thesis2RobainaRapisarda

thesis2RobainaRapisarda
Dissertation in Astronomy
submitted to the
Combined Faculties for the Natural Sciences and for Mathematics
of the Ruperto-Carola University of Heidelberg, Germany.
for the degree of
Doctor of Natural Sciences
presented by
Licenciado D. Aday Robaina Rapisarda
born in Las Palmas de Gran Canaria, Spain
Oral examination: 25th February 2010
Eight Gigayears of
of
Galaxy Mergers
Referees: Prof. Dr. Eric F. Bell
Prof. Dr. Klaus Meisenheimer
i
Abstract
Galaxy interactions are expected to play a crucial role in the build–up of stellar mass in any
cold dark matter cosmology. Of particular interest are the mergers between systems of a
comparable mass, as they are predicted to be one of the main modes of galaxy growth and
have a crucial impact in the shaping of galaxy morphologies and dynamics. In this thesis
I study two key aspects of the role that mergers play in galaxy evolution: a)What is the
contribution of major galaxy interactions to the star formation history of the Universe at
z < 1?, and b) How important are galaxy interactions for the build–up of the massive end of
the red sequence? To answer the first question I use photometric redshifts, stellar masses and
UV star formation rates from COMBO-17, 24µm star formation rates from Spitzer and galaxy
morphologies from two deep Hubble Space Telescope cosmological survey fields to study the
enhancement in star formation activity as a function of galaxy separation. I apply robust
statistical tools to find galaxies in close pairs, augmented with morphologically-selected very
close pairs (unresolved in the ground-based photometry) and merger remnants from the
Hubble Space Telescope imaging, finding that, on average, major galaxy interactions between
galaxies more massive than 1010 M⊙ at 0.4 < z < 0.8 enhance the star formation activity by
a factor of less than 2. I carry out detailed modeling of the methodology using a mock
galaxy catalog from the Millenium Simulation, finding that in the regime applicable to this
work the recovered enhancement in SF rate is accurate to better than 10%, smaller than
the other sources of uncertainty. Accounting for the fraction of merging and interacting
systems, I integrate the enhanced star formation to demonstrate that less than 10% of star
formation activity is directly triggered by those interactions. To answer the second question
I look for close pairs of galaxies on a sample drawn from the COSMOS and COMBO–17
galaxy surveys to find that the fraction of M∗ > 5 × 1010 M⊙ galaxies in close pairs (a proxy
for the fraction of objects involved in an interaction) were more common 7 Gyrs ago by a
factor ∼ 2. By converting this merger fraction to a merger rate I estimate that 70% of the
very massive galaxies (M∗ > 1011 M⊙ ) have undergone a merger since z = 1.2. This merger
rate is sufficient to explain the observed number density evolution of such massive galaxies
in the last 7 Gyrs. Merging plays, therefore, a dominant role in the formation of massive
galaxies in the Universe.
ii
Zusammenfassung
Es wird erwartet, dass Wechselwirkungen zwischen Galaxien in jeder, auf kalter dunkler
Materie aufbauenden Kosmologie eine entscheidende Rolle beim Aufbau stellarer Masse
spielen. Von besonderem Interesse sind Verschmelzungen von Systemen ähnlicher Masse.
Für diese wird vorhergesagt, einen der Hauptmechanismen für das Wachstum von Galaxien
darzustellen und einen entscheidenden Beitrag zu leisten Morphologie und Dynamik
von Galaxien zu formen. In dieser Arbeit untersuche ich zwei Schlüsselaspekte von
Verschmelzungen in Bezug auf Galaxienentwicklung: a) Was ist der Beitrag der Wechselwirkungen von Galaxien ähnlicher Masse zur Sternentstehungsgeschichte des Universums bei
z < 1?, und b) Wie wichtig sind Wechselwirkungen zwischen Galaxien um den massereichen
Teil der “roten Sequenz” aufzubauen? Um die erste Frage zu beantworten benutzte
ich photometrische Rotverschiebungen, stellare Massen und UV Sternentstehungsraten
von COMBO–17, 24µm Sternentstehungsraten von Spitzer und Galaxienmorphologien
von zwei tiefen kosmologischen Durchmusterungsfeldern des Hubble Weltraumteleskops,
um die Zunahme der Sternentstehungsaktivität als Funktion des Galaxienabstands zu
untersuchen. Ich wende dazu robuste statistische Methoden an, um Galaxien in engen
Paaren zu finden und reichere diese Auswahl mit morphologisch ausgewählten sehr
engen Paaren (nicht aufgelöst in bodengebundener Photometrie) und Galaxien in NachVerschmelzungszuständen aus Hubble Weltraumteleskop Aufnahmen an. Damit finde ich,
dass im Mittel Wechselwirkungen zwischen Galaxien ähnlicher Massen oberhalb von 1010 M⊙
bei 0.4 < z < 0.8 die Sternentstehungsaktivität um einen Faktor von weniger als 2 steigern.
Ich führe detailierte Modelierungen der Methodik unter der Benutzung eines künstlichen
Galaxienkatalogs aus der Millenium Simulation durch und finde dabei, dass in dem in
dieser Arbeit untersuchten Parameterbereich, die Erhöhung der Sternentstehungsrate mit
Unsicherheiten kleiner als 10% bestimmt wird, weniger als die anderer Fehlerquellen. Unter
Berücksichtigung des Anteils verschmelzender und wechselwirkender Systeme integriere
ich die erhöhte Sternentstehungsrate, um zu demonstrieren, dass weniger als 10% der
Sternentstehungsaktivität direkt von solchen Wechselwirkungen hervorgerufen wird. Um
die zweite Frage zu beantworten, betrachte ich enge Galaxienpaare in einer Auswahl aus
den COSMOS und COMBO-17 Galaxiendurchmusterungen und finde, dass der Anteil von
M∗ > 5×1010 M⊙ Galaxien in engen Paaren (stellvertretend für den Anteil von Objekten, die an
Wechselwirkungen beteiligt sind) vor 7 Milliarden Jahren um einen Faktor ∼ 2 grösser war.
Indem ich diesen Anteil der Verschmelzungsprozesse in eine Verschmelzungsrate umwandle
schätze ich ab, dass 70% der massereichsten Galaxien (M∗ > 1011 M⊙ ) seit einer Rotverschiebung von z=1.2 an einer Verschmelzung beteiligt waren. Diese Verschmelzungsrate ist
ausreichend um die beobachtete Entwicklung der Anzahldichte solch massereicher Galaxien
in den letzten 7 Milliarden Jahren zu erklären. Galaxienverschmelzungen spielen daher eine
dominierende Rolle in der Entstehung massereicher Galaxien im Universum.
To Silvia, my North Star
v
I gazed the skies looking for the heaven, but all I found were the devil’s eyes
Contents
1
Introduction
1.1
1.2
Galaxies in a dark Universe
. . . . . . . . . . . . . . . . . . . . . .
1
1.1.1
Evidence for the existence of dark matter . . . . . . . . . .
3
1.1.2
Dark matter and hierarchical structure formation . . . . .
5
1.1.3
Galaxy formation in a CDM–dominated universe . . . . .
6
1.1.4
The Λ-CDM paradigm . . . . . . . . . . . . . . . . . . . . .
7
Galaxy Evolution: An Empirical View . . . . . . . . . . . . . . . .
9
1.2.1
1.3
1.4
1.5
1
Colors and shapes: Two related problems? . . . . . . . . .
11
The Role of Mergers in Galaxy Evolution . . . . . . . . . . . . . .
13
1.3.1
Looking for galaxy mergers . . . . . . . . . . . . . . . . . .
16
Galaxy Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
1.4.1
COMBO-17, GEMS, STAGES and COSMOS . . . . . . .
19
Layout of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
vii
viii
2
Contents
1.5.1
Stars formed by galaxy interactions . . . . . . . . . . . . .
1.5.2
The growth of the most massive galaxies through merging 21
SFR Enhancement in Galaxy Interactions
23
2.1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
2.1.1
COMBO-17. Redshifts and stellar masses . . . . . . . . . .
26
2.1.2
GEMS and STAGES HST imaging data . . . . . . . . . . .
27
2.1.3
MIPS 24 µm , total infrared emission and star formation
rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
2.2
2.3
2.4
The Data
Sample selection and method
. . . . . . . . . . . . . . . . . . . . .
30
2.2.1
Projected correlation function . . . . . . . . . . . . . . . . .
31
2.2.2
Visual Morphologies
. . . . . . . . . . . . . . . . . . . . . .
33
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
2.3.1
Enhancement in the Star Formation Activity . . . . . . . .
40
2.3.2
How important are mergers in triggering dust-obscured
starbursts? . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
2.4.1
Comparison with previous observations . . . . . . . . . . .
49
2.4.2
What fraction of star formation is triggered by major
interactions? . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
Comparison with theoretical expectations
. . . . . . . . .
55
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
2.4.3
2.5
3
20
Systematic Errors in Weighted 2–point Correlation Functions
59
3.1
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
3.2
An idealized experiment
61
. . . . . . . . . . . . . . . . . . . . . . . .
ix
Contents
4
3.3
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
3.4
An example application to observations . . . . . . . . . . . . . . .
64
3.5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
The Merger–Driven Evolution of Massive Red Galaxies
69
4.1
Sample and method . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
4.2
Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . .
72
4.2.1
Comparison with previous works . . . . . . . . . . . . . . .
