity (from cool dust)
derived from cool dust emission
derived from total stellar mass in Vd-17871
derived from stellar mass in source A
from Gaussian fitting
from Gaussian fitting
Peak line flux, from Gaussian fitting
Integral under Gaussian fit
from ICO(5−4)
from ICO(5−4)
Using αCO = 0.8
Note. — The 12 CO line luminosity and gas mass of Vd-17871 are derived using the descriptions in Solomon and Vanden Bout (2005) and the findings of Downes and Solomon (1998). The
IR luminosity is computed from different templates and gray body models (see Section 6.3.3 for
details). The cool dust far-IR emission is the mean value of the best-fit single gray body and the
cool component of the double gray body fit. This value is used to constrain the star formation
rate (SFR) in Vd-17871. The far-IR based SFR is computed based on Kennicutt (1998b) converted to a Chabrier (2003) IMF resulting in SFR [M⊙ yr−1 ] ∼ 1000 × LIR [1013 L⊙ ]. Two values
for the specific SFR (SSFR) are stated. The lower value is derived from the total stellar mass
content measured for both rest-frame UV components likely comprising a common astronomical
system (see Section 6.3.2 for details and mass estimates). The higher value is derived from the
stellar mass content of source A which spatially coincides with the bulk of the Lyman-α as well
as the 12 CO emission.
⋆
Schinnerer et al. (2010)
Sanders et al. (2007)
‡ Lutz et al. (2011)
∐ Oliver et al. (in prep.)
†
104
6.4. The diversity of extreme starbursts at high redshift
Dust Continuum
CO(5-4)
5"
32 kpc
Radio Continuum
IRAC-3.6um
CO(5-4)
Dust Continuum
Radio Continuum
A
B
2"
ACS-F814W
13 kpc
UltraVISTA-Ks
Figure 6.7. – Postage stamps for the Vd-17871 system as seen in different bands. All contours
start at 2σ in steps of 1σ . At zCO = 4.622, 1" corresponds to a physical scale of 6.52 kpc.
By convention, all stamps are oriented such that north is to the top and east is to the left.
Top: 20” × 20” region around Vd-17871 as seen in 12 CO(5-4) emission (left) averaged over
291.429 MHz (850 km/s) and 3 mm dust continuum emission (right) averaged over the remaining ∼3.3 GHz line-free bandwidth the Plateau de Bure Interferometer (PdBI) provides.
The images have been CLEANed using the synthesized beams indicated in the lower left. The
cross depicts the phase center (source A as introduced below). Bottom: The left panel shows
a 10” × 10” Hubble Space Telescope/ACS-F814W region around Vd-17871 overlaid with (cool)
dust continuum (blue) and 12 CO(5-4) (red) contours from our PdBI observations. Two restframe UV emission knots are seen (labeled as source A and source B). Within the positional
uncertainties the cool dust and gas emission are spatially coincident with source A that was
targeted in our Keck/DEIMOS observations. A yellow/black cross denotes the position of the
1.4 GHz counterpart, centered halfway between sources A and B. The right panel shows the
same region, this time as seen in the KS -band (from the UltraVISTA survey) overlaid with
Spitzer/IRAC 3.6 µm (purple; covering the Hα line and spatially coincident with source A)
and 1.4 GHz radio continuum contours (yellow). Vd-17871 is marginally detected in the KS band and the absence of additional bright features rules out a nearby foreground object in
our line of sight. The radio emission is spatially offset by ∼ 0.6” from the other emission
sources except Spitzer/MIPS 24 µm (not shown) tracing the warm dust. The 1.4 GHz peak
and warm dust emission are likely powered by an AGN. It is possible that both sources (A and
B) are radio emitters blended into a single source since their angular separation equals the
1.5" resolution of our VLA imaging.
105
6. Extreme star formation within 1.5 Gyr after the Big Bang: a case study
106
7. Summary and outlook
We initially motivated the critical need for direct observational studies of cosmic evolution.
We argued that those need to focus on the luminous matter content of the universe which
is concentrated in galaxies. We thereby outlined how theoretical models and simulations
motivate these observations and why they are, in turn, crucial to constrain them. Within
the broad field of galaxy evolution the process of star formation was introduced as a key
element in studying the evolution of the interplay between dark and luminous matter over
time. In this spirit, the aims of this thesis have been formulated to obtain deeper insights
into the evolution of the global cosmic star formation activity.
Here we summarize the methodological and scientific achievements of this thesis and
discuss ongoing and potential future research directions related to the individual findings.
This Chapter is therefore organized as follows. First we provide essential context information before we recap individual key results and subsequently discuss the related future
prospects.
7.1. A newly developed image stacking routine
The method of image stacking has attracted substantial interest over the last years especially in the extragalactic community. It provides a powerful tool to use imaging data
beyond their sensitivity limits as long as average trends of observables are of interest and
positions of celestial objects are known from ancillary observations.
A goal of this thesis therefore was to design and implement a new image stacking routine
that can be used in a flexible and efficient way with a particular focus on radio continuum
stacking experiments in deep cosmological survey fields. The resulting routine, described
in detail in Chapter 3, has been thoroughly tested at radio wavelengths and provides the
fundament for the major scientific results presented in this thesis. A variety of statistical estimators has thereby been implemented and partially developed (see Appendices A.1
and A.2). Additionally, the measurement of total flux densities from radio interferometric
imaging has been automated and optimized for the processing of large data sets.
Due to the image processing capabilities implemented this newly developed image stacking routine is, however, not restricted to radio continuum wavelengths. Input imaging is
recognized by the routine based on the essential information stored in its fits-header and
astrometric calculations are performed regardless of the nature of the input image. There
are flexible input capabilities also with respect to the positions of objects to be stacked and
overall the processing options are steered externally by the user in a platform-independent
way. The routine can therefore be used in a variety of environments the user prefers and
its fast processing capabilities enable an efficient handling of huge data sets as often required. To summarize, the routine at its current stage has proven its abilities and matches
the requirements initially formulated.
Full automation of the workflow from arbitrary input data to a total flux measurement is,
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however, virtually impossible and perhaps not desirable to achieve. Especially the correct
measurement of fluxes needs to be treated differently for different input imaging and is
probably most exotic and least straight-forward to perform at radio wavelengths as extensively discussed in this thesis. It is furthermore the interplay between angular resolution
and sensitivity of the imaging to be stacked that might lead to blending problems and hence
significant inaccuracies in the flux measurement. While the new routine presented here has
pre-implemented capabilities to identify noise distortions and interloping detections in order to reject input sources further testing at multiple wavelengths is unavoidable. It is
hence an ongoing effort to investigate biases introduced by stacking experiments based
on simulations as well as to explore deblending strategies discussed in the recent literature. In its current implementation the routine has, however, proven efficient and valuable
especially in the context of large stacking simulation efforts.
A variety of scientific problems is currently being approached and a full overview of
current applications of the new image stacking routine at various wavelengths is given in
Section 3.3.4. Many more prospects for future application of this routine exist, including
those that make use of readily available survey data and imaging. Examples with high
relevance for the prospects of this thesis will be highlighted in the next Sections of this
Chapter.
7.2. The roughly stellar mass-independent evolution of the
average (specific) star formation rate
Recent initial observational results in the local universe (Brinchmann et al. 2004) and at
cosmic epochs corresponding to redshifts z . 1 (Noeske et al. 2007b; Elbaz et al. 2007)
revealed a surprisingly tight relation between the total star formation rate (SFR) of normal
star forming galaxies and their stellar mass content. The localized process of star formation
is consequently linked to a global galaxy property, suggesting that star formation histories
of individual galaxies are likely not dominated by stochastic processes such as galaxy mergers (e.g. Noeske et al. 2007b). The exact evolutionary properties of this relation are subject
to ongoing debates and insights based on a variety of SFR tracers are needed. Especially
the measurement of SFRs in a way unaffected from effects of dust are in need in order to
obtain an unbiased and (dust) model-independent view of the mass-dependent SFR evolution.
7.2.1. Results presented in this thesis
This motivated an extensive radio-stacking study presented in this thesis (see Chapter 4,
Karim et al. 2011a as well as Karim et al. 2011b, for a summary). In order to cover a
substantial baseline in cosmic time a rich galaxy sample was needed that remains representative at comparatively low stellar masses out to high redshift. The study is therefore
based on the panchromatic datasets from the 2 deg2 cosmic evolution survey (COSMOS;
see Scoville et al. 2007d, for an overview) that have provided very accurate photometric
redshifts (photo-z ’s) and stellar masses for a large mass-selected sample of galaxies (Ilbert
et al. 2010). This Spitzer/IRAC (mAB (3.6 µm) ≤ 23.9) selected sample of ∼114,000 galaxies with FUV to mid-IR as well as X-ray ancillary data has been used in combination with
1.5" and thus high angular resolution Very Large Array (VLA) radio continuum data in the
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7.2. The mass-uniform evolution of the average star formation rate
COSMOS field (Schinnerer et al. 2007, 2010) to measure the evolution of the average SFR
as a function of stellar mass out to z ∼ 3. SFRs derived from radio continuum emission
require only a simple K-correction and no correction for dust extinction, hence matching
perfectly the needs formulated above. The high resolution and low detection rate of the
VLA-imaging furthermore minimizes the risk of source confusion that would bias the stacking experiment. This is a major advantage compared to far-infrared stacking experiments
that also provide a dust-unbiased view.
We have applied various criteria to minimize contaminating radio flux from potential active galactic nuclei and have used the stellar population synthesis template-based, intrinsic
rest-frame (NUV − r+ )temp color from fits to the observed far-UV-mid-IR spectral energy
distributions (Ilbert et al. 2010) in order to separate star forming sources from quiescent
systems. We have also applied a newly developed scheme (see Appendix A.3) to evaluate
the statistical stellar mass-representativeness of the sub-samples resulting from binning
the data in stellar mass and redshift.
From the stacked median radio continuum flux densities obtained for each sub-sample
we find:
• The evolution of the average (S)SFR of stellar mass selected galaxies is approximately
mass-independent at least out to z ∼ 1.5 where the depth of our data allows the most
robust conclusions. A power-law relation between (S)SFR and mass represents well
the data at the high mass end.
• The (S)SFR of star forming sources at z < 3 also evolves basically independent of
mass while a power-law dependence of (S)SFR and mass generally extends over all
masses probed. Higher mass galaxies hence have lower SSFRs, regardless if quiescent galaxies are included in the analysis or not.
• There is tentative evidence for an upper bound to the average SSFR preventing a
further growth of the SSFR with z , starting at the low-mass end at z ∼ 1.5 − 2.
A major result of this thesis therefore is that we observe no differential, more rapid
evolution of high mass galaxies with respect to their average star formation activity as
often claimed before and proposed as one flavor of the so-called ‘downsizing’ paradigm.
The latter of the points listed above is supported by earlier observations at even higher
redshifts compared to our work (Stark et al. 2009; González et al. 2010). As an explanation
for this behavior we proposed that this upper limit to the average SSFR might represent an
effective gas accretion threshold. This is because the limit we find equals about the inverse
of a dynamical timescale of typical local but also higher z disk galaxies (e.g. Daddi et al.
2010b). While their dynamical and free-fall times are approximately equal in commonly accepted models of star formation (e.g. Krumholz et al. 2009), normal galaxies are assumed to
accrete their gas from their surroundings and to process it into stars at a constant efficiency
(e.g. Daddi et al. 2010a). Our proposed scenario has been appreciated and supported in a
recent study of the highest redshift normal star forming galaxies in the Hubble Ultra Deep
Field observed to-date that confirm the limiting value we find at lower z (McLure et al.
2011).
The rapidness of the SSFR-decline with cosmic time we observe constitutes a challenge
for semi-analytical models (Guo and White 2008). Our unprecedented precise measurement
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7. Summary and outlook
of SFRs over time is therefore used to constrain the next generation models (Somerville et
al. in prep.).
Finally, the results we present are consistent with recent far-IR based measurements that
draw on substantially smaller samples and therefore, typically, do not yield a consistent
view of the evolution of the average mass-dependent SFR over a broad redshift range from
a single technique.
Figure 7.1. – Panchromatic 5σ sensitivities of the COSMOS survey (blue) compared to other
deep fields (other colors). The recently released deep near-IR data from the UltraVISTA
survey in the COSMOS field (McCracken et al. in prep.) are indicated (blue dotted curve).
Image courtesy of Peter Capak (Caltech).
7.2.2. Prospects for ongoing and future research
Clearly not all questions have been answered in our study. While we showed that stellar
mass is the determining factor for the average SFR other parameters have not yet been
explored based on our approach and the existing data. Especially environmental effects
are typically suggested to be of second-highest importance (e.g. Peng et al. 2010; Peng
et al. 2011). Studying the evolution of the (S)SFR-sequence with respect to the additional
environmental parameter is already feasible with the data in hand.
Extensive environmental information from different diagnostics out to z ∼ 1 exist in the
COSMOS field. In particular galaxy group catalogs based on spectroscopic redshifts and
optical selection (Knobel et al. 2009) as well as X-ray selection (Finoguenov et al. in prep.)
can be readily used for a radio stacking analysis of the mass-dependent SFR evolution
in different environments. The accurate (spectroscopic) measurement of the density field
by Kovač et al. (2010) offers yet an alternative approach for such a radio-stacking based
study. Given these existing possibilities (including the well-tested image stacking routine)
it should soon be undertaken.