74
4.2.2
The impact of galaxy merging on the creation of red M∗ >
1011 M⊙ galaxies. . . . . . . . . . . . . . . . . . . . . . . . . .
76
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
4.3
5
Conclusions
79
Acknowledgements
83
Chapter 1
Introduction
Galaxies are clumps of stars, gas, dust and dark matter surrounded by huge
volumes of relatively empty space. In our current understanding, these objects
have been formed through the agglomeration of smaller clumps in a sort of
dance governed by the gravitational properties of dark matter, in which all the
visible components of the Universe are embebbed. As the building blocks of
the Universe, galaxies are one of the most important subjects of study in our
effort to push the limits of our comprehension.
1.1
Galaxies in a dark Universe
In the present-day Universe, a wide variety of galaxies is within the reach of our
telescopes. In an extremely simplistic view, galaxies can be assigned to one of
two groups: blue objects with disk-like structures and non-prominent bulges,
and red, spheroidal objects with old stellar populations. In the tradional
scheme for morphological galaxy classification, first defined by Edwin Hubble
back in 1926 (Hubble 1937), galaxies belonging to the first group were called
‘late type’ objects and those in the second group ‘early type’ objects. At
that time, it was believed that in the galaxy formation process, the first stage
was an approximately spherical, pressure supported object that would lead,
given enough time, to a stage in which a disk forms and spiral arms develop.
Nowadays we know this idea to be wrong, in the sense that interactions or
mergers between two disk galaxies are believed to lead to the formation of
an ’elliptical’ (Toomre & Toomre 1972), and a transformation in the opposite
direction is unlikely to occur (although not impossible Di Matteo et al. 2009).
Mergers are not the only astrophysical process leading to changes in galaxy
morphology but are clearly the most dramatic one.
1
2
CHAPTER 1
In reality, the picture is more complex. Elliptical galaxies come in different
flavors. There are relatively low mass early type galaxies with disky isophotes
(implying some degree of rotation), which usually present an excess of light in
the inner hundred of parsecs (pc). There are also very massive ellipticals with
boxy isophotes and negligible rotation which display a deficit of light in the
inner region (Kormendy et al. 2009). The common origin of all the galaxies
in the bulge-dominated family is a matter of intense discussion nowadays
(Kormendy et al. 2009; Ferrarese et al. 2006).
On the side of late-type galaxies things are not easier to describe. Although
the majority of disk-dominated galaxies present non-negligible levels of star
formation and blue optical colors, there is a fraction which seem to be relatively
red, with little or no ongoing star formation. The relative strength of the spiral
arms compared to the disk as a whole, the thickness of the stellar and gaseous
disk and the ratio of stellar mass in the bulge compared to that on the disk
differs dramatically from galaxy to galaxy.
Figure 1.1 Nearby spiral galaxies. From top left to bottom right: M31 (Andromeda Galaxy),
M100, M101 and NGC 4414
As I already mentioned, the components of a galaxy that we can see in the
INTRODUCTION
3
Figure 1.2 Nearby elliptical galaxies. From top left to bottom right: M87, Centaurus A,
NGC 4881 and M60 (together with the spiral NGC 4647).
electromagnetic spectra do not sum up 100% of its composition. The dominant
component, as far as gravitation is concerned, is hidden to our eyes and
instruments. The stars and the gas of a galaxy are embebbed in a halo of
mysterious sort of matter which does not interact electromagnetically (or if it
does, in an extremely weak fashion) and thus, does not emit any radiaton we
can detect. This unseen component of the Universe is commonly known as
Dark Matter.
1.1.1
Evidence for the existence of dark matter
Since the early 30’s, independent evidence for the existence of non-luminous
matter in the Universe have been found, but they were not put together until
the decade of the 60’s, when the basic idea of the Universe was revolutionized
in a way which would not be experienced again until the very end of the XX
century, when an acceleration in the expansion rate of the Universe was found.
4
CHAPTER 1
In 1933, Fritz Zwicky measured the radial velocities of clusters and large groups
within the Coma supercluster, finding for some of then velocity dispersions as
high as ≈ 1000, km/s. For the first time, he applied the Virial theorem to infer
the dynamical mass of the cluster, finding a value Mdyn /MLum ≃ 400 (Zwicky
1933)1 .
A particularly relevant piece of information came from the velocity curve of disk
galaxies starting with the study of M31 (the Andromeda galaxy) by Babcock
(1939). He found, using long-slit spectra, that the outer parts of the disk were
rotating faster than what one would expect from Keplerian orbits.
Figure 1.3 Rotation velocity as function of the radial position in a disk galaxy. The curve
A shows the expected velocity curve from Keplerian orbits when considereing the luminous
matter in the galaxy. The curve B shows the typical rotation curve measured in a disk
galaxy.
Further evidence comes from kinematical analysis of galaxy pairs (Kahn &
Woltjer 1959), theoretical studies about the stability of galactic disks, which
turn out to need the presence of a massive (unobserved) halo to reach stability
(Ostriker & Peebles 1973) and the gravitational lens effect.
When all these pieces are put together, one reaches the conclusion that there
are large amounts of mass in the Universe, but most of it is invisible in the
1
With a modern value for the Hubble constant H0 one would get a value closer to 50.
INTRODUCTION
5
electromagnetic spectrum. For this reason astronomers refers to this kind of
matter as dark matter (DM).
1.1.2
Dark matter and hierarchical structure formation
Beyond the direct evidence for the existence of non luminous matter shown
in the previous section, the very fact that we see structures in the Universe is
pointing in the same direction.
The hierarchy of cosmic structure is assumed to have grown from primordial
fluctuations (i.e., dense regions grow through the accretion of mass from its
surroundings). These fluctuations are described by the density contrast δ,
which is defined as the density fluctuation relative to the average density ρ.
δ=
ρ−ρ
.
ρ
(1.1)
The horizon size at the end of the radiation–dominated era (maximum distance
at which two points in the Unvierse are causally connected) sets the limit
between large structures which could grow without being suppressed during
the radiation era and the small ones which could not survive. The radii of this
horizon at the time of equality between matter and radiation is given by
3/2
c aeq
p
,
req =
H0 2Ωm,0
(1.2)
where aeq is the scale factor of the Universe at that time, H0 is the value of
the Hubble constant nowadays and Ωm,0 is the dimensionless matter density at
z = 0.
In Fourier space, the variance of the density contrast is called the power
spectrum, and under the assumption that the matter contained in fluctuations
of the size of req is constant over time and that the matter is cold2 (nonrelativistic), the power spectrum will behave as
2
Evidence for cold dark matter comes from direct observations of structure growth in the Universe. If
the DM is hot, the growth scenario will be top–down, where the biggest structures are formed first and
then the smallest structures. If the DM is cold the scenario would be bottom–up and the smalles structures
(protogalaxies) would form first and the largest structures (superclusters) later. The observations point
to a bottom-up scenario.
6
CHAPTER 1
Pδ (k) ∝
k if k ≪ k0
k
if k ≫ k0
−3
(1.3)
with k0 = 2πreq being the wave number of the horizon size at the beginning of
matter domination. As the size of the horizon req was very small and increases
with time, the smallest structures were formed earlier in time.
From Eq. 1.2 one can then obtain the dependency of the peak in the power
spectrum (k0) with the matter density:
k0 =
√
p
2 2πH0 Ωm,0
3/2
aeq
,
(1.4)
having into account that aeq = Ωr,0 /Ωm,0 . Then, a measurement of k0 would
provide an independent measurement of Ωm, 0.
The first succesful experiments in that direction have been carried out with
the Two-Degree Field Galaxy Redshift Survey and the Sloan Digital Sky Survey. By
using clustering measurements which used 2–point correlation functions, these
experiments have found that the total density of matter in the Universe, needed
to form the observed structures is Ωm,0 = 0.24 ± 0.02.
From the observed 4 He abundance in the local Universe and the deuterium
abundance derived from absortion systems in the spectra of high redshift
quasars, the Big–Bang nucleosynthesis predicts a fraction of baryons in the
Universe of Ωb = 0.037 ± 0.009, roughly an order of magnitude smaller than the
matter density needed to form the observed structures.
Direct observations of stars and cold gas in galaxies yield densities of Ω∗+gas ∼
0.0024, which accounts only for ∼ 10% of the baryon density expected from the
Big–Bang nucleosynthesis predictions. The problem of where are the missing
baryons is still an open question in modern Astronomy, but we believe that
they are in the warm/hot gas in the intergalactic medium.
When taking together all the evidence, direct and indirect, it is clear that in
order to reproduce the observed hierarchical structure growth in the Universe
and the dynamics of galaxies and clusters of galaxies we need to resort to the
dark matter. This dark matter has to account for roughly 80% of the matter
in the Universe.
INTRODUCTION
1.1.3
7
Galaxy formation in a CDM–dominated universe
After the radiation–dominated era, dark matter overdensities were able to
collapse faster as they only had to counteract the expansion of the Universe.
The first of these overdensities, which I will call haloes hereafter, were relatively
small and grew through the accretion of other haloes. Still, new small haloes
kept forming and being accreted by larger haloes.
As gravity is dominant interaction at these scales and dark matter dominates
gravitational processes (remember that 80% of the matter in the Universe is in
a non–luminous form), the baryonic content of the haloes follows the behaviour
of the dark matter. On the other hand, baryons suffer electromagnetic
interactions, so they act in some sense in a different way as the dark matter.
Baryons which could efficiently cool collapse into a dense core in the center of
the DM halo; this is what we usually call ‘galaxy’.
When the haloes merge, the galaxies in their center merge as well, therefore
galaxy merging is expected to be a key process in the formation and evolution
of galaxies. Furthermore, if our cosmological theories are correct, we should
be able to trace the growth of dark matter haloes by the observation of galaxy
mergers. In particular, mergers of galaxies of approximately equal mass are
predicted to be relatively rare but easy to detect, while the much more common
mergers between galaxies of very different mass are expected happen constantly
but are much more difficult to observe.
1.1.4
The Λ-CDM paradigm
In the last ∼10 years we have changed our view of the Universe. The
experiments studying the redshift–distance relations from type Ia supernovae
(Riess et al. 1998; Perlmutter et al. 1999) have discovered that our Universe
is not only not decreasing the rate of expansion, but it is accelerating.
The responsible for this acceleration is believed to be some sort of dark
energy, which has the particularity of producing a negative pressure (althoug
see Aguirre 1999; Robaina & Cepa 2007for a discussion of the systematic
uncertainties). The Cosmic Microwave Background (CMB) has also been
extensively studied in this period, specially thanks to the observations from the
Wilkinson Microwave Anisotropy Probe (WMAP, Spergel et al. 2007), which
have pointed to a flat Universe with a significant fraction of dark matter in a
8
CHAPTER 1
non-baryonic form. Every cosmology which takes into account the existence of
dark energy (in whatever exotic from) and dark matter is usually labelled as a
ΛCDM cosmology.
It is expected from cosmological simulations that dark matter haloes grow in
size as the Universe ages by means of mergers of smaller units, building up the
DM distribution we can infer today from wide-area galaxy surveys. Since the
DM largely dominates the clustering in the Universe, it is reasonable to imagine
that galaxy mergers, the topic of this thesis, will follow the trend imposed by
the merging of DM haloes. As the baryons are interacting particles, they are
subject to more processes than the DM, whose behaviour is largely governed
by gravity, as evidenced by the lack of electromagnetic emission3 . Friction,
collisions and other physical processes cause the exact behaviour of a galaxy
merger to deviate from that of the DM, specially in the latest phases of the
interaction, when the two dark matter haloes have already merged.
Figure 1.4 Dark matter distribution in the Universe as predicted by the Millennium
Simulation (Springel et al. 2005)
As we lack the capability of observing DM directly, an important fraction of
our knowledge about DM behavior comes from simulations. For the purpose of
understanding the physics of DM halo mergers, even when extremely successful
3
Also, recent studies have found very low upper limits for dark matter self-interaction cross–sections in
the cluster–cluster collision known as the ‘Bullet Cluster’ (Markevitch et al. 2004).
INTRODUCTION
9
numerical simulations as the Millennium Simulation (Springel et al. 2005) have
been produced, the computation of huge realizations with enough resolution is
prohibitevely expensive. A strong alternative is to run semi-analytical models
(SAM), which often base the treatment of the DM in the extended PressSchechter formalism (Press & Schechter 1974; Bond et al. 1991). The basic
idea of this formalism is the description of the mass history of particles in
a hierarchical Universe with gaussian initial perturbations, and specifically
it aims to provide the conditional mass function. It has been proved that
merger rates and halo survival times within this formalism agree with N-body
simulations (Lacey & Cole 1993, 1994), making SAMs a valuable tool for the
study of mergers in the Universe.
1.2
Galaxy Evolution: An Empirical View
One particularly interesting parameter space concerning studies of galaxies
is the one involving optical color and stellar mass (or luminosity). It has
been known for some time that the distribution of nearby galaxies in such a
diagram shows a bimodality: red galaxies appear in a relatively tight sequence
(for obvious reasons known as red sequence) while blue galaxies show a wider
dispersion and appear in the so-called blue cloud (e.g. Blanton et al. 2003).
Other studies, like Bell et al. (2004) or Taylor et al. (2009) have found that
such a bimodality is already in place at earlier times, in particular out to z ≃ 2.
Those works (e.g., Borch et al. 2006) also show that the global stellar density
of the Universe has grown by a factor of ∼ 2 in the roughly 8 Gyrs between
z ≃ 1 and z = 0 (see Fig. 1.6).
The intriguing aspect is that the stellar density corresponding to blue cloud
galaxies (where new stars are expected to be formed) has barely been altered,
implying that most of that growth has been produced in the red sequence
(Bell et al. 2004; Borch et al. 2006; Faber et al. 2007). This result has a
strong implication: in order to reproduce the observed evolution in the colorstellar mass diagram, galaxies have to migrate from the blue cloud to the red
sequence by means of a process in which the star formation (SF) in the galaxies
is quenched (Bell et al. 2007; Walcher et al. 2008)
It has also been observed that galaxies in the Universe are forming less and
less stars with time. In the time interval since z ∼ 1 the star formation density
has decreased by one order of magnitude (Madau et al. 1996; Lilly et al. 1996).
10
CHAPTER 1
Figure 1.5 Color–magnitude diagram of galaxies. Top panel: Galaxies from the SDSS.
Bottom panel: Galaxies from the DEEP2 survey. A clear bimodality is present at both
redshifts. Red galaxies tend to be found in a relatively narrow region while blue galaxies
show a larger dispersion. Figure taken from Blanton (2006)
Nowadays, we know that the bulk of the star formation takes place in the disk
of undisturbed blue galaxies Hammer et al. (2005); Bell et al. (2005). If the
majority of the stars are formed in disk galaxies at different redshifts and the
number density of such objects is approximately constant, this implies that
the evolution of the cosmic SFR is not only a consequence of the transition of
galaxies from the blue cloud to the red sequence, but also star forming galaxies
are also forming less and less stars as the Universe ages.
An independent point of view has been provided by the work from Noeske et al.
(2007), who have shown how the star formation among star-forming galaxies
scales both with the stellar mass and redshift. This is, at a given redshift, the
more massive star-forming galaxies are forming stars faster than lower mass
counterparts, and at a given mass, star-forming galaxies did form stars faster
at higher redshift.
Another interest aspect is the evolution of the massive galaxy population, which
seems to have increased considerably since z ∼ 1. Observations have found a
significant increase in the number density of L ≥ L∗ red galaxies since z = 1,
although systematic uncertainties in the photometry of L > 2 − 3L∗ galaxies
INTRODUCTION
Figure 1.6 Rest–frame B band luminosity
density as a function of redshift. Points show
different measurements while the solid line
shows the expected luminosity density evolution taking into account passive luminosity
evolution. The stellar-mass in red galaxies
needs to increase by a factor of 2 since z = 1.
Brown et al. (2007).
11
Figure 1.7 Star formation history of the
Universe. Data points show star formation
density. The SFR density has decreased by
one order of magnitude from z = 1 to z = 0.
Figure taken from Hopkins & Beacom (2006)
makes difficult the study of the evolution of such rare objects (Brown et al.
2007). As, by definition, quiescent galaxies do not form stars, the growth
of the massive end of the red sequence has to be caused either in a process
in which massive blue galaxies are rapidly transformed into red systems by
the quenching of their star formation or in a process which accounts for the
formation of massive galaxies from adding–up the stellar masses of lower mass
objects.
Overall, we believe that galaxies are being forced to migrate from the blue
cloud to the red sequence by some quenching mechanism (or mechanisms),
star-forming galaxies are rapidly decreasing their star formation rate and the
number of massive, quiescent galaxies is increasing.
12
1.2.1
CHAPTER 1
Colors and shapes: Two related problems?
When studying in depth large samples of galaxies in the local Universe, many
relations between different photometric and structural properties arise. A good
example are the results from Blanton et al. (2003), who found relations between
color, magnitude, central surface brightness and structure of the galaxies (see
Fig. 1.8). Focusing on the relations between color and structure, expressed as
the Sersic index of the light profile, it is evident that red galaxies tend to be
spheroidal (or at least concentrated) as indicated by their high Sersic index,
but also, spheroidal galaxies tend to be red in their optical colors. Moreover,
recent work from van der Wel et al. (2009) has shown that in the local Universe,
all quiescent massive galaxies are round. It is not ilogical to think, then, that
the process wich quenches the star formation could be related to the process
by which galaxies transform from disks to spheroids.
In what concerns the migration from the blue cloud to the red sequence, this
is, for the quenching of the star formation, several mechanisms have been
held responsible. Supernova and active galactic nuclei (AGN) feedback could
produce such a behaviour through their impact on the cold gas present in
the galaxy (Silk & Rees 1998). The total energy injection by those objects
could be enough to heat up the gas or even to expel it from the galaxy,
having the net effect of preventing the birth of new stars. Gas-heating by
virial shocks of gas infalling in a massive dark matter halo (Birnboim & Dekel
2003) or gravitational heating of the gaseous disk by clumpy mass infall (Dekel
& Birnboim 2008) could produce the same effect. In addition, environmentrelated processes like the different manifestations of Ram-pressure stripping
(stripping of cold gas from the disk or hot gas from the halo, preventing
subsequent cooling and infall) could also remove the cold gas from galaxies.
Some of these environment-related processes, like galaxy harassment could
produce the concentration of the surface brightness profile, and also the
accretion of cold gas from the cosmic web at z > 1 has been proposed to rapidly
form massive bulges in disk-like galaxies (Dekel & Birnboim 2008). Although
these processes can certainly produce the concentration of the light profile,
none of them has been proved to be capable of the formation of a massive,
symmetric elliptical galaxy.
INTRODUCTION
13
Figure 1.8 Relations between different properties of galaxies in the SDSS. g-r is the optical
color, µ the central surface brightness, n the sersic index and M the absolute magnitude.