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7.2. The mass-uniform evolution of the average star formation rate
Since the radio-view on the SSFR-sequence is dust-unbiased the radio data and stacks
can be used to shed light on the stellar-mass dependence of dust correction factors that
need to be applied at shorter wavelengths. This project is already possible with the current
data and has been recently started (see below).
Further insights in the context of our study require deeper radio continuum data as discussed in the following.
EVLA-COSMOS: new insights from deep radio continuum observations at 3 GHz
Recently new 3 GHz radio continuum observations with the Expanded VLA (EVLA; Perley et al. 2011) of the entire COSMOS area have been proposed (principal investigator V.
Smolčić, co-investigator A. Karim). The net (total) observing time of 333 (416) hours is
supposed to be split in such a way that 90 % of the time the most extended A configuration
will be used while 10 % are observed with the C array using all 27 antennas. The resulting sensitivity would be 2 µJy/beam (1σ ) while the observations would reach sub-arcsecond
resolution (∼ 0.65”). The observing strategy is such that two campaigns would be carried
out twice per month over the full area and the course of four months. This will allow for
variability measurements of bright radio sources in the field.
A main science driver for this outstanding observing program is the study of star formation over time. Based on the results presented in this thesis the sensitivity proposed will
be such that the star forming main sequence can be probed out to z ∼ 1.2 via ∼ 3, 000
direct (> 5σ ) radio detections of star forming galaxies at least down to the characteristic
mass for star formation. Detecting these objects means that the intrinsic dispersion of the
(S)SFR sequence can be studied out to this redshift in full detail which is out of reach for a
stacking-based study. While it is usually claimed that the relation between stellar mass and
SFR is tight (intrinsic scatter of ∼ 0.3 dex) at all cosmic epochs (e.g. Elbaz et al. 2007) so
far no conclusive study over the full stellar mass-range of interest has been conducted outside the local universe to investigate the nature of the scatter: Is it intrinsic, pointing to a
physical cause or just a mere effect of too large uncertainties? Is star formation proceeding
mainly secular or are major mergers a significant source of contribution?
The new data will allow us to study the star formation–stellar mass relation not only as
a function of redshift, but also of environment to unprecedentedly low masses as well as
galaxy type (morphology, color) to identify if these other parameters do indeed play a role
as well. It has been suggested that the lowest scatter in the star forming main sequence
can be achieved if rigorous morphological selection (of pure disks) is applied (Salmi et
al. in prep.). Hence, direct detections are critical for any follow-up project that explores
morphological information as an additional parameter.
Only recently data from the deep near-infrared UltraVISTA survey (principal investigators Dunlop, Franx, Le Fèvre and Fynbo) in the COSMOS field have been released (see
Figure 7.1; McCracken et al. in prep.). It is an ongoing effort to construct source catalogs
from those data and to incorporate them in the global photometric catalogs from COSMOS.
These deep near-IR imaging will probe significantly lower stellar masses at high redshift
than reached with the current stacking study, enabling at the same time vastly improved
options for studying the influence of environment on the average star formation rate of
galaxies. Clearly, the new EVLA data are also critical to constrain the potential upper limit
to the average SSFR proposed in this thesis. Altogether this will substantially improve our
understanding of the stellar mass build-up in the universe.
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7. Summary and outlook
The additional band provided by the 3 GHz observations will furthermore enable detailed
studies of the evolution of the synchrotron spectral index for star forming sources when
combined with the current 1.4 GHz data in stacking experiments as well as using direct
detection. We pointed out in this thesis that the spectral index is important for estimating
radio-based SFRs since K-corrections in the radio continuum depend on this quantity. A
reliable determination of its non-evolution is still lacking and critically needed to accurately
confirm the validity of our results.
In the following we will highlight more applications for these new radio continuum data
for future projects related to the scientific projects presented in this thesis.
The mass-dependence of dust-extinction corrections As discussed in this thesis,
shorter wavelength SFR indicators than radio emission suffer from uncertain dust extinction corrections. We have also shown that our results are in good agreement with those
studies that are based on these alternative indicators and that apply strongly stellar massdependent dust corrections (e.g. Gilbank et al. 2010b). It is typically found that the extinction is substantially higher at higher masses.
Particularly Pannella et al. (2009) showed – based on a radio stacking approach – that
for BzK-selected galaxies at z ∼ 2 average SFRs derived from ultraviolet data need to be
corrected in a strongly mass-dependent fashion in order to achieve an agreement with the
radio-derived ones. With the COSMOS data and our stacking routine in hand this finding
can be tested at different redshifts in order to reveal potential evolutionary trends.
However, also direct radio detections are valuable to assess mass-dependent dust corrections based on different diagnostics. Only recently the extensive zCOSMOS (Lilly et al.
2007) spectroscopic sample of 10,000 galaxies with emission line information became available to the COSMOS team. We can use these data to derive SFRs from the Hα (z < 0.45) and
[OII]λ3727 (0.75 < z < 1.5) emission lines (e.g. Moustakas et al. 2006). Additionally, the Hβ
emission line can be used at intermediate redshifts. These data can be directly compared
to the radio-based SFRs for individual objects. In order to prepare this project the emission
line SFRs have already been derived after cleaning the sample from unreliable data using
various quality criteria. The resulting catalog has been cross-matched with the deep VLACOSMOS radio catalog as well as with the multi-wavelength photometric sample including
the stellar mass information from the IRAC-selected sample used in this thesis. All following work is currently in progress. The upcoming steps are to force the emission-line derived
SFRs to agree with the radio-based ones in order to obtain the mean dust-corrections as a
function of stellar mass. Based on this full sample the mean extinction can also be derived
from the Hα/Hβ decrement yielding an independent estimate. In total this enables a study
of the evolution of dust extinction corrections.
It is clear that any such study of dust correction factors will profit from the deep proposed 3 GHz radio continuum data which will yield a much more extensive sample of direct
detections but also enables vastly improved options for a stacking approach.
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7.3. The mass-resolved cosmic star formation history
7.3. The cosmic star formation history over ∼ 9 Gyr and a
constant characteristic mass for star forming galaxies
The cosmic star formation history (CSFH), i.e. a measure of the global cosmic star formation activity over time in the comoving frame, is of central interest in the research field of
galaxy evolution. A number of literature results suggest a rapid (roughly one order of magnitude) decline of the total comoving star formation rate density (SFRD) since a redshift
of z ∼ 1. The CSFH therefore is considered a key manifestation of the impact of cosmic
evolution on luminous matter and it is critical to reveal the drivers behind the global trends
observed.
7.3.1. Results presented in this thesis
Our measurement of the average star formation rates (SFRs) of star forming galaxies down
to a low limiting stellar mass forms the basis of an accurate constraint for the comoving
evolution of the global cosmic star formation activity and yields valuable as well as new insights into the relative contribution of differently massive galaxies as a function of time (see
Chapter 5, Karim et al. 2011a as well as Karim et al. 2011b, for a summary). The key finding is that the stellar mass distribution function of the SFRD at any epoch is well described
by a Schechter function that reveals a constant characteristic mass of star formation since
z ∼ 3. Its integral finally constrains the total SFRD at any redshift probed.
The road to our findings was paved by a combination of our measurement and independent results by Ilbert et al. (2010) on the evolution of the stellar mass distribution (stellar
mass function) of star forming galaxies. While star forming sources exhibit this remarkably shape-invariant SSFR-mass relation throughout cosmic time in our study (see above),
it is worth noting that their stellar mass functions are found to show a similar constancy
of their Schechter profile (e.g. Ilbert et al. 2010). As both phenomena involve a power-law
in stellar mass, the product of the SSFR-mass relation and the mass function at a given
cosmic epoch also yields a Schechter function for the mass distribution of the comoving
SFR density (SFRD).
The potential upper SSFR-limit discussed above might alter the low-mass end shapes significantly only at the highest redshifts, the galaxy mass at which the function peaks at any
epoch is M∗ ∼ 1010.6 M⊙ , regardless of the assumption of an SSFR-limit. Galaxies (almost)
as massive as our Milky Way have hence always been the main sites of star formation.
The existence of this characteristic mass of star forming galaxies challenges a ‘downsizing’
paradigm in which the dominant contributors to the CSFH have been massive sources in
the cosmic past and low-mass galaxies at present times. It does, however, not rule out that
low-mass sources gain more relative importance over time.
Literature results from alternative SFR diagnostics at different wavelengths confirm our
results while they are mostly restricted to a phenomenological discussion and do not attempt to reveal the underlying analytical functional form. It is also worth noting that no
other study to-date constrains the trends out to such high redshifts.
The sum of our direct radio stacking-based measurements of the SFRD for individual
mass bins yields lower limits to the total SFRD at any redshift and hence lower constraints
to the global CSFH. At a given redshift the Schechter SFRD function enables us to obtain
the remainder of the total SFRD, integrated below our observational mass limits. For this
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7. Summary and outlook
integration we assume the upper bound to the average SSFR motivated above.
Our approach enables a detailed disentangling of the influence of mass and time on the
CSFH and therefore indirectly sheds light on its internal drivers as summarized in the
following. Since z ∼ 1 the stellar mass density of star forming galaxies is approximately
constant (e.g. Ilbert et al. 2010) and also the relative fractions of objects at different masses
within this population are conserved due to the shape-invariance of their mass function. In
this redshift range the CSFH is therefore entirely controlled by the mass-uniform evolution
of the average SFR. Given a constant star formation efficiency, a strong and global decline
in the mass density of molecular gas thus entirely explains the observed decrease of the
integrated SFRD with cosmic time. Towards earlier epochs it is predominantly the – again
mass-uniform – decrease in star forming stellar mass density that leads to a shallower
evolutionary behavior. The CSFH since z ∼ 3 is hence well described by a broken powerlaw.
Among the existing and constantly growing number of attempts to constrain the CSFH
comparatively few studies use radio continuum emission and its advantages as an SFR
tracer. It is thereby worth noting that the agreement between our study and recent farinfrared based measurements is striking, underlining the reliability of radio-based SFRs
out to high redshifts. Since our results are outstanding in that they constitute the to-date
most extensive and hence statistically most robust study of the CSFH, they are appreciated
as such in recent theoretical studies (in particular Leitner 2011) that provide analytical
estimates of average star formation histories and evolutionary paths of galaxies.
7.3.2. Prospects for ongoing and future research
Our study – as well as any other measurement of the CSFH – relies on extrapolations to
the faint (or low mass) end of the galaxy population. This holds true even at comparatively
low redshifts (z < 1). The depth of the panchromatic COSMOS data especially at near
and mid-infrared wavelengths allowed us to reduce the importance of extrapolations and
opened a new road to constrain the low mass end. Following this road further, even deeper
near-infrared data are needed to constrain the stellar mass function at its low end but also
to reveal the positions of a representative sample of low mass galaxies in order to constrain
their SFR, e.g., from a stacking experiment.
Deeper CSFH studies using COSMOS data are in reach using the upcoming recently
released COSMOS UltraVISTA data. Follow-up studies are certainly not restricted to the
COSMOS field but alternative surveys reaching a comparable depth in the selection band
typically have substantially less areal coverage and provide hence smaller galaxy samples
which leads to significantly worse statistics, in particular in the context of a stacking experiment. The new near-IR data will allow one to constrain the stellar mass functions to higher
accuracy and to higher redshifts. The new deep 3 GHz radio continuum observations that
have been proposed (see above) in combination with the deep near-IR data will allow us to
probe the results presented in this thesis based on direct detections, extend the findings to
lower masses via stacking and reach higher redshift limits.
While deeper data in the galaxy sample selection band assure lower limiting masses at
all redshifts, low mass extrapolations will, clearly, remain more prominent at high-z . The
importance of deeper near-infrared data beyond z ∼ 3 lies in the improvement of photometric redshifts in order to reliably select clean high redshift samples. Near-IR medium band
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7.4. Extreme starbursts < 1.5 Gyr after the Big Bang
filters provide another valuable extension of the COSMOS data sets as the study of Bezanson et al. (2011) shows. These data from the NEWFIRM survey will hence improve the
photometric redshift accuracy while only a part of the COSMOS field is covered by these
observations.
Constraining the high-mass part of the high redshift SFRD is a valuable and necessary
exercise in its own right. The results presented in this thesis suggest that the peak of
the CSFH is not yet reached at z ∼ 3 and it hence remains a puzzle if the SFRD indeed
abruptly drops beyond this redshift (a widely accepted scenario; e.g. Bouwens et al. 2009,
2011b), if it keeps increasing as suggested by hydrodynamic simulations (Springel and
Hernquist 2003) or reaches an extended plateau. It is worth noting in this context that
already the current SFRD measurements at z & 1.6 lead to an overgrow in stellar mass if
compared to the total stellar mass density measured at those epochs (Leitner 2011) which
may point to the need for variations of the initial mass function of stars (e.g. Wilkins et al.