1.3
The Role of Mergers in Galaxy Evolution
The first evidence for the impact of interactions on the global picture of galaxy
evolution can be traced to the times of the World War II. In a pioneering
work, Holmberg (1940) realized that the morphology of a galaxy depends on
the number of close companions:
“This simplified scheme of distribution of nebular types suggests strongly that the type of
an object is in some way dependent on the existence of physical companions. Furthermore,
it suggests that the separation of the companions has some bearing on the problem of type
[...]. Each passage of the components through pericenter poduces, however, certain tidal
effects, and consequently the orbits gradually contract [...]. The tidal effects corresponding
14
CHAPTER 1
to successive pericenter passages may result in gradual changes in the form and the size
of the nebula, just as the orbit is gradually contracted [...]. The following mechanism is
suggested for the transformation of types of nebulae belonging to a double (or multiple)
system, i.e., for the transformation of late spirals into early spirals or elliptical objects
[...].”
Early simulations by Holmberg (1941)4 and Toomre & Toomre (1972) showed
that collisions between disk-galaxies lead to remnants with properties similar
to spheroidal galaxies, and that idea has been repeatedly used since then to
explain the origin of massive galaxies, in good agreement with predicitons of
the Λ −CDM hierarchichal cosmology. With time, the idea that mergers of disk
galaxies lead to the formation of elliptical galaxies gained strength to the point
that is frequently invoked as the dominant (if not unique) process capable of
creating a massive, quiescent, truly red and dead, elliptical galaxy (van der
Wel et al. 2009).
Although it is clear that the orbits of stars in such collisions are ‘heated’ and
consequently randomized with the consequence of the transformation of disks
into ellipticals, the exact process by which the star formation is quenched
is still a matter of debate. Major mergers between gas-rich galaxies have
been traditionally expected to trigger starbursts (Mihos & Hernquist 1996a),
which could produce the depletion of the gas reservoir in a relatively short
timescale. Furthermore, the starburst will produce a relatively high number of
supernovae, commonly invoked to explain the heating of the cold gas, and the
feedback caused by the energy deposition on the interstellar medium (ISM)
by the AGN (which would be also triggered by the funnelling of gas to the
central region during the interaction) would have a similar effect Kauffmann
& Haehnelt (2000).
Independently of the exact mechanism responsible for the quenching of the star
formation activity it is clear that galaxy interactions involving blue, gas-rich
galaxies have the net effect of moving galaxies from the blue cloud to the red
sequence in a color-mass diagram (e.g., Ruhland et al. 2009; Bell et al. 2007).
An obvious consequence of any galaxy merger is the creation of a remnant
more massive than the individual progenitors, this is, the creation of a more
massive galaxy without the need of further star formation.
4
In 1941 Erik Holmberg performed what is believed to be the first N-body simulation applied to an
astronomical problem by using light-bulbes as the mass particles and the light intensity on each light-bulb
as a tracer of the gravitational force.
INTRODUCTION
15
Figure 1.9 Gas-rich galaxy mergers in the local Universe. From top left to bottom right:
Arp 220, The Antennae Galaxies (NGC 4038/NGC 4039), The Bird (IRAS 19115-2124),
Stephan’s Quintet (NGC 7317, 18a, 18b, 19, 20).
In addition to mergers involving blue galaxies, dry5 mergers between passive
galaxies are yet another mechanism that could shape the color-mass diagram.
As the galaxies involved in such an interaction are already quenched, and
by definition red, they do not produce migration from the blue cloud to the
red sequence, but re-shape the latter by moving objects within that sequence
causing a tilt in the massive end and a decrease of the color dispersion (Skelton
et al. 2009). Observational evidence of those interactions (van Dokkum 2005;
Bell et al. 2006a) points to an scenario in which this process is very relevant
for the formation of the most massive elliptical galaxies in the Universe.
Unfortunately, even when some studies have tried to quantify which fraction of
red sequence/massive galaxy growth is caused by galaxy merging (e.g., Bundy
et al. 2009), uncertainties related to number statistics and merging timescales
make necessary a deeper study of the problem.
5
In this context, ‘dry’ refers to the absence of cold gas, and therefore dissipation in the form of star
16
CHAPTER 1
Figure 1.10 Dissipationless (dry) mergers. The absence of prominent tidal features make
these objects extremely difficult to find.
Another interesting aspect of galaxy merging is, as opposite to the SF
quenching, the already mentioned SF enhancement that they produce for a
short period when two gas-rich galaxies interact (Mihos & Hernquist 1996a;
Cox et al. 2008). Early studies of ultraluminous infrared galaxies (ULIRGS) in
the local Universe found that ∼ 90% of such extreme starbursts present evidence
of a recent merger (Sanders et al. 1988), but the (wrong) interpretation that
mergers could be important for the SFR in a cosmological context came a
few years later. In the late 90’s, it was noted that the strong decrease of
the cosmic SFR density between z = 1 and z = 0 (Lilly et al. 1996, Madau
et al. 1996) was not dissimilar from the relatively rapid drop in merger rate
inferred (at that time) from close pairs and morphologically-selected mergers
(Le Fevre et al. 2000). If much of the star formation at z > 0.5 were triggered
by merging, the apparent similarity in evolution between SFR and merger rate
would be a natural consequence. More recently, studies about the fraction of
SF in morphologically-selected interacting and merging galaxies at intermediate
formation
INTRODUCTION
17
redshifts z < 1 have demonstrated that, in fact, the bulk of star formation is in
quiesciently star-forming disk-dominated galaxies (Hammer et al. 2005, Bell
et al. 2005).
Still, even when we know that galaxy mergers are not the main driver of the
evolution of the cosmic SFR density, there are some key questions unanswered,
like the exact amount of stellar mass that galaxy mergers add to the global mass
budget of the Universe or how enhanced is the SFR in interacting galaxies when
compared to objects not undergoing an interaction.
1.3.1
Looking for galaxy mergers
Overall, mergers are, potentially, an important ingredient in the recipe of
galaxy evolution, so finding the exact rate at which galaxies merge is crucial
to understand the global picture. Measurements of the merger rate (number
of mergers per unit time or equivalently, number of mergers that a galaxy
goes through in a given time) have been pursued abundantly in the literature
following different methodologies and finding a variety of results, although in
the latest times the results tend finally to converge.
The main problem in order to measure a merger fraction is the identification
of those objects. The process of merging is long, and the galaxies undergoing
a merger go through a variety of phases from the early state when they ‘feel’
the gravitational potential of the companion for the first time to the final stage
in which they have coalesced and the remnant presents an spheroidal, relaxed
shape.
There are mainly two approaches to find galaxy mergers: the first one is the
the morphological analysis of the interacting system, which typically generates
clear signs of gravitational interaction like tidal tails, bridges and shells6 and
the second is the identification of the individual galaxies as a close pair before
coalescence.
A number of uncertainties come into the game of the morphological analysis.
The strength of the tidal features is strongly shaped by structural parameters
as the bulge-to-total ratio (B/T), gas fraction or mass ratio between the two
galaxies. Orbital parameters like relative orientation of the disks or impact
6
Although the morphological identification of dissipationless mergers is extremely hard because of the
low surface brightness of tidal tails and bridges.
18
CHAPTER 1
parameter, are also going to affect strongly the tidal debris (Di Matteo et al.
2007; Cox et al. 2008). The selection of the sample plays also a key role in
the merger fraction found, as luminosity-selected samples (opposed to massselected) are more sensitive to issues like M/L ratio variations because of purely
passive luminosity evolution or because of merger-triggered SF.
Figure 1.11 Recent galaxy merger fractions estimated from galaxy morphologies. Dottedline region shows the estimate for major mergers-only from Jogee et al. (2009). Figure
taken from Lopez-Sanjuan et al. (2009).
In Fig. 1.11 I show a compilation of recent results of galaxy merger fractions
estimated through morphology. A variety or results have been found for both
the zeropoint of the merger fraction and its evolution with redshift. This large
spread between different studies is too big to be caused by cosmic variance, and
it is mainly a result of different sample selection plus different identification
techniques. To make it even worse, it is extremely expensive, in terms of
manpower, to visually classify samples of thousands or tens of thousands of
galaxies, and automated galaxy classifiers like CAS (Concentration, Asymmetry and Clumpiness, Conselice et al. 2003) or Gini/M20 (Lotz et al. 2004) at
intermediate and high redshift usually give as an output merger fractions higher
than the visually-classified merger fractions7 . In a recent work (Jogee et al.
2009) we have found that this is mainly due to the misclassification of lopesided
or slightly irregular, non interacting disk galaxies. When one puts together
7
The reader should remember that automated methods have been tuned to reproduce the visual
classifications in the local Universe.
INTRODUCTION
19
the poor performance of automathed classifiers, the systematic uncertainties
related to orbital parameters or galaxy structure and the lack of information
about the progenitor galaxies, the reliability of galaxy morphologies in order
to extract physical information is in jeopardy.
The other widely-used method to find galaxy mergers, is the identification of
close galaxy pairs which are in an early stage of the interaction. The main
advantage with respect to morphological studies is that the identification of
interacting systems does not depend on orbital or structural parameters and
that progenitor galaxies can be studied in detail. On the other hand, projection
effects (galaxies which are relatively close on the plane of the sky but separated
by large distances in the line-of-sight dimension) have been a concern for the
community. This concern about projection effects has given more reliability to
pair fractions from spectroscopic surveys, which produce, when compared to
spectro-photometric redshift surveys, higher-quality redshift determinations.
In the last years, the projection effect issue in the spectro-photometric redshift
surveys has been overcome by the use of two-point correlation function
techniques applied to the study of close physical pairs, which allow astronomers
to use wide-area surveys without having to deal with systematic effects
present in spectroscopic surveys like fiber collisions, or in general, instrumental
problems caused by the small distance (∼ galaxy size) between the two galaxies
on the focal plane (Masjedi et al. 2006; Bell et al. 2006b; Masjedi et al. 2008).
1.4
Galaxy Surveys
In order to study the galaxies in the Universe, one should make use
of information about all the components of a galaxy.
Stars, gas, dust
and accelerated particles like electrons and cosmic rays produce different
electromagnetic spectra, and force the astronomers to sample the global spectra
of the galaxies in as many windows of the spectra as possible.
Stars emit most of their light in the ultraviolet (λ . 3800Å), visible (3800Å7500Å) and near-infrared (7500Å-6µm). Dust absorbs part of the UV radiation
produced by massive stars and AGNs and reemits it as mid and far-infrared
(6µm - 1mm). Cold gas like molecular hydrogen or CO is detected in the
radio wavelenghts, as well as the non-thermal processes involving synchrotron
radiation at low energies used to trace particles accelerated by AGNs or star
20
CHAPTER 1
forming regions. On the high energy side, some galaxies also display an
spectra ranging from the soft X-rays (a few keV) to extremely energetic TeV,
again produced by particles accelerated by an AGN or by processes involving
extreme objects like pulsars, micro-quasars or wolf-rayet stars through physical
mechanisms like inverse-compton and p-p and p-γ interactions.
Figure 1.12 Multiwavelegth view of a tile in the GEMS field. Left: In UV as seen by Galex.
Center: In visible as seen by HST. Right: In 24 µm as seen by Spitzer.
It’s clear that the observations needed are strongly shaped by the question
one wants to answer. The experiments I’ll carry out in the next chapters will
make use, directly or indirectly, of visible and NIR light to characterize the
stellar populations, UV and mid-infrared to study the SF properties (through
the tracking of the dust-obscured and unobscured light from young stars) and
of X-rays to track the contribution of AGNs to the heating of dust.
1.4.1
COMBO-17, GEMS, STAGES and COSMOS
The first step in order to perform an appropiate study on galaxy evolution is to
get information about the spectra of galaxies. It’s extremely important to know
the redshift of galaxies, as a proxy for the age of the Universe at the time the
radiation (this is, the information) was emited. There are two options, either
perform a spectroscopic survey to extract high resolution information and get
an accurate redshift measurement or to perform a photometric survey, in which
the redshift information would be acquired by the fitting of the photometric
points to a set of template spectral energy distributions (SED). The first
INTRODUCTION
21
approach has the clear advantage of the resolution, but the disadvantage of
being extremly expensive in terms of telescope time, as one would have to
integrate for long times in order to get an appropiate signal to noise and will
be limited by the number of spectra which can be obtained simultaneously by
current spectrographs placed in large enough telescopes (needed to get spectra
at intermediate and high z) as VIMOS (VLT), FORS (VLT) or DEIMOS
(KECK).
In this thesis I’ll work with spectro-photometric redshift surveys like COMBO17 (Wolf et al. 2003, 2004). COMBO-17 was designed to give accurate photo-z’s
(∆z/(1 + z) ∼ 0.03 down to mR = 23.5) and stellar masses (Borch et al. 2006).
Observations in 5 broad bands and 12 medium bands were performed in 5
fields, giving a total of 1.25 square degrees, of which two or three fields will be
used for the work presented here.
Two of the COMBO-17 fields (ECDFS and A901/2) have been also observed
with the Hubble Space Telescope (HST) in the projects GEMS (Galaxy Evolution from Morphologies and SEDs) and STAGES (Space Telescope A901/902
Galaxy Evolution Survey) with the aim to study galaxy morphologies. GEMS
(Rix et al. 2004) has imaged 0.25 square degrees in F606W and F850LP bands,
roughly corresponding to V and Z band respectively, down to mAB (F 606W ) =
28.3(5σ) and mAB (850LP ) = 27.1(5σ). It’s still the biggest color galaxy evolution
survey performed with HST and has produced more than 8000 matches for
COMBO-17 galaxies. If GEMS was targeting the evolution of galaxy properties
with redshift, STAGES (Gray et al. 2009) main aim is the study of the
environmental dependencies of those properties. The 0.25 square degree field
(in F606W band) encompasess an extremely complex multicluster system which
includes the galaxy clusters A901 and A902, as well as the groups A901b and
the South-West group. In §2 I’ll make use of these data, together with Spitzer
mid-IR photometry in order to study the effect of galaxy interaction on the
SFR of galaxies.
COSMOS (Scoville et al. 2007) is a galaxy survey wich comprises multiwavelength information from X-rays to radio including the biggest single-band
mosaic taken by HST. Its large area makes of COSMOS an ideal data sample
in order to perform many studies of galaxy evolution, specially those involving
morphologies of galaxies at intermediate redshifts. In §4 I’ll use COSMOS data
in order to study the impact of major mergers on the evolution of massive, red
spheroidal galaxies.
22
CHAPTER 1
1.5
Layout of the Thesis
It is clear that galaxy mergers affect the build-up of stellar mass in galaxies in
two main ways: the formation of new stellar mass (i.e., merger-triggered star
formation), and the rearrangement of already-existing stars into more massive
galaxies with (potentially) different structures. I study both of these modes of
growth here.
1.5.1
Stars formed by galaxy interactions
As I have explained, the role played by galaxy mergers on the star formation
activity of galaxies is crucial, as they can both enhance the star formation rate
in the inicial phases and suppress it in a more advance phase. Early studies on
extremely bright IR galaxies in the local Universe (Sanders et al. 1988) had a
considerably impact on the astronomical community, and for many years the
idea of a cosmic star formation history driven by merger activity was seriously
considered. More recently, studies showing that galaxy mergers host less than
30% of the star formation density at z < 1 have disproved such a scenario, but
still, if galaxy interactions are directly responsible for all that star formation
that would have large consequences on the mass distribution between the blue
cloud and the red sequence. As major mergers are expected to lead to red
spheroidal galaxies, an extra 30% of stellar mass would imply a dominant role
of the quenching of blue galaxies over the build–up of mass from mergers
between already existent red galaxies. Moreover, as the merger–induced
starburst is expected to be centrally concentrated, the color, surface brightness
and alpha–enhancement8 of merger remnants should show strong gradients.
In Chapter 2 I will use photometric redshifts, stellar masses and UV SFRs
from COMBO-17, 24µm SFRs from Spitzer and morphologies from two deep
Hubble Space Telescope (HST) cosmological survey fields (ECDFS/GEMS and
A901/STAGES) to study the enhancement in SFR as a function of galaxy
separation and find which fraction of star formation is directly triggered by major
galaxy interactions. In Chapter 3 I will also produce a toy–model, based on
the Millenium Simulation, which will be used to test the statistical tools that are
frequently applied to the study of the enhancement of galaxy properties as a
8
Excess of α-elements with respect to iron expected to be present if the timescale for the star formation
is shorter than ∼ 1 Gyr, the time needed for type Ia supernovae to enrich the interstellar medium with
iron.
INTRODUCTION
23
function of galaxy separation.
1.5.2
The growth of the most massive galaxies through merging
The stellar mass in galaxies grows through the formation of new stars from
cold gas (the mode we study in Chapters 2 and 3), and through the addition of
already-formed stars to a galaxy through mergers. A cursory investigation of
the properties of low-mass disk-dominated galaxies leads one to expect that the
accretion of gas and formation of new stars is the dominant mode of growth for
these low-mass, disk-dominated, typically rather gas-rich galaxies. Yet, highmass galaxies tend to lack cold gas, making growth through star formation less
relevant. For these galaxies, the main mode of growth may be through galaxy
merging.
Unfortunately, there are very few observational studies trying to asses the
real impact of galaxy mergers in the creation of massive red spheroids, and
from those (e.g., Bundy et al. 2009), no conclusive evidence can be inferred.
In Chapter 4 I will quantify the impact of galaxy mergers on the evolution of
massive red galaxies. I will measure the fraction of galaxies in close (r < 30 kpc)
physical pairs at z < 1.2 by using robust 2–point correlation function statistics
on a sample of ∼ 18000 M∗ > 5 × 1010 galaxies drawn from the COSMOS and
COMBO–17 surveys and I will compare the observed evolution in the number
density of very massive red galaxies with the evolution implied by the measured
merger rate.
Chapter 2
SFR Enhancement in Galaxy Interactions
In the previous chapter I have presented the open issues in the relation between
galaxy mergers and SFR. I will extend now the motivations for the study of
such relation and the possible implications.
Observational evidence from a variety of angles indicates that galaxy interactions and mergers of galaxies can lead to dramatically-enhanced star formation
(Sanders et al. 1988; Barton et al. 2000; Lambas et al. 2003; Barton et al. 2007).
This appears to hold true at all redshifts where one can recognize mergers
through galaxy morphologies (z ≤ 1 with rest-frame optical morphologies;
Melbourne et al. 2005; Hammer et al. 2005; 1 ≤ z ≤ 3 using less certain
UV morphologies Chapman et al. 2004). Ultra-luminous infrared galaxies
(ULIRGs), representing the highest-intensity star formation events at low
redshifts, are almost invariably hosted by merging galaxies (Sanders et al.
1988). For a number of applications the quantity of interest is the average
enhancement in star formation (SF) triggered by merging (ensemble average
over the population of major mergers/interactions, or equivalently, temporal
average over major merger events during a merger lifetime), not the highintensity tail (e.g., Barton et al. 2000; Lambas et al. 2003; Lin et al. 2007; Li
et al. 2008; Jogee et al. 2009). Barton et al. (2007) carefully quantified the
star formation rate (SFR) enhancement in mergers in low-mass halos at low
redshift, using the Two-Degree Field Galaxy Redshift Survey (Colless et al.
2001). They found that roughly 1/4 of galaxies in close pairs (separated by
< 50 kpc) in low-mass halos with MbJ < −19 have SFR enhancements of a factor
of five or more1 .