2008). Robust dust-unbiased SFRD-limits at z > 3, e.g. from deep radio continuum data,
are critical, especially to challenge the low dust corrections to UV-based high-z SFRDs
currently proposed (e.g. Bouwens et al. 2009, 2011b).
Our result of a constant characteristic stellar mass finally poses the questions whether
this corresponds to a constant characteristic dark matter halo mass. This can be expected
if the SSFR-sequence originates from the net dark matter halo gas accretion rate which
is proportional to the halo mass (Dutton et al. 2010). A telling quantity to compare to
the SFRD function we discussed in this thesis is the multiplicity function of star formation
which is a dark matter halo mass distribution function of the halo mass normalized star
formation rate (Springel and Hernquist 2003). Hydrodynamic simulations (Springel and
Hernquist 2003) predict the peak of this function to downsize, unlike the peak of our SFRD
function. The same simulations, however, also disagree with the observed CSFH because of
a predicted mild evolution at low-z . There is hence a clear potential for new hydrodynamic
simulations to challenge the current results.
7.4. Extreme starbursts < 1.5 Gyr after the Big Bang
There is growing evidence that massive elliptical galaxies with little ongoing star formation
activity exist already at redshifts as high as z ∼ 3 (e.g. Kriek et al. 2006, 2008a; Williams
et al. 2009; Marchesini et al. 2010). Direct observations of these oldest ‘red and dead’
systems reveal optical colors that suggest those galaxies to be in a post-starburst phase
with ages of < 1 Gyr (e.g. Kriek et al. 2008b).
A progenitor population of massive, probably major merger-driven starbursts might account for this early red sequence. If so, the constituents of this starburst population should
resemble the properties of the known population of SMGs (e.g. Blain et al. 2002, for a review), sources first identified at (sub-)millimeter wavelengths that mostly reside at z ∼ 2
(e.g. Chapman et al. 2005). Those sources typically show large molecular gas fractions with
high central densities (e.g. Tacconi et al. 2006, 2008) and are predominantly mergers (e.g.
Engel et al. 2010) with extreme SFRs of several hundreds of solar masses per year. These
are the ingredients needed to build up the massive quiescent galaxies at even earlier times.
A generally higher importance of merger driven starburst activity at redshifts of z >
4 has been postulated (Khochfar and Silk 2010) in order to theoretically reproduce the
observed trends of a constant SSFR at z ≫ 1.5 as suggested in this thesis and also by direct
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7. Summary and outlook
observations out to z ∼ 7 (e.g. Stark et al. 2009; González et al. 2010; McLure et al. 2011).
While such starbursts at z > 4 have long sought after (e.g. Dannerbauer et al. 2002)
they could only been observationally detected around the start of this PhD project (Capak
et al. 2008; Schinnerer et al. 2008). Only rare examples of these sources exist to-date and
many questions regarding their nature and their relation to the z ∼ 2 SMGs remain open.
These sources provide critical constraints on cosmological models (e.g. Baugh et al. 2005)
and could be the signposts of the early galaxy overdensities expected in a hierarchically
growing universe, as a first observational example demonstrates (Capak et al. 2011).
7.4.1. Results presented in this thesis
Following the road of pre-selecting high redshift star forming systems at optical wavelengths via the broad-band dropout technique and the subsequent search for radio continuum counterparts we were able to uncover seven candidate sources. For this a newly
developed routine to find weak radio counterparts in an efficient and reliable way was used.
A case study of one object (Vd-17871) is presented in this thesis. Its high redshift nature
had been confirmed in optical spectroscopic observations. It was furthermore interferometrically detected in its 1.2 mm and 3 mm continuum as well as 12 CO (CO in the following)
line emission in observations carried out during this thesis work. Together with the extensive COSMOS ancillary data, including the only recently released Herschel/PACS and
SPIRE catalogs, this source could be studied in detail (see Chapter 6). As a key result we
showed that it is not only a massive and gas-rich star forming object but that it also hosts
a powerful and dust-obscured active galactic nucleus (AGN). Due to its hidden nature this
AGN could only be revealed by a detailed analysis of the dust and radio continuum emission
in combination with Lyman-α diagnostics. This source is the most distant obscured AGN
discovered to-date and demonstrates the diversity of the high-z starburst population. Interestingly, the better studied population of z ∼ 2 SMGs is known to be as diverse. Our source
as well as the only nine remaining z > 4 starbursts for which CO-data is available in the
recent literature appear furthermore indistinguishable from the z ∼ 2 SMGs with respect
to their far-infrared to CO-line luminosity ratio, commonly interpreted as a star formation
efficiency indicator. In short, massive starbursts appear homogeneous in their global star
forming nature at all z ≫ 1 while no clear hints exist that the highest redshift objects form
a separate population. The intrinsic diversity of this population might, however, point to an
evolutionary merger sequence. As the timescales between the different merger stages is
expected to be comparatively short, this scenario does not give rise to clear redshift trends.
As a result, the state and distribution of the molecular gas in the individual members of the
high-z starburst population might, however, be very different as initial literature results
suggest (e.g. Carilli et al. 2010; Riechers et al. 2010).
7.4.2. Prospects for ongoing and future research
The aim of this ongoing project is to assemble a comprehensive sample of z > 4 starbursts
over a contiguous area. Such a sample is needed for a robust observational number density estimate to compare with the predictions of cosmological structure formation models.
Large progress has been made during this thesis in consistently selecting these sources and
to start the observational follow-up programs needed to confirm their starburst nature. Ob-
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7.4. Extreme starbursts < 1.5 Gyr after the Big Bang
servations at these faint levels have been challenging so far even given the comparatively
high infrared (IR) luminosities of these sources.
In order to entirely characterize a single source even larger efforts are necessary than
those presented in the pilot study of the source in this thesis. As the example of Vd-17871
shows higher spatial resolution is critical to disentangle the individual contributions of the
two optical sources that are most likely associated with this astronomical system. This
holds true for radio continuum as well as for the far-IR and CO line emission data.
Existing and upcoming instruments such as the Atacama Large Millimeter Array (ALMA),
the EVLA but also the next generation bolometer array camera GISMO (Goddard-IRAM Superconducting 2-Millimeter Observer, principal investigator Johannes Staguhn) – currently
installed at the IRAM 30 m telescope – will substantially boost our efforts. Detailed observing plans and strategies for these instruments have been worked out already.
More extreme starbursts at z > 4 in the COSMOS field Our radio counterpart search
to dropout sources revealed seven candidates. Detection of Lyman-α emission in ongoing
spectroscopic follow-up observations of five sources revealed three of them to be at z > 3.9.
The 1.1 mm continuum – tracing the cold dust emission near its peak – of the least redshifted source (AzTEC-5) was previously detected in the combined JCMT/AzTEC (Wilson
et al. 2008b) and SMA (Ho et al. 2004) survey of the COSMOS field (Scott et al. 2008;
Younger et al. 2007). The other two spectroscopically confirmed sources were detected in
subsequent single dish runs at 1.2 mm or 2 mm with the MAMBO-II (Kreysa et al. 1998)
respectively GISMO (Staguhn et al. 2008) bolometer arrays installed at the IRAM 30 m
telescope. These cold dust continuum detections thus confirmed the massive star forming
nature of all sources and thereby the successful selection strategy. The spectroscopically
confirmed sources Vd-17871 (presented in this thesis) and AK03 as well as the remaining
candidates AK05 and AK06 are shown in Figure 7.2. AK03 is particularly interesting due
to its apparent photometric and geometric similarity to Vd-17871. It also shows multiple
emission components at rest-frame ultraviolet wavelengths, significant emission at 24 µm
and radio continuum emission that appears too high to be powered solely by star formation. This is suggestive that AK03 might also harbor an obscured AGN. With a recent 2 mm
detection of 0.8 mJy (3σ ) it is comparatively faint at mm wavelengths, yet another similarity
to Vd-17871. We have seen, however, that observed far-IR data are critical to constrain the
hot dust emission in such sources. AK03 was not detected in the Herschel/PACS observations of the COSMOS field (Lutz et al. 2011). Deeper follow-up observations with the same
instrument at 100 µm and 160 µm have been proposed recently (principal investigator P.
Capak, co-investigator A. Karim). This explains why only the source with sufficient data
coverage (Vd-17871) has been discussed in the case study presented in this thesis.
Clearly, the success rate of our selection strategy does not reach 100 %. Two dropout
sources with weak radio continuum counterparts do not belong to the high-z massive
starburst population. They are, however, interesting in their own right. The source Vd9167 is suggested to be a high redshift massive quiescent object probably hosting an AGN
(Mobasher et al. in prep.). It was not detected in mm-bolometer observations carried out
during this thesis and not at any other observed wavelengths longer than 24 µm. Another
source, AK04, is detected at a 3σ level in the LABOCA (Siringo et al. 2009) survey of the
central square degree of the COSMOS field (Albrecht et al. in prep.). However, optical
spectroscopy revealed that it is a low-z interloper. It therefore seems to be an exceptionally
117
7. Summary and outlook
cold source. The true nature of both sources remains to be clarified.
Other millimeter-bright sources at z > 4 are the highest redshift known massive starburst AzTEC-3 (Riechers et al. 2010; Capak et al. 2011) and the brightest source in the
JCMT/AzTEC survey of the COSMOS field, AzTEC-1 (Smolčić et al. 2011). AzTEC-3 at
z = 5.3 could not be found in our automatic counterpart association because of its nondetection in the VLA-COSMOS survey. Deeper radio data such as those that would be obtained in the deep EVLA 3 GHz observations proposed (see above) are hence needed to find
much higher redshifted sources based on our approach. AzTEC-1 in turn is firmly detected
at radio wavelengths and formally also qualifies as a dropout source. Its nature, however,
remains unclear as its largely featureless optical spectrum complicates a robust redshift
determination. No CO line emission could be detected in interferometric observations at
millimeter wavelengths with the receivers tuned to the purported redshift of z = 4.64. Another high-redshift candidate is the source CARMA-1 (Smolčić et al. in prep.) for which
high resolution mm-continuum data but currently only photometric evidence for its high
redshift nature exists. A blind redshift determination based on multiple CO transitions (following the prescriptions of Weiß et al. 2009a) and using the IRAM 30 m telescope awaits
scheduling (principal investigator V. Smolčić, co-investigator A. Karim).
Confronting observations with cosmological models Our combined dropout and radio continuum selection technique provides a well-defined and homogeneous selection function. This is an ideal prerequisite for tests against predictions from semi-analytical cosmological models. These include the evaluation of source properties based on existing models
(van Kampen; private communication) as well as robust number count comparison. Also
model comparisons with respect to the relative importance of extreme versus average star
formation at high redshifts are in reach with a comprehensive, observed z > 4 starburst
sample in hand. This requires also a representative but clean sample of normal star forming galaxies at these redshifts. Recent advances on the photometric side, in particular deep
Subaru z + band as well as UltraVISTA near-IR data, in combination with improved V-band
dropout criteria (Capak et al. in prep.) will result in an extensive sample with a low level of
contamination from z ∼ 1 interlopers. These data plus the ongoing spectroscopic efforts are
also valuable to reveal whether our other extreme starbursts are embedded in proto-cluster
structures. Using photometric redshift information first hints exist that the spectroscopically confirmed sources indeed reside in overdensities of dropout sources (Capak et al. in
prep.). A precise observational determination of the abundance of such overdense regions
provides critical constraints to our understanding of cosmic structure formation.
It has been debated (Baugh et al. 2005) that current models can only reproduce the
(sub-)mm source number counts if a top-heavy initial mass function (IMF) for starbursts is
assumed with recent theoretical arguments against this scenario (Hayward et al. 2011b).
Dwek et al. (2011), however, recently yielded observational support for a top-heavy IMF
for an extreme starburst at z > 4 and Papadopoulos et al. (2011) provided theoretical
arguments for a top-heavy IMF to be generally needed in the densest star forming regions.
Coppin et al. (2009) point out that current model predictions (e.g. Baugh et al. 2005) would
underscore the number density particularly of the z > 4 starbursts by an order of magnitude
if all massive quiescent galaxies at z ≫ 2 had undergone a burst. The current observed
number count of the extreme starbursts at z > 4, in particular in the COSMOS field, is
already in excess of the model predictions.
118
7.4. Extreme starbursts < 1.5 Gyr after the Big Bang
Vd−17871 J1000+0234
ACS+VLA
V
r+
z+
3.6um
24um
V
r+
z+
3.6um
24um
z=4.542
z=4.625
AK06
AK05
AK03
z=4.757
ACS+VLA
Figure 7.2. – Confirmed, consistently optically selected massive starbursts at z > 4 with
weak radio continuum counterparts as well as candidates thereof. The postage stamp series shows (from left to right) VLA 1.4 GHz contours (starting at 2σ in steps of 1σ ) overlaid
on the HST/ACS i-band images centered at the position of the V -band dropout, the Subaru V ,
r+ and z + bands as well as the Spitzer/IRAC 3.6 µm and MIPS 24 µm channels. All postage
stamps are 10” × 10” in size. Sources with confirmed redshifts from Lyman-α spectroscopy using the DEIMOS spectrograph (Capak et al. in prep.) are labeled with the redshift value (red).
The top row shows the first ever discovered z > 4 starburst, J1000+0234, (Capak et al. 2008;
Schinnerer et al. 2008) which was found only shortly before the start of this thesis project.
All other sources (including Vd-17871; see Chapter 6) have been found during this thesis
work using a newly written radio continuum counterpart finder (see Section 3.3.3). Follow-up
observations using the MAMBO-II (1.2 mm) and GISMO (2 mm) bolometer cameras at the
IRAM 30m telescope have been proposed and scheduled during this thesis work. The candidate sources AK05 and AK06 await confirmation from optical spectroscopy as well as from
millimeter observations. Not shown is the mm-bright source AzTEC-5 (Younger et al. 2007;
Scott et al. 2008) at a Lyman-α based redshift of z = 3.9 which has been selected first from
(high resolution) sub-mm observations. Formally, it also qualifies as (B-band) dropout with
weak radio counterpart so that it forms part of our full sample of z & 4 massive starbursts.
119
7. Summary and outlook
To summarize, a top-heavy IMF might be theoretically as well as observationally required
for extreme starbursts while, independently, models struggle to reproduce the observed
number counts of massive starbursts at z > 4. Both issues require further efforts from the
observers’ as well as the modelers’ side and demand a robust observed sample of these
sources.
Follow-up observations at millimeter and radio wavelengths More observations are
needed to comprehensively study massive starbursts at z > 4. First of all – based on
dust continuum observations at millimeter wavelengths – it needs to be confirmed that the
remaining sources show the purported elevated star formation activity. Ideally, high resolution interferometric mm-continuum data would be used to achieve accurate positioning of
the cool dust continuum but also morphological information on the dust distribution. These
would most vitally be combined with high resolution CO line data that additionally needs to
be obtained in order to clarify whether gas emission and dust continuum really arise from
the same location or even object since this must not be the case as seen in local ULIRGs
(Wilson et al. 2008a). Given the evidence for multiple sources in a system like Vd-17871
such information is essential. Finally we need to constrain the size of the dust emitting,
i.e. star forming, region which, due to the overall similarity of our sources to z ∼ 2 SMGs,
is expected to be fairly compact. This allows for estimates of the star formation surface
density and will hence shed light on the star formation law in these sources.
Detection of the typically strong (e.g. Stacey et al. 2010) 158 µm [CII] fine-structure line
– which is known to be an important coolant for the neutral gas – can be obtained in parallel
to high resolution dust continuum observations. Despite hints for a [CII] emission deficit
in local IR luminous sources (e.g. Graciá-Carpio et al. 2011), there is evidence that the
[CII] line emission is a more reliable tracer for the SFR in their high redshift cousins (e.g.
Stacey et al. 2010). Given our consistently selected sample, the [CII] line observations are
critical to finally settle whether the ratio of atomic gas to dust emission indeed follows a
tight relation for massive but purely star forming sources. In this case, the [CII] line will
provide an independent way to estimate the star formation density in our highest redshift
targets while its profile compared to the one of the CO line will reveal how closely the star
formation activity follows the molecular gas distribution.
Both with respect to angular resolution as well sensitivity all this is already efficiently
doable with ALMA in its current state of construction. Less than two hours of on-source
integration time would be needed to detect CO line emission in any of our sources while a
statistical detection of the [CII] line and its underlying continuum would require less than
ten minutes.
Multiple CO transitions, especially at lower J levels are needed in order to shed light on
the excitation and state of the molecular gas emission. These data are valuable as (rare)
evidence exists at z > 4 that massive but purely star forming sources show substantially
different gas distribution and excitation properties compared to those extreme starbursts
hosting a powerful unobscured QSO (e.g. Riechers et al. 2010). A more diffuse lowerexcitation gas component in addition to a higher excited gas phase might be a feature
only pure starbursts posses while denser, highly excited gas appears to characterize the
unobscured QSOs (e.g. Riechers et al. 2006). Observations of the corresponding emission
lines for our sources are feasible with the EVLA but – due to the faint line fluxes expected
– still challenging.
120
7.4. Extreme starbursts < 1.5 Gyr after the Big Bang
Figure 7.3. – Current and future (sub-)mm surveys in the COSMOS field (east is to the left
and north is to the top). Dashed blue lines denote fields with available (sub-)mm data from
LABOCA (outer square; Albrecht et al. in prep.), AzTEC/SMA (north western diamond-shaped
field; Scott et al. 2008; Younger et al. 2007), AzTEC (large diamond shaped area; Aretxaga
et al. 2011) and MAMBO-II (central square; Bertoldi et al. 2007). The proposed region for
2 mm observations (PIs A. Karim & J. Staguhn) with the GISMO bolometer is indicated by
solid red lines. LABOCA sources are denoted as red points. Confirmed extreme starbursts at
z > 4 (Capak et al. 2008; Schinnerer et al. 2008; Riechers et al. 2010; Smolčić et al. 2011 &
in prep.; Karim et al. in prep.) as well as candidates are labeled by their names and depicted
by green symbols. Among those AzTEC-3 at z = 5.3 resides in a proto-cluster region (Capak
et al. 2011). Sources found as part of this thesis work are also shown in Figure 7.2. In the
background the pointings from the 1.4 GHz VLA COSMOS survey (Schinnerer et al. 2007,
2010) are shown and the outer dashed area marks the low-noise area of the VLA-COSMOS
field that has been used for extensive radio stacking experiments as presented in this thesis
(see Chapter 4 for the main stacking results as well as Karim et al. 2011a).
121
7. Summary and outlook
Our targets will profit from the higher resolution 3 GHz radio continuum data proposed
to be obtained in the COSMOS field using the EVLA (see above). The ∼ 0.65” resolution
that would be achieved in these observations are sufficient to reveal if the individual radio
sources associated with our extreme starbursts consist of multiple blended sources. The
source Vd-17871 studied in this thesis is a vital example for the presence of more than
one rest-frame ultraviolet sources that are likely part of a single starburst system. At the
currently available resolution of 1.5” the associated radio emission is spatially offset from
both UV sources and indeed located in between those. Disentangling the actual source
geometry at radio wavelengths will yield important insights into the nature of the radio
emission, whether it is compact or extended and what fraction each object contributes in
case of multiple sources. Globally, the synchrotron spectral index can be studied in detail
from multiple frequencies as recently also 610 MHz data became available for the COSMOS
field (Klöckner et al. in prep.).1 This is of special importance for AGN hosts. Depending on
the shape of the radio continuum, whether it is steep, flat or gigahertz-peaked the geometry
of radio jets and hence the viewing angle towards the AGN can be evaluated as detailed
lower redshift studies of, e.g., Martínez-Sansigre et al. (2006a) and Klöckner et al. (2009)
show. In some obscured quasars these studies found evidence for AGN obscuration by the
cool dust of the host galaxy that is distributed on kpc scales as some of the jets appear to be
seen face-on. This suggests that AGN obscuration is not necessarily solely a viewing angle
dependent phenomenon as suggested by the unified models (see, e.g., Urry and Padovani
1995, for a review).
A pilot deep field survey in the COSMOS field with the new 2 mm GISMO camera has been
proposed recently as shared open and guaranteed time programs (COSMO survey; principal
investigators A. Karim & J. Staguhn; see Figure 7.3). It covers an area of 20′ × 20′ to a 1σ
depth of 0.35 mJy and may reach 0.2 mJy within 42 (60) hours of net (total) integration
time depending on the final instrument sensitivity and performance. The shallower depth
is already sufficient to match those of the existing (sub-)mm surveys in the COSMOS field
of (1.2-1.3) mJy (Bertoldi et al. 2007; Scott et al. 2008; Aretxaga et al. 2011) at ∼ 1 mm
and ∼ 4 mJy at 870 µm (Albrecht et al. in prep.). Since the proposed survey area is fully
covered by all other facilities hence multiple (sub-)mm colors for all known sources will
be available. Together with the extensive ancillary data at other wavelengths and ongoing
optical spectroscopic efforts this allows one to break the prominent degeneracy between
cool dust temperature and redshift current surveys suffer from (e.g. Greve et al. 2004).
As recent initial deep observations with GISMO in the Hubble Deep Field-North (HDF-N;
Staguhn et al. in prep.) suggest, substantially more sources at z > 4 could be revealed by
the COSMOS 2 mm observations, bearing the potential to even double the current number
counts of five sources inside the field proposed. This also demonstrates that the rest-frame
far-IR properties of the z > 4 sources are not well reflected by typical IR-SED models (e.g.
those from Chary and Elbaz 2001, which have been used to estimate the expected 2 mm
number counts). The additional 2 mm HDF-N sources are, however, mostly unidentified at
other wavelengths so that currently their true nature remains unknown.
Finally, the GISMO map will allow for extensive image stacking experiments using the
available COSMOS ancillary data.
1
Note that the 610 MHz data will be valuable already in the ongoing analysis. Also 327 MHz data are available
in the COSMOS field (Smolčić et al. in prep.) but they are too shallow to be conclusive for our z > 4 sources.
122
Appendix
123
Appendix
124
A. Statistical background
Here essential background information on (noise weighted) statistical estimators used in
an image stacking experiment (see Chapter 3) and calculation of their uncertainties are
presented. For the sample selection process prior to a stacking experiment statistical tools
are also needed to assess how representative a flux density limited galaxy sample is with
respect to a given galaxy property. The techniques presented here have been implemented
in the IDL-package StackAttack as well as in dedicated sample selection routines. Some
of these techniques and all software routines themselves have been newly developed during
this thesis work.
In the following a set of N pixels will always be written as XN , regardless if the constituents xi (i = 1, . . . , N ) are noise pixels or a sample of peak flux densities. We will specify
at any stage, if we are referring to background noise, in which case we will use the upper
case indication ’bg’. Major parts of this Appendix are part of the publication
A. Karim, E. Schinnerer, A. Martínez-Sansigre, M. T. Sargent, A. van der Wel, H.-W. Rix,
O. Ilbert, V. Smolčić, C. Carilli, M. Pannella, A. M. Koekemoer, E. F. Bell & M. Salvato, 2011,
ApJ, 730, 61, The star formation history of mass-selected galaxies in the COSMOS field
A.1. Noise weighted estimators
Due to the often non-uniform noise distribution in a survey map used for a stacking experiment, the input samples used for stacking are ill-defined to some extent. Solely discarding
the typically high-noise edge regions does not remedy the fact, that there is significant variation of the rms background noise in the cutout postage stamps originating from a broad
spatial distribution across the field. Our aim is to find the best estimator for the representative value of the underlying population. Therefore the sample should consist of a random
and independent set of sources drawn from this population under equal circumstances.
To approach the last condition, that is not achievable in observational reality, we have to
compare the outcome of the stacked sample to that of a weighted sample, in which those
stamps gain more influence, that lie in low noise regions.
Regarding the mean-stacking technique it is statistically well known, that appropriate
weights are found in the reciprocal variance of each particular stamp’s
sample
noise pixel
bg,i
where the variance of the ith stamp is defined as Vari ≡ Var XN bg
bg,i
explained above XN bg
bg
bg
≡ xi1 , . . . , x bg .
bg,i
2
. As
XN
= σbg
bg
iN
The noise-weighted mean of the sample XN of peak fluxes can thus be considered the mean
eN , where the constituents x
eN are defined as
of the weighted sample X
ei of X
Var−1
x
ei = w
ei xi ≡ N P i −1 xi
i Vari
where xi ∈ XN .
(A.1)
125
A. Statistical background
P
With the definitions Wi = Var−1
i and wi = Wi /
i Wi it is easily shown, that the mean of the
x
ei defined in (A.1) indeed equals the noise-weighted mean of the xi :
e =
hXi
P
X
Wi xi
1 X
1 X
x
ei =
w
ei xi =
wi xi = Pi
.
N
N
i Wi
i
i
(A.2)
i
The above discussion leads to the suggestion, that in the presence of varying rms-noise in
eN is the appropriate one to consider not only with respect to
a given sample, the sample X
the mean value of the sample. It seems reasonable, that also its median is the best estimator for the median of the underlying population, because both computed quantities, the
median and the mean, are then referring to the same sample. We will refer to this choice
of an estimator in the following as a noise-weighted median.
Little information on weighted medians can be found in the literature and our choice
might therefore be rather innovative and, perhaps, cannot be regarded as common statistical practice. An alternative and possibly more common method (D. Hogg, private communication) for computing a weighted median is to sort the sample constituents by increasing
value and apply the same sorting scheme to the normalized weights. A normal median, by
definition, would be simply the central value in the sorted list, leaving the same number of
sample constituents on either side. The weights can now be regarded as distances along a
path of unit length due to the normalization. Therefore, adding up the sorted list of weights
until the sum reaches the value 0.5 yields an alternative weighted median at the position in
the sorted list of sample values corresponding to the position of the last weight added. We
implemented both methods and found the results to agree within the uncertainty ranges.
For this reason and due to better reliability with respect to numerical stability StackAttack routinely uses the scheme presented first in this Section.