It has also been noted that the strong decrease of the cosmic SFR density
1
This corresponds roughly to a mass cut of 5 × 109 M⊙ , assuming a stellar M/LbJ ∼ 1, appropriate for
a star-forming blue galaxy with a Chabrier (2003) stellar IMF.
25
26
CHAPTER 2
between z = 1 and z = 0 (e.g., Lilly et al. 1996; Madau et al. 1996; Hopkins
2004; Le Floc’h et al. 2005) was not dissimilar from the relatively rapid drop
in merger rate inferred (at that time) from close pairs and morphologicallyselected mergers (Le Fèvre et al. 2000). If much of the star formation at z > 0.5
were triggered by merging, the apparent similarity in evolution between SFR
and merger rate would be a natural consequence. More recently, studies of the
fraction of star formation in morphologically-selected interacting and merging
galaxies at intermediate redshifts z < 1 have demonstrated that, in fact, the
bulk of star formation is in quiesciently star-forming disk-dominated galaxies
(Hammer et al. 2005; Wolf et al. 2005; Bell et al. 2005; Jogee et al. 2009).
Similarly, it has long been argued that early-type (elliptical and lenticular)
galaxies are a natural outcome of galaxy mergers (e.g., Toomre & Toomre
1972; Schweizer & Seitzer 1992). In any hierarchical cosmogony mergers are
expected to play a large role; a wide range of work — observations of the
increasing number density of non-star-forming early-type galaxies from z = 1
to the present (Bell et al. 2004; Brown et al. 2007; Faber et al. 2007), the
kinematic and stellar populations of local early-type galaxies (Trager et al.
2000; Emsellem et al. 2004), or the joint evolution of the stellar mass function
and star formation rates of galaxies (Bell et al. 2007; Walcher et al. 2008;
Pérez-González et al. 2008) — has given support to the notion that at least
some of the early-type galaxies assembled at z < 1 have done so through galaxy
merging. In such a picture, the average SFR enhancement from merging is
of interest for interpreting the SF and chemical enrichment history of earlytype galaxies, inasmuch as it gives an idea of what kind of fraction of stars
in present-day early-type galaxies we can expect to have formed in the burst
mode, and what fraction we can expect to have formed in a quiescent mode in
the progenitor galaxies.
Direct observational constraints on the enhancement in SFR caused by merging
provide an important calibration for modeling triggered star formation in
cosmologically-motivated galaxy formation models. Hydrodynamic simulations
of interacting galaxies in which gas and star formation are explicitly modeled
have demonstrated that torques resulting from the merger can efficiently
strip gas of its angular momentum, driving it to high densities and leading
to significant enhancement in star formation (e.g., Barnes & Hernquist
1996; Mihos & Hernquist 1996b; Cox et al. 2006, 2008; Di Matteo et al.
2007). However, state-of-the-art cosmological simulations lack the dynamic
range to accurately simulate the internal structure of galaxies in significant
SFR ENHANCEMENT IN GALAXY INTERACTIONS
27
volumes, so estimates of the global implications of merger-driven star formation
enhancement have had to rely on semi-analytic calculations (e.g. Somerville
et al. 2001; Baugh et al. 2005; Somerville et al. 2008). Furthermore, as the
progenitor properties play a key role in the simulated SFR enhancements
(e.g., Di Matteo et al. 2007; Cox et al. 2008), inaccurate progenitor property
values (e.g., incorrect gas fraction or internal structure) will lead to incorrect
estimates for the average fraction of SF in mergers even if the SF in each
individual merger were modeled perfectly.
Therefore, to constrain galaxy evolution models and to understand the physical
processes responsible for the main mode of star formation at z < 1, it is
of interest to determine observationally the typical enhancement2 in SFR
averaged over the duration of the entire major (stellar-mass ratio between
1:1 and 1:4) galaxy merger or interaction and to constrain the overall fraction
of SF triggered by mergers/interactions at intermediate redshift. In a recent
work (Jogee et al. 2009) we focus on the rate of merging and also present a
preliminary exploration of the average change in the SFR caused by late-stage
major and minor merging (see also Kaviraj et al. 2009), finding an average
mild enhancement within the restrictions imposed by the sample size. In this
chapter I present a statistically-robust analysis of the properties of star-forming
galaxies at 0.4 < z < 0.8 including all relevant merger phases and aimed at
providing a satisfactory answer to two key questions. What is the average
enhancement in star formation rate as a function of galaxy pair separation
compared to their SFR before the interaction? What fraction of star formation
is directly triggered by major mergers and interactions?
There are a number of conceptual and practical challenges in such an
experiment. Enhancements in SFR produce both a boost in luminosity, but
also increase dust content and extinction. At a minimum, one therefore needs
dust-insensitive SFR indicators. In addition, simulations have indicated that
SF can be enhanced at almost all phases of an interaction from first passage
through to after coalescence (e.g., Barnes & Hernquist 1996; Di Matteo et al.
2007); although close pairs will inevitably include some fraction of galaxies
before first pass and galaxies with unbound orbits. Therefore, an analysis
needs to include both close pairs of galaxies (those before coalescence) and
morphologically-classified mergers (primarily those near or after coalescence).
Morphological classification is not a straightforward art (see Jogee et al. 2009for
2
When I refer to SFR enhancement, I define this as the ratio of SFR in some subsample (e.g., close
pairs) to the average SFR of all systems in that mass bin.
28
CHAPTER 2
a comparison between automated classifications and visual morphologies), even
in ideal cases (Lisker 2008). Finally, galaxy mergers are rare and short-lived,
necessitating large surveys to yield substantive samples of mergers.
In this work, I address these challenges as far as possible (see also Lin et al.
2007 and Li et al. 2008). I use estimates of redshift and stellar mass from
the COMBO-17 survey (Wolf et al. 2003; Borch et al. 2006) to define and
characterize the sample. Stellar mass selection should limit the effect of
enhanced star formation and dust content on the sample definition. I use SFR
indicators that are constructed to be dust extinction insensitive, by combining
ultraviolet (UV; direct, unobscured light from young stars) and infrared (IR;
thermal emission from heated dust, powered primarily by absorption of UV
light from young stars) radiation (Bell et al. 2005). Finally, I study a very
well-characterized sample of galaxy pairs at 0.4 < z < 0.8 using weighted
projected two-point correlation functions (Skibba et al. 2006; Li et al. 2008),
supplementing them at very small separations < 15 kpc with very close pairs or
merger remnants morphologically selected from two wide HST mosaics, GEMS
(Rix et al. 2004) and STAGES (Gray et al. 2009), in an attempt to account for
all stages of galaxy interactions.
The plan of this chapter is as follows. In §2.1 I discuss the data and the
methods used to estimate the stellar masses and the SFRs. In §2.2 I describe
the sample selection and the method used for the analysis. In §2.3 I present
my estimates of the enhancement in SFR as a function of projected separation.
In §2.4, I compare with previous observations, constrain the fraction of SF
triggered by major mergers and interactions at 0.4 < z < 0.8, and compare with
simulations of galaxy merging. Finally in §2.5 I summarize the main findings
of this chapter. All the projected distances between the pairs used here are
proper distances. I assume H0 = 70 km s−1 Mpc−1 , ΩΛ0 = 0.7 and Ωm0 = 0.3.
2.1
2.1.1
The Data
COMBO-17. Redshifts and stellar masses
COMBO-17 has to date fully surveyed and analyzed three fields to deep limits
in 5 broad and 12 medium pass-bands (Extended Chandra Deep Field South
(ECDFS), A901/2 and S11, see Wolf et al. (2003) and Borch et al. (2006)).
SFR ENHANCEMENT IN GALAXY INTERACTIONS
29
Using galaxy, star and quasar template spectra, objects are classified and
redshifts assigned for ∼ 99% of the objects to a limit of mR ∼ 23.5 (Wolf
et al. 2004). The photometric redshift errors can be described as
σz
∼ 0.007 × [1 + 100.8(mR −21.6) ]1/2 ,
1+z
(2.1)
and rest frame colors and absolute magnitudes are accurate to ∼ 0.1 mag
(accounting for distance and k-correction uncertainties). The astrometry is
accurate to ∼ 0.1” and the average seeing is 0.7”. It is worth noting that
Eq. 2.1 leads to typical redshift errors of σz ≃ 0.01 for bright (mR < 21) and
σz ≃ 0.04 for faint (21 < mR < 23.5) galaxies in the 0.4 < z < 0.8 interval.
The stellar masses were estimated in COMBO-17 by Borch et al. (2006)
using the 17-passband photometry in conjunction with a non-evolving template
library derived using the PEGASE stellar population model (see Fioc & RoccaVolmerange 1997, 1999) and a Kroupa et al. (1993) initial mass function (IMF).
Note that the results assuming a Kroupa (2001) or a Chabrier (2003) IMF
yield similar stellar masses to within ∼ 10%. The reddest templates have
smoothly-varying exponentially-declining star formation episodes, intermediate
templates have a contribution from a low-level constant level of star formation,
while the bluer templates have a recent burst of star formation superimposed.
The masses are consistent with those using M/L estimates based on a single
color (e.g., Bell et al. 2003). Random stellar mass errors are < 0.3 dex on a
galaxy-by-galaxy basis, and systematic errors in the stellar masses were argued
to be at the 0.1 dex level (see Borch et al. 2006 for more details). Bell & de
Jong (2001) argued that galaxies with large bursts of recent star formation
could produce stellar M/L values at a given color that are lower by up to
0.5 dex; this uncertainty is more relevant in this work than is often the case.