A.2. Bootstrapping
In Sections 3.3.2 and 4.3.1 we justified that neither the observed nor the intrinsic distribution of peak fluxes are expected to be gaussian. This needs to be taken into account
no matter if we are looking for an appropriate uncertainty range to the median or mean
estimator for a given sample. In order to obtain a 68 % confidence interval not relying on
normality of the underlying parent distribution we therefore chose a bootstrapping technique for the statistical parameter of choice. This Section follows closely the descriptions
in Lunneborg (2000).1
In each case (median or mean statistics) we obtain the limits of the confidence interval
by a bootstrapped Student’s t-distribution. This technique is called studentizing. A (1 − α)
confidence interval for a parameter X in traditional statistics is given by
s
CIα/2 = X ± tα/2 √X ,
N
sX : standard deviation of X.
(A.3)
Here tα/2 denotes the α/2 percentile of the classical t-distribution which is equal to the
(1 − α/2) percentile due to the symmetry of Student’s distribution. Bootstrapping a t1
For a comprehensive summary of the (for our purposes) essential parts of Lunneborg (2000) we refer the
reader to http://www.uvm.edu/∼dhowell/StatPages/Resampling/Resampling.html.
126
A.3. Estimating the stellar mass representativeness of a flux-limited sample
distribution means to circumvent the assumption of a normally distributed population by
deriving the quantity
∗
t∗i =
Xi − X
√
s∗ ∗ / N
(A.4)
Xi
for i = 1, . . . , Nbootstrap samples drawn from the original sample of peak fluxes with replacement. In case of X ≡ hXi being the sample mean one thus has to compute the sample mean
hXi as well as all means of the bootstrapped samples hX ∗ ii including standard deviations
s∗hX ∗ ii . The resulting distribution of Nbootstrap t∗ -values is then used to compute the upper
and lower confidence limits by taking its α/2 and (1 − α/2) percentiles:
s
1−α
CIup
= X + t∗α/2 √X
N
s
1−α
∗
CIlow = X − t1−α/2 √X ,
N
(A.5)
(A.6)
where in general we chose 1 − α = 0.68 obtaining thus a 68 % confidence interval. Here
sX ≡ shXi still is just the standard deviation of the original sample. In case of X ≡ Med(X)
denoting the sample median as the parameter of choice we have to face the problem that
the denominator of (A.4) does not provide us with an estimator of the standard error of
the median. In order to estimate this latter quantity we need to access the empirical standard deviation of a sample of medians being representative for the median of the current
bootstrapped sample. Starting from this sample we thus generate a number of new bootstrapped samples hence performing a bootstrapping within the bootstrapping procedure2 .
The standard deviation s∗M ed(X ∗∗ ) of these subsamples’ medians is then used as an estimator
i
for the standard error of the single outer bootstrapped median as given by the denominator of Eq. (A.4). In order to use Eq. (A.5, A.6) we furthermore need the standard error
of the original sample’s median. This is estimated by computing the median of each outer
bootstrapped sample and taking the standard deviation sM ed(X ∗ ) of this sample of medians
as the standard error.
A.3. A statistical estimator for the stellar mass
representativeness of a flux density-limited sample
In principle one could roughly estimate stellar mass completeness limits by visual inspection of Figure 4.1. Given a flux density limit (i.e. F3.6 µm ≈ 5 µJy for all and F3.6 µm ≈ 1 µJy
for star forming (SF) galaxies; see Section 4.2.6) below which no objects of a given spectral type (Section 4.2.4) should be considered one would select by eye a stellar mass limit
upward from where there are no objects below the flux density threshold. As pointed out
in Section 4.2.6 it is, however, necessary to analytically derive these stellar mass limits in
order to ensure that – within a narrow mass-range just at any limiting mass – we are dealing
with a distribution of flux densities that can be considered representative for the one of the
underlying population. A statistical estimator is needed for obtaining the actual level of
representativeness we achieve at a given stellar mass.
2
The number of outer bootstrapped samples is typically chosen to be an order of magnitude larger compared
to the one of the inner bootstrapping.
127
A. Statistical background
Figure A.1. – Analytic evaluation of the statistical 95 % statistical completeness in different
redshift bins, based on a flux density threshold of F3.6 µm = 5 µJy (mAB (3.6 µm) = 22.15) corresponding to the 90 % level of intrinsic catalog completeness for all galaxies (black circles).
For star forming galaxies (blue stars) the evaluation is based on a flux density threshold of
F3.6 µm = 1 µJy (mAB (3.6 µm) = 23.9, i.e. the magnitude limit of the catalog). For a detailed
discussion of the meaning of statistical completeness, the choice of flux density thresholds
and the implications on sample representativeness with respect to star formation see Section
4.2.6. The photometric redshift slices depicted in the individual panels are the same as in
Figure 4.1. The quantity (x/y)obs measures how well the distribution of flux densities at the
faint end within a given sample in a narrow mass bin (∆ log(M∗ ) = 0.2) follows the decreasing
wing of a Gaussian distribution. Where it crosses the dashed horizontal line the Gaussian is
cut at the 0.95 percentile and the anticipated statistical completeness limit (vertical lines) is
reached. The method is described in detail in Appendix A.3. Lines connecting the data points
are meant to guide the eye.
Our aim is to compare the properties of the exponential decline of the observed distribution of 3.6 µm flux densities – i.e. the distribution of low values of flux density towards
the flux density limit in our selection band – within a narrow bin in logarithmic stellar mass
to the analogously exponentially declining Gaussian distribution. As explained in the following it is sufficient for this comparison to derive the relative distance between (a) the
0.95 percentile of the observed distribution of flux densities to the flux density limit and
(a) the 0.9 to the 0.95 percentile of the same observed distribution. The choice of the two
percentiles mentioned is hereby entirely arbitrary.
128
A.3. Estimating the stellar mass representativeness of a flux-limited sample
First we have to derive the corresponding ratio of distances for an arbitrary normal distribution that is cut at a given percentile. This percentile sets the representativeness we
want to achieve, i.e. 0.95 in our case. Since the width of and hence the lengthscale defined
by a Gaussian is determined by a single parameter σ any ratio of distances between given
percentiles is independent of the actual value of σ or the normalization. Given for instance
a quantity x defined as the distance between the 0.9025 (= 0.95 × 0.95) percentile of a given
normal distribution and its 0.95 percentile as well as a quantity y defined as the distance
from the 0.855 (= 0.95 × 0.9) to the 0.9025 percentile of the same distribution, their ratio
(x/y)Gauss yields a value of 1.467 that is universal, i.e. independent of the actually chosen
normal distribution. It was obtained by taking advantage of the cumulative distribution
function that connects a percentile to the corresponding actual value xσ defined by the
specific Gaussian of width σ centered at µ via the error function (erf):
xσ − µ
1
√
1 + erf
.
Φµ,σ (xσ ) =
2
σ 2
(A.7)
Differences in percentiles ∆Φµ,σ = Φµ,σ (xσ ,j ) − Φµ,σ (xσ ,i ) thus translate into physical distances ∆xσ = xσ ,j − xσ ,i solely defined by the scale σ .
Assuming that our data in narrow bins of stellar mass and redshift follows a normal distribution the distance from the 0.95 percentile of the observed distribution of 3.6 µm flux
densities to the flux limit of the sample yields a value xobs in units of flux density. Accordingly the distance between the 0.9 and the 0.95 percentiles of the observed distribution
defines a value yobs and the dimensionless ratio (x/y)obs ≡ xobs /yobs can be compared to the
aforementioned value of (x/y)Gauss . Given the case that the flux density limit is located far
in the tail of the observed distribution, (x/y)obs will exceed (x/y)Gauss and the observed distribution is statistically representative of the underlying population of objects. As the flux
density limit approaches the peak of the observed distribution the observed ratio becomes
lower. As soon as it overlaps with the 0.95 percentile of the (unknown) distribution of the
underlying population the limiting case of 95 % statistical completeness – and hence the
desired lower level of representativeness – is reached so that (x/y)obs = (x/y)Gauss .
For our sample this effect is shown in Figure A.1 where (x/y)Gauss is indicated as a dashed
horizontal line for individual ranges in photometric redshift. The finally chosen stellar mass
representativeness limits are denoted by vertical lines. The data points result from an implementation of the method described in this section that additionally takes into account
the detection completeness levels of the catalog as a function of 3.6 µm flux density. Here
we therefore obtain the mentioned percentiles using flux densities weighted by the corresponding inverse catalog detection completeness.
It is worth noting that the Gaussian distribution is just one possible parameterization
and not a necessary requirement for the method described here. Indeed, the underlying
distribution of flux densities is not even required to be symmetric. Our method simply
ensures that the observed distribution is smoothly, approximately exponentially declining
to low levels of flux density, as one may realistically expect from random processes such
as photon noise and confusion. It is simply a practical, quantitative improvement over the
alternative method of visual inspection as the latter is, essentially, assuming an unphysical
step-function rather than a continuos distribution function.
129
A. Statistical background
130
B. Calculus and formulae
This Appendix summarizes essential formulae used in this thesis and provides background
information on fundamental calibrations and calculations.
B.1. Measures of cosmological distances
The need for different cosmological distance measures in an expanding universe arises due
to its non-Euclidean nature of space-time on large scales. An excellent summary on cosmological distance measures has been presented by Hogg (1999) to which we refer the
reader. Textbook references therein provide the fundaments of all calculations and should
be consulted for a thorough introduction into our mathematical understanding of the universe within the physical framework of general relativity. Here, we summarize the most
important aspects for this thesis from Hogg (1999) and assume that the universe is homogeneous and isotropic on sufficiently large scales.
The expansion of the universe is conventionally described by a cosmic scale factor a(t).
For an individual cosmological object, such as a galaxy, the only direct observable related
to expansion1 is its redshift which is defined by the fractional frequency shift of emitted (e)
to observed (o) light2 :
z=
νe
νe − νo
⇐⇒ 1 + z =
νo
νo
(B.1)
which can be re-written in terms of wavelength by using νo/e = c/λo/e where c denotes
the speed of light. We explicitly assume a cosmological nature for all redshifts reported in
this thesis. In this case, redshift and scale factor are related as
a(t) =
1
1+z
=⇒
da(t) = −(1 + z)−2 dz = −a2 (t)dz.
(B.2)
We introduce the Hubble function (often called the Hubble parameter) as the logarithmic
time derivative of the cosmic scale factor a(t):
H(a) =
ȧ(t)
.
a(t)
(B.3)
The Hubble function is fundamental in that it relates expansion velocity of the universe
and its ’size’ at a given cosmic epoch.
A cosmology is a parameterization describing the geometry of the universe. The dimensionless matter and vacuum density parameters are given as
1
For nearby objects redshift can be interpreted as recessional velocity in the sense of a Doppler shift. For this
to hold the object’s observed redshift must not exceed a value of 10 %.
2
In the following we will conveniently omit subscripts for quantities in the observed frame and indicated the
rest-frame of the light emission with a subscript ’rf’ unless indicated otherwise.
131
B. Calculus and formulae
ΩM =
8πGρ0
,
3H02
ΩΛ =
Λc2
,
3H02
(B.4)
where G is the gravitational constant, ρ0 is the total (dark and baryonic) matter density
at the present epoch and Λ is the cosmological constant. We also use the Hubble constant
at the present epoch H0 which, for small redshifts, relates recessional velocity and distance
of cosmological objects in an expanding universe. Another dimensionless parameter, Ωk =
1 − ΩM − ΩΛ , describes the curvature. Here we assume a flat universe, Ωk = 0, as it is
observationally supported (e.g. Komatsu et al. 2009).
In this parameterization and a matter-dominated universe the redshift-dependent Hubble
function can be conveniently re-written as
H(z) = H0 E(z) = H0
p
ΩM (1 + z)3 + Ωk (1 + z)2 + ΩΛ = H0
p
ΩM (1 + z)3 + ΩΛ
(B.5)
which defines the function E(z) where we explicitly use the assumption of a flat universe
in the last step. The function E(z) is of central importance for all cosmological distance
calculations as we will see in the following
We are seeking for a convenient infinitesimal distance measure in which two nearby objects that partake in the general expansion (the so-called ’Hubble-flow’) would have the
same value of separation regardless of cosmic epoch. We might call this a comoving distance element. It differs from a proper distance (the separation of the objects in the frame
they would be observed at the same time)3 in that it accounts for the change in scale factors.
It can be found by combining Eq. (B.3) and (B.5) as well as using Eq. (B.2):
ȧ(t)
1 da(t) dz
dz
−c dt
c dz
=
= −a(t)
= H0 E(z) ⇐⇒
=
,
a(t)
a(t) dz dt
dt
a(t)
H0 E(z)
(B.6)
where the different signs on both sides of the equality reflect the different time ’directions’ of redshift and cosmic time t. For a photon whose speed c is constant in all inertial
frames c dt defines a proper distance corresponding to the infinitesimal redshift interval the
photon would have crossed. The last step of Eq. (B.6) therefore defines a comoving distance as it is divided by the scale factor at cosmic time t. Introducing the Hubble distance
DH = c/H0 , one obtains the total comoving distance to redshift z along the line of sight by
integration:
Z
z
DC = DH
0
dz ′
.