While this will inevitably remain an uncertainty here, I note that the Borch
et al. (2006) templates do include bursts explicitly, thus compensating for the
worst of the uncertainties introduced by bursting star formation histories. In
§2.3.1 I will explicitly study the impact that such uncertainties have on my
results.
In what follows, I use COMBO-17 data for two fields: the ECDFS and Abell
901/902 fields, because of their complementary data: deep HST/ACS imaging
from the GEMS and STAGES projects respectively (allowing an investigation
of morphologically-selected merger remnants and very close pairs), and deep
24µm imaging from the MIPS instruments on board Spitzer, required to measure
30
CHAPTER 2
obscured SF.
2.1.2
GEMS and STAGES HST imaging data
F606W (V-band) imaging from the GEMS and STAGES surveys provides
0.1” resolution images for my sample of COMBO-17 galaxies. Using the
Advanced Camera for Surveys (ACS; Ford et al. 2003) on board the Hubble
Space Telescope (HST), areas of ∼ 30′ × 30′ in each of the ECDFS and the
A901/902 field have been surveyed to a depth allowing galaxy detection to a
limiting magnitude of mAB
lim (F 606W ) = 28.5 (Rix et al. 2004; Gray et al. 2009;
Caldwell et al. 2008). These imaging data are later used to visually classify
galaxies, allowing very close pairs (separations < 2”) and merger remnants to
be included in this analysis. I choose not to use F850LP HST data available
for the GEMS survey in order to be consistent in my classification between the
two fields (only F606W is available from STAGES).
2.1.3
MIPS 24 µm , total infrared emission and star formation
rates
The IR observatory Spitzer has surveyed two of the COMBO-17 fields: a 1◦ ×0.◦ 5
scan of the ECDFS (MIPS GTO), and a similarly-sized field around the Abell
901/902 galaxy cluster (MIPS GO-3294: PI Bell). The final images have a
pixel scale of 1”.25/pixel and an image PSF FWHM of ≃ 6”. Source detection
and photometry are described in depth in Papovich et al. (2004) and catalogue
matching in Bell et al. (2007)3 . Based on those works, I estimate that my
source detection is 80% complete at the 5σ limit of 83µJy in the 24µm data
in the ECDFS for a total exposure of ∼ 1400 s pix−1 . The A901/902 field has
similar exposure time, but owing to higher (primarily zodiacal) background
the 5σ limit (80% completeness) is 97µJy, with lower completeness of 50% at
83µJy. I use both catalogs to a limit of 83µJy.
To include both obscured and unobscured star formation into the estimate of
the SFR of galaxies in my sample, I combine UV emission with an estimate
of the total IR luminosity in concert. As the total thermal IR flux in the
3
In this work, I are interested in SFR enhancements in close pairs of galaxies, where the closest pairs
may fall within a single Spitzer/MIPS PSF. Accordingly, in this work I choose to explore the total SFR in
the pair (avoids deblending uncertainties) rather than the individual SFR occuring in both galaxies.
SFR ENHANCEMENT IN GALAXY INTERACTIONS
31
8–1000µm range is observationally inaccessible for almost all galaxies in my
sample, I have instead estimated total IR luminosity from the observed 24µm
flux, corresponding to rest-frame 13–17µm emission at the redshifts of interest
z = 0.4 − 0.8. For this exercise, I adopt a Sbc template from the Devriendt et al.
(1999) SED library (Zheng et al. 2007b; Bell et al. 2007). The resulting IR
luminosity is accurate to a factor of . 2: local galaxies with IR luminosities
in excess of > 1010 L⊙ show a tight correlation between rest-frame 12–15µm
luminosity and total IR luminosity (Spinoglio et al. 1995; Roussel et al. 2001;
Papovich & Bell 2002) with a scatter of ∼ 0.15 dex. Furthermore, Zheng et al.
(2007b) have stacked luminous (LT IR > 1011 L⊙ ) z ∼ 0.7 galaxies at 70µm and
160µm , finding that their average spectrum is in good agreement with the Sbc
template from Devriendt et al. (1999), validating at least on average my choice
of IR SED used for extrapolation of the total IR luminosity.
I estimate the SFR by using both directly observed UV-light from massive stars
and dust-obscured UV-light measured from the mid-infrared. As in Bell et al.
(2005) I estimate the SFR ψ by means of a calibration derived from PEGASE
synthetic models assuming a 100 Myr-old stellar population with constant SFR
and a Chabrier (2003) IMF:
ψ/(M⊙ yr−1 ) = 9.8 × 10−11 × (LTIR + 2.2LUV ).
(2.2)
Here LTIR is the total IR luminosity and LUV = 1.5νlν,2800 is a rough estimate
of the total integrated 1216Å–3000Å UV luminosity. This UV luminosity
has been derived from the 2800Å rest-frame luminosity from COMBO-17
lν,2800 . The factor of 1.5 in the 2800Å-to-total UV conversion accounts for
UV spectral shape of a 100 Myr-old population with constant SFR, and the
UV flux is multiplied by 2.2 to account for the light emitted longwards of
3000Å and shortwards of 1216Å by the unobscured stars belonging to the
young population.
For all galaxies detected above the 83µJy limit, I have used the IR and UV to
estimate the total SFR. For galaxies undetected at 24µm , or detected at less
than 83µJy, I use instead UV-only SFR estimates.
32
CHAPTER 2
IR emission from AGN-heated dust
Possible contamination of mid-IR-derived SFRs from AGN heated dust is often
addressed by estimating the fraction of star formation held in X-ray detected
sources. In my case < 15% of the star forming galaxy sample were detected in
X-rays, in good agreement with the results found by i.e. Silva et al. (2004) or
Bell et al. (2005).
Yet, there are two limitations of this estimate. Firstly, this does not account
for any contribution from X-ray undetected Compton-thick AGN, which could
drive up the expected contribution from AGN in my sample. For example,
applying an mR = 24 cut to the sample of Alonso-Herrero et al. (2006), I
estimate the fraction of X-ray undetected AGN to be ∼ 30%, while Risaliti
et al. (1999) find ∼ 50% of local AGN to be Compton thick. On this basis, it is
conceivable that up to 30% of 24µm luminosity is from galaxies with AGN4 .
Secondly, even in galaxies with AGN, not all of the IR emission will come
from the AGN. Although the data does not currently exists to answer this
question conclusively, it is possible to make a rough estimate of the effect. In
order to estimate the fraction of mid-IR light that comes from the AGN (as
opposed to star formation in the host), I have made use of the results of Ramos
Almeida et al. (2007), who attempted to structurally decompose mid-infrared
imaging from Infrared Space Observatory for a sample of both Seyfert 1 and 2
AGN in the local Universe, some of which are very highly-obscured in X-rays.
Analyzing the results in Tables 2 and 3 of Ramos Almeida et al. (2007), I have
found that only a small fraction of the IR radiation at ∼ 10µm (in this chapter
I work at rest-frame 13-17µm ) comes from the central parts of the galaxies in
the Seyfert 2 population, finding a total contribution of:
AGN
FIR
= 0.26 ± 0.02.
total
FIR
(2.3)
This result should be viewed as indicative only: obviously, the systems being
studied will be different in detail from those in my sample. Furthermore,
the 10µm luminosities of the nuclei will be preferentially affected by silicate
AGN
total
absorption, making it possible that my value of FIR
/FIR
is a lower limit.
4
Although note that in a recent investigation of X-ray undetected IR-bright galaxies in the CDFS,
Lehmer et al. (2008) found that radio-derived (1.4GHz) SFRs agree with the UV+IR-derived ones. This
implies that the relative strength of any AGN component is not dominant when compared to the host
galaxy.
SFR ENHANCEMENT IN GALAXY INTERACTIONS
33
Despite the various levels of uncertainty, taking the different lines of evidence
together demonstrates that < 30% of the IR luminosity in my sample comes
from systems that may host an AGN, and that it is likely that < 10% of the
IR luminosity of my sample is powered by accretion onto supermassive black
holes. Given the other uncertainties in my analysis, I choose to neglect this
source of error in what follows.
2.2
Sample selection and method
The goal of this chapter is to explore the star formation rate in major
mergers between massive galaxies, from the pre-merger interaction to after
the coalescence of the nuclei. I chose a stellar mass–limited sample with
M⋆ ≥ 1010 M⊙ in the redshift slice of 0.4 < z ≤ 0.8 (see Fig. 1). This roughly
corresponds to MV = −18.7 for galaxies in the red sequence and MV = −20.1 for
blue objects. I only included galaxies that fall into the footprint of both the
ACS surveys GEMS and STAGES and of existing Spitzer data. These criteria
resulted in a final sample of 2551 galaxies.
Given the flux limit mR . 23.5 for which COMBO-17 has reasonably complete
redshifts (Wolf et al. 2004) I are complete for M∗ > 1010 M⊙ blue cloud galaxies
over the entire redshift range 0.4 < z < 0.8. For red sequence galaxies, the
sample becomes somewhat incomplete at z > 0.6, and at z = 0.8, the limit is
closer to 2 × 1010 M⊙ . I chose to adopt a limit of 1010 M⊙ in what follows, despite
some mild incompleteness in the red sequence, for two reasons. First, adopting
a cut of 2 × 1010 M⊙ across the whole redshift range reduces the sample size
by a factor of 30%, leaving too small a sample for the proposed experiment.
Second, the vast majority of the star forming galaxies are blue cloud galaxies
(83% of the star formation is occuring in blue galaxies), making the modest
incompleteness in the red sequence of minor importance.