E(z ′ )
(B.7)
An expression for the lookback time tlb as well as for the cosmic age tage can be found
in the same way. The lookback time is the difference between the current cosmic age and
the one reported by a distant light emitter at the moment of emission. Therefore we need
to solve Eq. (B.6) for dt using Eq. (B.2) in order to obtain the lookback time element and
compute the lookback time to redshift z again via integration:
tlb = tH
3
Z
z
0
dz ′
,
(1 + z ′ )E(z ′ )
(B.8)
In other words, a proper distance from us to another object is the distance of the other object at the time
measured in its rest-frame when it emitted the light
132
B.1. Measures of cosmological distances
where we introduced the Hubble time tH = 1/H0 . The cosmic age at redshift z is obtained
by simply integrating from z to infinity.
As Hogg (1999) points out, one can regard the line-of-sight comoving distance DC – which
equals the transverse comoving distance DM for a flat cosmology – as the fundamental cosmological distance indicator as it relates to all other distances frequently used. The redshift
integral over 1/E(z) will therefore be frequently needed for measuring cosmological distances and is solved numerically. Clearly, E(z) depends on the cosmology chosen. A reader
assuming a flat cosmology but different values than ΩΛ = 0.7 and H0 = 70 (km/s)/Mpc for
the vacuum energy density and the Hubble constant, respectively, will compute different
distance values and hence also different results for all quantities that depend on the cosmological distances (e.g. luminosities and physical scales) compared to this work.
Throughout this thesis we make frequent use of two common cosmological distance indicators, the angular diameter distance DA and the luminosity distance DL . The angular
diameter distance at redshift z measures the ratio of the physical (transverse) extent to its
observed angular size (in radians) and is related to the comoving distance as
DA =
DM
d0
=
.
θ
1+z
(B.9)
Intuitively one would assume that DA should monotonically increase with redshift such
that objects at higher redshift would always appear smaller compared to those at lower
redshift of the same intrinsic size. This is, however, not the case as DA reaches a maximum
around z = 1.6 for the cosmology assumed in this work and decreases towards higher
z . Objects hence appear larger beyond this redshift threshold compared to their lower-z
siblings. Apparently, in a flat universe the angular diameter distance measures the proper
distance from us to an object at the cosmic epoch when the light was emitted.
The luminosity distance is the distance measure for which we can define a standard
relation between bolometric luminosity and flux of a spherically emitting source:
DL =
r
L
= (1 + z)2 DA = (1 + z)DM .
4πF
(B.10)
The relation between luminosity distance and angular diameter distance can be derived
from the cosmic microwave background. Its emission is close to that of an ideal black body
which is known not to change its spectral shape with redshift but only its temperature as
Trf = (1 + z)T . According to the Stefan-Boltzmann law the energy per unit surface area
emitted by a blackbody is furthermore proportional to the fourth power of its temperature,
hence leading to a factor (1 + z)4 . Accounting for the full emitting spherical surface the total power the cosmic background emitted at a given redshift equals its luminosity which is
related to the observed cosmic microwave background flux via the square of the luminosity
distance as given in Eq. (B.10). Relating source and angular size by definition only a factor
2 survives together with the factor (1 + z)4 mentioned before.
DA
Having found a comoving distance element along the line of sight (Eq. (B.6)) one obtains
a comoving volume element by multiplication with a comoving transverse area element.
Since the angular diameter distance measures a proper distance an observed infinitesimal
2 . Divided
solid angle dΩ is converted into a proper area element by multiplication with DA
133
B. Calculus and formulae
by the square of the scale factor (or multiplied by (1 + z)2 ) this proper area element is
converted into a comoving area element so that the comoving volume element reads
dVC = DH
2
(1 + z)2 DA
dΩdz.
E(z)
(B.11)
Integrating dVC between redshift slices over a given angular survey area yields the corresponding comoving volume. A given comoving volume will always contain the same number
of non-evolving objects partaking in the Hubble flow, regardless of cosmic epoch. Therefore global quantities normalized to unit comoving volume that are observed to evolve are
intrinsically evolving, i.e. the underlying galaxy population evolves with respect to this
global quantity. A prominent example thoroughly studied in this thesis is the cosmic star
formation rate density (see Chapter 5).
B.2. K-corrections at radio continuum and millimeter
wavelengths
In Eq. (B.10) we introduced the luminosity distance DL to relate luminosity and flux as bolometric quantities. It is, however, much more common in observational reality to deal with
monochromatic flux densities Fν (defined per unit frequency) and corresponding differential luminosities Lν . This is also the case for radio continuum emission frequently used in
this thesis. A complication arises since emitted and observed bands are not the same for a
cosmologically redshifted source. Intrinsic luminosity and observed flux density are therefore determined at different frequencies and, generally, also through different passbands.
One often wishes, however, to determine the source’s intrinsic monochromatic luminosity
at the observed frequency, e.g., in order to apply standard conversions calibrated in the
local universe in a given band. Postulating that energy is conserved one finds
Fν dν =
Fν
=
Lνrf
dνrf
4πDL2
(1 + z)Lνrf
Lν Lν
= (1 + z) rf
,
2
Lν 4πDL2
4πDL
(B.12)
(B.13)
where the rest-frame frequency is given by νrf = (1 + z)ν and in the last step we made
the connection of intrinsic luminosity and observed flux density determined in the same
(observed) passband. If the spectrum of the emitter is known and reasonably simple Eq.
(B.13) can be determined analytically. At radio continuum frequencies, e.g. at observed
1.4 GHz, where the spectral shape is well described by a power-law and where no (broad)
emission or absorption features occur this is the case. As introduced in Section 4.3.2,
Lνrf /Lν = (1 + z)αrc , the intrinsic 1.4 GHz luminosity can hence be determined from the
observed 1.4 GHz flux density using a K-correction that depends on the radio spectral index
αrc (here αrc = −0.8, e.g. Condon 1992). In convenient units this reads
2
−(1+αrc )
.
L1.4 GHz [W/Hz] = 1.12 × 1014 F1.4 GHz [µJy] DL [Mpc]
1+z
(B.14)
In general, the situation is more complicated. For a more profound description of this
so-called K-correction in the most general case we refer the reader to Hogg et al. (2002).
References therein provide the essential background information and original definitions
134
B.3. Visualizing luminosity and mass functions in the Schechter representation
as well as applications of the K-correction.
Another interesting phenomenon in the context of K-corrections occurs at (sub-)mm wavelengths. As explained below (Section B.5), at sufficiently long rest-frame wavelengths
≫ 100 µm the thermal dust continuum emission of star forming galaxies also follows a
power-law described by a spectral index of αSMM = 2 + β with β & 1. At high redshift
z ≫ 2, i.e. well beyond its peak, the angular diameter distance decreases approximately
with (1 + z)−1 for the cosmology assumed here. The luminosity distance therefore increases
approximately with (1 + z) according to Eq. (B.10). Assuming a spectral shape and hence
differential luminosity for a distant galaxy of a given bolometric luminosity the observed
flux is therefore expected to increase with redshift as (1 + z)1+β instead of decreasing. This
effect is often referred to as negative K-correction (e.g. Blain et al. 2002) and can be fully
exploited at very high redshifts (even z ∼ 10 or more) only if observed at sufficiently long
wavelengths (∼ 2 mm). Note that the negative K-correction also affects 12 CO rotational
emission lines observed at (sub-)mm wavelengths as outlined below (see Section B.4).
B.3. Visualizing luminosity and mass functions in the
Schechter representation
Even though appearing mathematically trivial the visual representation of luminosity and
mass functions is sometimes a source of confusion. Since in this thesis we are dealing only
with mass functions in the Schechter representation it is useful to illustrate the essential
steps from the mathematical definition to the actual plot based on this specific function.
The transformation discussed below would, however, likewise affect any other parameterization of luminosity functions. To some extent this Appendix covers a broader range of
problems as similar transformations would need to be performed if the concern was with
other measures of density distributions such as spectral energy distributions of galaxies.
A luminosity function of any form is often represented by a parametric model to reproduce the observed number density of a given galaxy population per unit comoving volume
and luminosity interval. This luminosity typically is monochromatic. As a most trivial example for extended application of the luminosity function concept, number densities with
respect to galaxy properties that are linearly related to a monochromatic luminosity can
hence be represented by the same mathematical function.
In reality, like in this work, a not directly observable quantity like stellar mass might
not be linearly derived from a monochromatic luminosity but a number density distribution
with respect to this quantity might still follow a parameterization that is well established
for luminosity functions. This is the case for the galaxy populations studied in this thesis
where (see Chapter 5) the mass functions are well parametrized by a power law with an
exponential cutoff at a characteristic mass M ∗ as introduced by Schechter (1976) of the
form of
Φ(M∗ )dM∗ = Φ∗ (M∗ /M ∗ )α × exp (−M∗ /M ∗ ) d(M∗ /M ∗ ).
(B.15)
The parameter M∗ denotes the stellar mass in units of solar mass. However, it is convenient to plot Φ per logarithmic stellar mass (instead of stellar mass) interval as a function
of logarithmic stellar mass. Introducing the quantity M∗ := log(M∗ ) and the Schechter
135
B. Calculus and formulae
parameter M∗ := log(M ∗ ), i.e. the logarithm of the cutoff (characteristic) stellar mass (in
units of M⊙ ) Eq. (B.15) transforms into
∗
∗
Φ(M∗ )dM∗ = ln(10) Φ∗ 10(M∗ −M )×(1+α) × exp 10(M∗ −M ) dM∗ ,
∗
(B.16)
since d(M∗ /M ∗ ) = 10(M∗ −M ) × ln(10) dM∗ . The most prominent effect of this transformation therefore is that the power-law slope in logarithmic representation appears different
in the plot from what would be expected based on its numerical value: α → (1 + α). Note
that the same effect occurs if a luminosity function is to be represented per unit magnitude
interval since absolute magnitude by definition is logarithmically related to luminosity.
B.4.
12
CO line emission and its relation to global molecular
gas properties in galaxies
In this thesis we derive molecular gas properties of a distant starburst based on its millimeter 12 CO line emission. Here we want to introduce the fundamental physics and concepts
underlying our calculations. A profound and virtually complete overview on molecular
emission lines originating from the interstellar media of (distant) galaxies has been presented in Chapter 2 of Riechers (2007) to which we refer the reader. The review presented
by Solomon and Vanden Bout (2005) summarizes all important definitions with respect to
molecular line emission properties, the relation between 12 CO line emission and the total
molecular gas content of galaxies as well as a thorough overview on the detections of molecular gas in distant galaxies. In this Appendix we summarize the most important insights for
our work from Riechers (2007) and Solomon and Vanden Bout (2005), hence follow closely
the argumentation and notation in both works.
Carbon monoxide (CO) is a linear but electrically asymmetric molecule that hence possesses a permanent dipole moment (meaning its center of mass and center of charge do
not coincide). It is highly abundant in the interstellar medium (ISM) of galaxies following closely the distribution of molecular hydrogen H2 . H2 itself is symmetric and does not
have a dipole moment. Observationally, this means that CO will show detectable emission
lines if brought into rotation through collisions with other H2 particles whereas H2 will not.
CO is therefore frequently used by observers to trace the H2 -dominated molecular ISM in
galaxies and hence the raw material needed for star formation.
Molecular rotation is quantized, meaning that a given molecule has discrete rotational
excitation levels. Rotation is, generally, possible about three mutually perpendicular axes
and three corresponding moments of inertia can be defined. In a linear (i.e. cylindrically
symmetric) molecule like CO (or H2 ) only two distinct moments of inertia, I⊥ and Ik , exist
where the moment of inertia defined along the binding axis is substantially smaller (Ik ≪
I⊥ ). Since rotational energy scales reciprocally with the moment of inertia, parallel rotation
is unlikely to be excited in the environments of interest for this thesis so that we will deal
in the following solely with I ≡ I⊥ .
The discrete energy levels of molecular rotation, working in the Born-Oppenheimer approximation and hence neglecting higher order terms, are found as energy eigenvalues of
136
B.4. 12 CO line emission tracing molecular gas
the Schrödinger equation as
Erot =
J(J + 1)~2
,
2I
J = 0, 1, 2, 3 . . .
(B.17)
where ~ is the (reduced) Planck constant (~ = h/2π ). The photon energy, ∆Erot = hνif ,
released by radiative de-excitation4 from the initial level i = J to the final level f = J − 1
hence reads
∆Erot =
~2 J
2I
⇐⇒
νif =
~J
= νCO(1−0) J ′ ,
2πI
(B.18)
where J ′ = J for all J ≥ 2 and νCO(1−0) = 115.271202 GHz5 denotes the fundamental
frequency of the CO-spectrum in the sense that all higher J -transitions are harmonics of
this lowest possible transition. Within certain restrictions (Riechers 2007) the fundamental
frequency for the CO molecule is, hence, solely determined by its dominant moment of
inertia.6 Due to this simple discretization one sometimes refers to such a line spectrum as
a rotational ladder.
Given that a main channel for rotational excitation of molecules in a given molecular
cloud is through collisions7 , a minimum excitation temperature for any energy level can be
derived by equating rotational energy (Eq. (B.17)) and the kinetic temperature of the gas.
Generally, higher levels have higher minimum excitation temperatures while also having
substantially higher critical densities (Riechers 2007). In the case where more than one
gas phase exists along one line of sight8 towards a given galaxy the J = 5 → 4 transition
studied in this thesis is thus more likely to probe those regions that are denser. Compared
to other molecules (such as HCN), however, CO line emission is generally a good tracer for
lower density environments while still tracing a broad range of temperatures.
The CO emission line is expected to show some Doppler broadening if one assumes that
the molecular gas is observed in a rotating disk and the line profile should hence follow
a Gaussian function. However, such an ordered rotation is not necessarily expected in
a (possibly merger-driven) starburst environment and there are plenty of other physical
reasons that would change the line profile from this simple shape (see Riechers 2007).
On the other hand, a Gaussian profile, constituting a one-parameter model, is often the
most simple choice to obtain reasonable measures of line peak flux and line width from the
typically low signal-to-noise data obtained for such faint emission lines from high redshift
objects. In velocity units9 the model profile of width σ , centered at a reference velocity10
4
Note that quantum mechanical optical selection rules prohibit all transitions except those between neighbored energy levels.
5
A list of theoretically predicted emission line frequencies and corresponding laboratory measurements is
found at http://splatalogue.net/
6
This statement holds also for other linear molecules which explains why rotational transition lines of various
molecular species are found at (sub-)mm wavelengths.
7
Strictly speaking, collisional excitation dominates only over radiative excitation if the environmental conditions are such that the density is higher than a certain critical density. In this situation the gas is then
referred to as being in local thermal equilibrium.
8
Within the telescope beam, respectively, if we are dealing with unresolved emission.
9
We could work in frequency units in exactly the same way. It is, however, common practice in molecular
studies to state velocity-related quantities.
10
In this Appendix we denote velocities as v instead of v used elsewhere in this thesis in order to avoid confusion
with the frequency ν .
137
B. Calculus and formulae
v0 , hence reads
A1 −(v−v0 )2
G(v, σ) = √ e 2σ2 + A2 ,
σ 2π
(B.19)
where we introduced two other free parameters, the line peak flux SCO ≡ A1 and the
continuum flux level Scont ≡ A2 . The full width at half maximum (FWHM) is related to the
width of the Gaussian by
√
∆vFWHM = 2 2 ln 2 σ ≈ 2.35 σ.
(B.20)
The integrated line flux, often presented as11 SCO ∆v (in units of Jy km s−1 ), is found by
analytical integration of the Gaussian profile:
SCO ∆v =
Z
∞
π
dv G(v, σ) = √
SCO ∆vFWHM ≈ SCO ∆vFWHM .
2 ln 2
−∞
(B.21)
Using Eq. (B.12) we can derive a luminosity of the CO line by integrating the luminosity
over the spectral range covering the line:
Z
Z
dν 4πDL2 Sν (ν)
Z
(1 + zCO )−1 νCO
dv Sν (v),
= 4πDL2
c
LCO =
dνrf Lνrf =
(B.22)
(B.23)
where we used c dν = νPeak dv = (1 + zCO )−1 νCO dv, relating not only observed frequency
and velocity but also the observed peak frequency νPeak and the rest-frame (i.e. laboratory)
frequency of a given CO-transition.
If we change to convenient units the flux integral in Eq. (B.23) can be expressed (e.g.
Solomon and Vanden Bout 2005) in relation to the integrated line flux given by Eq. (B.21):
LCO [L⊙ ] = 1.04 × 10−3 SCO ∆v [Jy km s−1 ] (DL [Mpc])2 (1 + zCO )−1 νCO [GHz],
(B.24)
where one could also directly use the observed peak frequency νPeak for the redshifted
rest-frame transition (1 + zCO )−1 νCO .
A particularly useful concept in dealing with 12 CO line emission is, however, a luminosity
definition in relation to the intrinsic (i.e. rest-frame) source brightness temperature averaged over the source. The concept of brightness temperature is physically meaningful only
if we are dealing with an optically thick emitter. In optically thick emitters the brightness
temperature and intrinsic temperature of the emitting body are the same as the molecular
gas at a given transition level is in thermal equilibrium with its own radiation (and the surrounding medium collisionally exciting it). When several several rotational transition levels
are optically thick, emission of all these transitions will be of the same (intrinsic) equilibrium temperature. Line luminosities individually related to this unique temperature will
therefore always show mutual ratios of unity. On the other hand, a brightness-temperature
related line-ratio other than unity informs us that the intrinsic state of the molecular gas
cannot be thermalized up to the higher of the two transitions.
11
Note that in this thesis we also use the notation ICO for the observed velocity-integrated line flux.
138
B.4. 12 CO line emission tracing molecular gas
This alternative line luminosity, L′CO , is derived from the product of the velocity-integrated
brightness temperature and the (proper) source area (e.g. Solomon and Vanden Bout 2005).
The latter is derived from (see Appendix B.1) the product of observed source solid angle
2 . For optically thick emission at suffiand the square of the angular diameter distance, ΩDA
ciently low rest-frame frequencies rest-frame brightness temperature and intrinsic source
intensity are related through the Raleigh-Jeans approximation (hν ≪ kB T ) of the black body
intensity such that rest-frame brightness temperature and observed flux density are related
as (e.g. Riechers 2007)
Trfb =
(1 + z) c2
Sν .
2
2kB νPeak
Ω
(B.25)
The line rest-frame frequency of < 600 GHz (i.e. a rest-frame wavelength of > 500 µm)
we are dealing with in this thesis justifies the above definition of brightness temperature as
it is still well within the Raleigh-Jeans tail of any reasonable thermal emission. Brightness
temperature hence measures the intrinsic thermal temperature of the emitting body in our
case.
Using Eq. (B.25) the line luminosity L′CO can finally be derived:
L′CO =
=
=
Z
DL2
c2
2
2kB νPeak (1 + zCO )3
Z
DL2
c2
dv Sν (v)
2 (1 + z
2kB νCO
CO )
2
dv Trfb ΩDA
=
Z
dv Sν (v)
c3
3 LCO ,
8π kB νCO
(B.26)
(B.27)
(B.28)
where the latter step makes the connection to the line luminosity as defined in Eq. (B.23).
This translates into (e.g. Solomon and Vanden Bout 2005)
L′CO [K km s−1 pc2 ] = 3.25 × 107 SCO ∆v [Jy km s−1 ]
(DL [Mpc])2
(νCO [GHz])−2
(1 + zCO )
(B.29)
Note that this relation strictly holds only if the source is smaller than the telescope beam.
Otherwise SCO ∆v does not measure the total source-averaged brightness temperature. For
a source at high redshift – as studied in this thesis – Eq. (B.25) is, however, fully applicable.
As we have seen in Appendix B.2 continuum emission at (sub-)mm wavelengths benefits
from a negative K-correction at high redshifts. We see now that the same holds true for
molecular line emission in the same observing range since the velocity integrated line flux
−2
(1 + z)3 ≈ (1 + z) at sufficiently high redshift (as outlined above) for a given
scales with DL
′
LCO . For a given observing window covering a low-J CO-transition at z = 0 (e.g. the 3 mm
band) a higher transition will be detectable if the source is at a high enough redshift that
the line is shifted into the same window. The CO-detection presented in this thesis plus
the detections of 35 distant starbursts, about the same number of high-z quasars and some
other bolometrically bright objects residing at high redshifts and reported in the literature
have observationally proven the usefulness of this concept. As a caveat one should be aware
that – for this to be useful – the high-J transitional levels require adequate environments
to be thermalized. This does not seem to be the case in local normal star forming objects.
Thus blind CO-searches at long mm-wavelengths are hence expected to be biased against
139
B. Calculus and formulae
highly excited objects at high redshift, comparable merely to starburst environments in the
local universe.
A CO line luminosity is directly converted into a molecular gas mass by a linear relation
(e.g. Solomon and Vanden Bout 2005):
Mgas = αCO L′CO ,
(B.30)
where Mgas denotes the total molecular gas mass (incl. H2 as well as Helium). There is
ample evidence that, for the Milky way, αCO = 4.6 M⊙ (K km s−1 pc2 )−1 holds. This value
can be derived from the virial theorem under observationally confirmed assumption on the
dynamics of gravitationally bound individual molecular clouds as well as from independent
observational diagnostics (see Solomon and Vanden Bout 2005, for a summary of mutually
agreeing results).
In local starbursts, however, it has been argued (Downes et al. 1993) that the assumption
of an ensemble of virialized clouds might not hold due to the substantially higher central
mass densities in such objects. In the centers of massive starbursts we are merely dealing with a single bound medium of gas and stars. Downes et al. (1993) point out that
this leads to the fact that the CO line luminosity cannot be regarded as a pure gas mass
tracer anymore but rather traces the geometric mean of gas and dynamical mass. The
galactic αCO factor introduced before would hence over-predict the gas mass if applied to
CO-observations of starbursts. Indeed, the gas masses reported for such extreme objects
based on a Galactic conversion factor often exceed the dynamical mass estimates, hence
observationally favoring a lower conversion factor (see, e.g., Downes et al. 1993, Solomon
and Vanden Bout 2005, and references therein).
A commonly accepted value for local starbursts has been suggested by Downes and
Solomon (1998) as αCO = 0.8 M⊙ (K km s−1 pc2 )−1 and is often used for their high-redshift
cousins (e.g. Solomon and Vanden Bout 2005).
In this thesis we make use of the Downes and Solomon (1998) conversion factor for a
z ∼ 4.6 starburst in order to estimate the total molecular gas mass in this object. For
similar objects at comparably high redshift this conversion has been used as well. While
those rare objects for which the CO excitation could be constrained based on multiple CO
transitions (Riechers et al. 2010; Carilli et al. 2010) two distinct gas phases have been
reported which, if the starburst conversion applies, contribute about equal amounts to the
total gas content in these system. Also for these objects dynamical mass arguments favor a
low conversion factor but it remains elusive if the apparently more diffuse lower excitation
gas component might not resemble the molecular conditions of local disk galaxies. It should
be noted that the dynamical mass estimates themselves are hard to constrain due to the
uncertain assumptions on the dark matter distribution in those objects. Molecular gas mass
estimates for high redshift objects should therefore be treated with caution.
B.5. Dust emission properties of star forming galaxies and
derivation of dust mass
Dust in the interstellar media of galaxies is dominantly composed of amorphous carbon
and silicate-like grains (Draine 2003). They are exposed to the interstellar radiation field,
140
B.5. Dust emission properties and derivation of dust mass
mostly heated by blue UV light emitted from young stars to temperatures of T & 20 K and
they constitute predominantly thermal (in most cases isotropic) emitters. The dust mass
in star forming objects is usually dominated by a cool component that can be described
by a single temperature (typically < 50 K; e.g. Kovács et al. 2006; Hwang et al. 2010) and
assuming a single species of dust grains. If the galaxy hosts an active galactic nucleus
(AGN) the dust in its vicinity is dominantly heated by this central engine to temperatures
of 100 K or more (peaking at ∼ 20 µm in the rest-frame), bolometrically outshining the
cool dust component. AGN may, however, also contribute to the heating of the cooler dust
grains typically distributed on much larger (kpc) scales (e.g. Martínez-Sansigre et al. 2009,
and references therein). In presence of an AGN cool dust emission is hence not necessarily
directly proportional to the star formation rate (SFR), rather constraining an upper limit to
the SFR.
Mathematically, a single species dust emission is usually well described by a modified
black body at a temperature TD (also referred to as gray body emission). However, at high
redshift it is also useful to account for the contribution of the redshifted cosmic microwave
background emission of temperature TBG = 2.73 K × (1 + z) (e.g. Weiß et al. 2007). In total,
the flux density in the observed frame then reads
Fν =
Ω
[Bνrf (TD ) − Bνrf (TBG )] (1 − e−τνrf ),
(1 + z)3
(B.31)
where νrf = (1 + z)ν denotes the frequency in the rest-frame of the source and ν the
observed one. Following the notation in Aravena et al. (2008) we introduced Ω = π(d0 /DA )2 ,
the solid angle the source subtends on the sky defined by the ratio of the equivalent source
size d0 and the angular diameter distance DA at the redshift of the source.12 The emission
of a black body Bνrf at a temperature T is described by the Planck function as
−1
2hνrf3
hνrf
,
exp
−1
Bνrf (T ) = 2
c
kB T
(B.32)
where h is Planck’s and kB is Boltzmann’s constant, c denotes the speed of light and
we use the rest-frame notation for consistency with Eq. (B.31). The optical depth τνrf
introduced in Eq. (B.31) follows a frequency-dependent description proportional to the
illuminated dust mass MD :
τνrf =
κνrf MD
2Ω .
DA
(B.33)
The explicit frequency dependence is thereby contained in the mass-absorption coefficient κνrf = κ0 (νrf /ν0 )β . Note that this simple power-law description with a dust emissivity
index β is valid only within certain limits. Empirically, based on laboratory experiments
combined with observational evidence, emissivity curves have been studied for individual
dust species. E.g. Draine and Lee (1984) show that the power-law description is a good
approximation for silicates/graphites exposed to interstellar radiation fields for rest-frame
wavelengths above ∼20/40 µm. There is hence experimental support to model long farinfrared to (sub-)mm data observed for z > 4 sources studied in this thesis under this
power-law assumption. Observationally, it is hard to constrain the exact value of the index
12
The factor (1 + z)−3 in Eq. (B.31) results from the effect of surface brightness dimming, (1 + z)−4 , and the
redshifting of the bandpass which produces a factor of (1 + z).
141
B. Calculus and formulae
β because of degeneracies between colors and temperature (Blain et al. 2003), unless the
peak region of the dust emission (and thus the dust temperature) is accurately sampled.
For dust-rich sources in the distant universe values of 1 < β < 2 have been reported (e.g.
Priddey and McMahon 2001; Kovács et al. 2006, for high redshift quasars as well as e.g.
Blain et al. 2002, and references therein for sub-mm galaxies), perhaps with growing evidence that quasars and composite objects cluster somewhat more at the higher end of this
range.
The reference value for the mass-absorption κ0 probably is the most uncertain parameter
which explains why inferred dust masses should be treated with caution. Different authors
report fairly different values for κ0 while also probing different reference wavelengths.
Extrapolating different measurements to the same reference wavelengths by assuming a
typical value for β translates into about a factor of three scatter (Blain et al. 2002). Explicitely, two commonly used literature values are κ1.2mm = 0.04 m2 kg−1 (Alton et al. 2004;
Kruegel and Siebenmorgen 1994) and κ125µm = 2.64 m2 kg−1 (Dunne et al. 2003) which nominally agree within a factor of two when extrapolated to the same reference wavelength in
the observed frame by assuming a typical value for the index β .
In the presence of N dust components with emissivities β i at temperatures TDi individually
described by Eq. (B.31) the (far-)infrared (FIR) luminosity is obtained by integrating over
all frequencies and adding up all dust components as
LFIR
4π DL2
=
(1 + z)
Z
dν
N
X
i
Fνi (β i , TDi )
=
2
4π DA
(1
3
+ z)
N Z
X
dνFνi (β i , TDi ),
(B.34)
i
where DL = (1 + z)2 DA denotes the luminosity distance to redshift z and we exchanged
– for convenience – summation and integration in the last step.
Typically, the order of operations starts from fitting gray body components according to
Eq. (B.31) to the observed photometry. The fit then delivers the temperatures and masses
of the dust components and a luminosity can be estimated according to Eq. (B.34) from
the best-fit models. For most objects at high redshifts the data coverage is rather sparse so
that, usually, the emissivities β i are not treated as free parameters in the fit but are fixed
to empirically justified values (see above).
Eq. (B.31) explicitly accounts for optically thick (τνrf > 1) dust emission. While it is often assumed that dust emission is optically thin at far-infrared wavelengths, Downes et al.
(1993) argue that the situation changes in presence of large, spatially concentrated dust
reservoirs typically found in (local) starbursts. The limit at which the dust emission becomes optically thick can be derived from Eq. (B.33) in dependence of the source size and
dust mass, hence the density of the dust. For example Aravena et al. (2008) find for a z ∼ 1.8
starburst/QSO composite object – for which a source extent of 1.5 kpc was estimated based
on 12 CO emission line observations – that the dust mass computed for the dominant cool
component suffices to make the dust emission optically thick at rest-frame wavelengths below 130 µm. Given that the cool dust emission from this source peaks around rest-frame
wavelengths of ∼ 90 µm (i.e. in the typical range for starbursts) only its Raleigh-Jeans tail
should be treated in the optically thin approximation. The Raleigh-Jeans approximation for
the cool dust component, in turn, directly leads to a sub-mm spectral index of αSMM = 2 + β .
It is hence a prominent characteristic of a modified black body spectrum at long wavelengths that it falls off significantly steeper than a standard black body.
142
B.5. Dust emission properties and derivation of dust mass
It should be noted that – due to a current lack of very high-resolution data – little is known
about the actual dust distribution in distant starbursts so that the assumption of a single
compact dust reservoir might not hold at high-z . In the near future the Atacama Large
Millimeter Array (ALMA) will resolve the dust distribution in high redshift objects. One
should still generally be cautious when applying the optically thin approximation globally.
In the optically thin approximation, τνrf ≪ 1, at sufficiently long rest-frame wavelengths
Eq. (B.31) simplifies to:
Fν
κνrf MD
2 (1 + z)3 [Bνrf (TD ) − Bνrf (TBG )]
DA
β
νrf
MD (1 + z)
= κ0
[Bνrf (TD ) − Bνrf (TBG )] ,
ν0
DL2
=
(B.35)
which is now independent of the solid angle and, thus, also of the source size. The far-IR
luminosity is again computed from Eq. (B.34), this time for a single dust component. With
Eq. (B.32) and the substitution x = hνrf /kB T we arrive at an integral for which an analytic
solution exists via the Gamma and Riemann zeta functions (e.g. Martínez-Sansigre et al.
2009):
Z
LFIR ∝
dx
x3+β
= Γ(4 + β)ζ(4 + β).
ex − 1
(B.36)
This approach resembles the derivation of the Stefan-Boltzmann law so that pre-factors
2π 5 k 4
can be collected to a large extent in the Stefan-Boltzmann constant σSB = 15c2 hB3 while the
temperature dependence becomes even stronger pronounced than in the Stefan-Boltzmann
law:
LFIR = 4πMD κ0
kB
ν0 h
β
Γ(4 + β)ζ(4 + β)
4+β
4+β
,
T
−
T
σ
SB
D
BG
π 5 /15
(B.37)
where any explicit redshift dependence canceled out since we integrated in the rest-frame.
In practice, Eq. (B.37) is used to substitute the unknown dust mass in Eq. (B.35) yielding
a model to fit the observed photometry of the cool dust emission when treating LFIR , TD and
β as free parameters. This way also the uncertain reference value κ0 of the mass absorption
coefficient cancels out. This might be regarded as a particular advantage of the optically
thin approximation over the full model in Eq. (B.31) because at least the far-infrared luminosity and dust temperature can be estimated without this additional source of error. In
turn, a single observed monochromatic flux density can be used to roughly constrain LFIR
when fixing the values of β and TD . This is useful in the – at high redshift – common case
that for a source only a single measurement, e.g. from (sub-)mm-observations, is available.
For completeness, the full parametric model for the observed flux density in the optically
thin approximation at sufficiently long wavelengths reads
Bνrf (TD ) − Bνrf (TBG )
LFIR (1 + z) π 5 /15
Fν =
2
σSB Γ(4 + β)ζ(4 + β) T 4+β − T 4+β
4πDL
D
BG
hνrf
kB
β
(B.38)
Bearing in mind the caveats discussed above, the cool dust mass is finally estimated by
solving Eq. (B.37) using the data-constrained parameters. Alternatively, Eq. (B.35) can be
used to estimate the dust mass from any given monochromatic flux density in the observed
frame.
143
C. Fundamental constants, units and
definitions
Many of the relations and calibrations that led to the results presented in this work make
use of fundamental and convenient (astro-)physical constants. Here we list the numerical
values of these constants and, if applicable, their relation to other fundamental constants.
Furthermore the list includes distance and flux density units conveniently used in astronomical contexts.
Cosmological quantities used in this thesis are defined in Appendix B.1 along with their
numerical values assumed here.
144
Table C.1.
Fundamental physical constants
Constant
Symbol
Speed of light (vacuum)
Value
299792458
c
Elementary charge
Newton gravitational constant
Planck constant
Boltzmann constant
Stefan-Boltzmann constant
e
G
h
kB
σSB =
4
2π 5 kB
15c2 h3
1.602176565 × 10−19
6.67384 × 10−11
6.62606957 × 10−34
1.380658 × 10−23
5.670373 × 10−8
SI unit
m s−1
Def.
As = C
m3 kg−1 s−2
Js
J K−1
W m−2 K−4
Note. — Values taken from P.J. Mohr, B.N. Taylor, and D.B. Newell (2011), The
2010 CODATA Recommended Values of the Fundamental Physical Constants (Web
Version 6.0). This database was developed by J. Baker, M. Douma, and S. Kotochigova. Available: http://physics.nist.gov/constants. National Institute of Standards and Technology, Gaithersburg, MD 20899.
Table C.2.
Unit
Symbol
Parsec
Solar mass
Solar luminosity
Erg
Hertz
Angstrom
Jansky
pc
AB magnitude
M⊙
L⊙
erg
Hz
Å
Jy
mAB (ν)
Astronomical and SI-derived units
Value
(SI) unit / information
3.08568025 × 1016
1.98892 × 1030
3.839 × 1026
10−7
1
10−10
10−26
2.99792458 × 10−5
−2.5 log
Fν [Jy]
3631
≈ −2.5 log(Fν [µJy]) + 23.9
m
kg
W
J
s−1
m
W m−2 Hz−1
−1
erg s−1 cm−2 Å × (λ [Å])−2
For flux density Fν
at observed frequency ν
Note. — Values and definitions can be found in any standard astronomy textbook.
For an overview on often used unit conversions in astronomy we refer the reader to
http://astro.wku.edu/strolger/UNITS.txt.
145
Acknowledgments
This thesis started with Kafka and the main street of the village which never reaches the
castle. It is known that the protagonist – called K. – will never reach the castle (his purported destination) either. This sounds quite negative and in case of K. it certainly is. The
question remains, however, what we can learn from the metaphor for science and perhaps
for life. Sometimes it might be better, on the one hand, not to know the ultimate destination. In an astronomical context a famous example for this might be the quite serendipitous
observational discovery of the cosmic microwave background. On the other hand, sometimes it might be better not to follow the main road. Be aware, however, that finding the
most promising alternative way demands a good portion of creativity, actual talent as well
as some luck and hence courage. The author of this thesis lacks the self confidence and
perhaps the arrogance to claim those traits for himself in sufficient amount. He might have
often looked for the side streets anyway. Leaving the main road often (maybe naturally?)
also means to leave the straight way. It is the author’s opinion that this thesis profited from
this approach in some parts. In others it might have dramatically failed. In which fraction
did it fail or did it work? In equal parts? Even worse? I am glad that higher powers than
me have to judge this.
I wish to thank Professor Hans-Walter Rix and Professor Ralf Klessen for having taken
over the challenge to be those higher powers. Thanks to Dr. Henrik Beuther and Professor
Luca Amendola the committee for my doctoral exam is complete and I am glad that both
found time in their certainly tight schedules. I thank my advisor, Dr. Eva Schinnerer, for
having given me the opportunity to work in the exciting and most familiar environment the
Max-Planck-Instute for Astronomy offers. She was brave enough to accept me as her student given that my scientific background was on tiny scales compared to any astronomical
context (let alone cosmic evolution!). I also thank her for sharing her unchallenged scientific intuition with me. She furthermore introduced me into how science works. I often
tried to compensate her efforts in returning my opinion on how science should work. I hope
nobody became desperate from these debates for longer periods of time.
I thank all my colleagues and the entire COSMOS collaboration – consisting of more than
a hundred scientists around the globe – who contributed to this work in several ways, in
particular in providing data products, making suggestions and giving guidance. Those who
are listed as co-authors of the published (and soon to be published) parts of this thesis
thereby deserve special acknowledgment. Particularly, I thank Dr. Mark Sargent, Dr. Alejo
Martínez-Sansigre, Dr. Vernesa Smolčić, Dr. Arjen van der Wel and Dr. Manuel Aravena for
their support, their help and for countless hours of their time before and around proposal
deadlines as well as before paper and thesis submissions. Many thanks also to Chris Carilli
for his enlightening suggestions and, not less, for simply being Chris Carilli. I want to thank
Dr. Brent Groves and Dr. Andrea Maccio for reading parts of this manuscript (Appendix and
Introduction) and providing helpful suggestions which certainly improved the text. Another
’thank you’ to Dr. Johannes Staguhn for making me a GISMO team member. I am sure
146
GISMO and its successor will rock the world! Finally, I thank Professor Ian Smail for giving
me the opportunity to carry out my future work at Durham University.
Thanks to Dr. Julian Merten for providing the LATEX-style file for this thesis (I hope he is
fine with the numerous modifications I applied). I thank him and all my friends in Heidelberg for the great time we had together and all my friends in larger distances (however, not
yet comparable with the distances this thesis is dealing with) for being sufficiently patient
with respect to my rare presence. This group of friends includes Dr. Arno Witzel and Gunther Witzel who gave me invaluable support as well as guidance along my scientific way,
especially when I was looking for the right direction after the defense of my diploma thesis.
Abschließend, jedoch sicherlich nicht zuletzt, danke ich meiner Familie für jegliche Unterstützung auf meinem bisherigen Weg. Wie schon meine Diplomarbeit sei diese Dissertation Clemens und Leonie, den Kindern meiner Schwester Dagmar und ihres Mannes
Stephan Epe gewidmet, da sie ihren (Paten)onkel nach wie vor zu selten sehen. Meine Eltern, Monika und Dr. Ayad Karim, haben mich stets nach Kräften unterstützt und sämtliche
Etappen wohlwollend und geduldig begleitet. Für viel Verständnis und noch mehr Unterstützung danke ich Dir, Lisa, ganz besonders.1
1
Finally, I must not forget to thank Mr. M, Mr. R, Mr. G and all other members of their gang. Those who
should will understand...
147
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