Later, I will use a subsample composed of star forming galaxies. I will refer
to ’star formers’ as galaxies defined by having either blue optical colors or
having been detected in the MIPS 24µm band. I select optically-blue galaxies
adopting a stellar mass-dependent cut in rest-frame U − V color, following Bell
et al. (2007): U − V > 1.06 − 0.352z + 0.227(log10 M∗ − 10)5 (see Fig. 2.1). I include
5
Due to minor magnitude and color calibration differences between the two fields, the red sequence
cut is slightly field dependent, with the intercept at 1010 M⊙ and z=0 being U-V=1.01 and 1.06 for the
ECDFS and the A901/902 fields.
34
CHAPTER 2
all objects detected above the 24µm limit of 83µ Jy as star-forming.
In order to track star formation in very close pairs (< 2” and hence unresolved
by the ground-based COMBO-17 data) and merger remnants, I include only
merging systems (from the ACS data) with M∗ > 2 × 1010 M⊙ : i.e. the minimum
possible mass for a merger between two galaxies in my sample.
Figure 2.1 Stellar mass vs. color distribution of COMBO-17 selected galaxies in the ECDFS
and A901/2 field with 0.4 < z < 0.8. The vertical line shows the mass limit M⋆ > 1010 M⊙
used to select my sample. This mass selected sample is complete except for red sequence
galaxies at z > 0.6. The blue line shows the cut used to separate red sequence and blue
cloud galaxies. Red symbols denote 24 µm detected galaxies with ¿83µ Jy.
2.2.1
Projected correlation function
The correlation function formalism is a convenient and powerful tool to
characterize populations of galaxy pairs (e.g. Davis & Peebles 1983). Here,
I use weighted projected two-point correlation functions because redshift
uncertainties (1-3%) from COMBO-17 translate to line-of-sight distance errors
of ∼ 100 Mpc, necessitating the use of projected correlation functions to explore
the properties of close physical pairs of galaxies (Bell et al. 2006b). For my
SFR ENHANCEMENT IN GALAXY INTERACTIONS
35
sample at hand, I estimate the weighted (or marked) two-point correlation
function (Boerner et al. 1989; Skibba et al. 2006; Skibba & Sheth 2009), using
both the SFR and the specific SFR (SFR per unit stellar mass) as the weight.
The projected correlation function w(rP ) is the integral along the line of sight
of the real-space correlation function:
w(rp ) =
Z
∞
ξ([rp2 + π 2 ]1/2 )dπ,
(2.4)
−∞
where rp is the distance between the two galaxies projected on the plane of
sky and π the line-of-sight separation. A simple estimator for this unweighted
correlation function is w(rp ) = ∆(DD/RR − 1), where ∆ is the path length being
integrated over, DD(rP ) is the histogram of separations between real galaxies
and RR(rP ) is the histogram of separations between galaxies in a randomlydistributed catalogue (this is the same estimator used in Bell et al. 2006b).
Basically, the aim is to find the excess probability (compared to a random
distribution) of finding a galaxy at a given distance of another galaxy. This
estimator accomplishes that by subtracting the random probability of finding
two galaxies at a given separation from the probability in the real data sample
and normalizing to the probability in the random case. Other estimators (i.e.
∆[(DD−DR)/RR] or ∆[(DD−2DR+RR)/RR]) for the 2-point correlation function
give results different by < 5% (less than other sources of uncertainty). Thus:
X
DD(rP ) =
Dij
ij
RR(rP ) =
X
Rij
ij
where the sum is over all non-repeated pairs in the sample, and Dij (Rij ) equals
1 only if the pair selection criteria are satisfied in the real (random) galaxy
catalogue, and is equal to 0 otherwise. The first criterion is that the stellarmass ratio falls between 1:1 and 1:4. I further only allow a maximum redshift
√
difference ∆z = ∆ = 2σz , where σz is the error in redshift of the primary
galaxy (see Equation 2.1), and, depending on the case, either the primary or
both galaxies in the pair have to be star formers (see §2.3).
I can then study the possible enhancement of (specific) star formation rate by
means of a projected marked (or weighted) correlation function, which can be
defined:
1 + W (rp )/∆
,
(2.5)
E(rp ) =
1 + w(rp )/∆
36
CHAPTER 2
where W (rp ) = ∆(P P/P PR − 1) and,
P P (rP ) =
X
Pij Dij
ij
P PR (rP ) =
X
Pij Rij .
ij
Pij is the mark (or weight). I adopt two different weights Pij in what follows,
one is the SFR of the pair of galaxies:
Pij = Sij = SF Rij = SF Ri + SF Rj ,
and the other is the specific SFR of the galaxy pair:
Pij = sij = Specific SF Rij =
SF Ri + SF Rj
.
M⋆,i + M⋆,j
Then, the estimator that I use for E(rp ) is:
E(rp ) =
P P/DD
,
hPij i
(2.6)
where hPij i is the average value of the weight used (SFR, or specific SFR) across
the sample. This normalization is the average value of pair SFR or SSFR for
the actual pair samples used in this analysis, out to a projected separation
of 8 Mpc, in order to probe galaxy pairs sampling different environments
to build a representative cosmic-averaged weight. The SFRs or SSFRs of
individual galaxies used to find the normalization are exactly the same as
for the numerator, as described in § 2.1.3. It is worth noting that with my
definition of the enhancement given in eq. 5 the random histograms RR and
P PR cancel in the process of obtaining the expression in eq. 6, so they are not
used in the computation of my enhancement.
In the present work I perform two analyses: the cross-correlation of star
forming galaxies (as defined above) as primary galaxies with all galaxies as
secondaries, and the autocorrelation of star-forming galaxies. I will estimate
the errors in my mark by means of bootstrapping resampling.
SFR ENHANCEMENT IN GALAXY INTERACTIONS
2.2.2
37
Visual Morphologies
A particular challenge encountered when constructing a census of star formation in pairs and mergers is accounting for systems with separations of
< 2” (which corresponds to < 15 kpc, the radius within which I can no longer
separate two massive galaxies using COMBO-17; Bell et al. 2006b). In order to
pick up the SF in all the stages of the interaction, I need to have an estimate
of the SFR not only in galaxy pairs with separations > 15 kpc but also in
extremely close pairs and in recent merger remnants. I conduct my census of
such close physical pairs by including in the < 15 kpc range sources that are not
resolved by COMBO-17, but appear to be interacting pairs or merger remnants
on the basis of visual classification of the ∼ 0.1” resolution ACS images. I try to
recover visually all < 15 kpc separation pairs of two M∗ > 1010 M⊙ galaxies with
a mass ratio between 1:1 and 1:4 missed by COMBO-17. In addition to those
extremely close pairs, I also account for the SF in recent merger remnants
M∗ > 2 × 1010 M⊙ (two times the minimum mass of a galaxy in the sample and
the minimum possible mass of a galaxy pair as defined before).
Discussion of visual classifications
My goal is to include very close pairs or already-coalesced major merger
remnants into the census of ‘mergers’ in order to account for any SF triggered
by the merger/interaction process6 .I do so on the basis of visual classification of
the sample. The motivation for visual classification is a pragmatic one: while a
number of automated morphological classification systems have been developed
in the last 15 years (i.e. Abraham et al. 1996; Conselice et al. 2003; Lotz et al.
2004etc.), it seems that the sensitivity of the observables used (asymmetry,
clumpiness, Gini coefficient, second order moment of the 20% brightest pixels)
is insufficient for matching the performance of visual classification in current
intermediate redshift galaxies with the same level of precision that they display
in the local Universe samples used for their calibration (Conselice et al. 2003;
Lisker 2008; Jogee et al. 2009).
Yet, there is a degree of subjectivity to what one deems to be a major merger
remnant. Many factors shape the morphology of a galaxy merger that are
6
Note that a consistent comparison with the projected correlation function sample requires the inclusion
of all non-interacting pairs that are physically-associated (in the same cluster, filament, etc), are seen to
be close projected pairs on the sky, but may be separated by as much as a few Mpc along the line of sight.
38
CHAPTER 2
beyond the control of the classifier. Bulge-to-total (B/T) mass ratios have an
strong effect on both the intensity of the SFR enhancement and the time at
which the intensity peak shall occur (e.g., Mihos & Hernquist 1996b). Orbital
parameters strongly shape the development of easily recognizable tidal tails
and bridges (coplanar or not, retrograde vs. prograde, etc). Prior dust and gas
content of the parent galaxies (‘dry’ vs. ‘wet’ mergers) will make a difference
to the appearance of the final object during the coalescence. Furthermore,
merging timescales will depend on whether the galaxies are undergoing a
first passage or are in the final stages of the merger. Finally, there is a
degeneracy between all these parameters and the relative masses of the galaxies
undergoing the interaction, which makes difficult in some cases to distinguish
the morphological signatures of a major merger from those of a minor merger.
Some of these factors (e.g. gas fraction, B/T ratios, etc) will also affect the
enhancement of the SFR during the interaction (e.g. Di Matteo et al. 2007,
2008; Cox et al. 2008). While there is considerable merger-to-merger scatter,
encounters of two gas rich disk galaxies with parallel spins tend to develop,
on average, the strongest morphological features, but at the same time are
more likely to throw out large amounts of cold gas in tidal tails, preventing
the funneling of this gas to the central regions. Thus, samples selected to have
the strongest morphological features may have an average SFR enhancement
different from the actual mean enhancement7 .
One practical issue is that of passband choice and shifting. I choose to classify
the F606W images of the GEMS and STAGES fields (in STAGES because that
is the only available HST passband and in GEMS for consistency and because
F606W has higher S/N that the F850LP data). This corresponds to rest-frame
∼ 430(330)nm at redshift 0.4(0.8). In previous papers (Wolf et al. 2005; Bell
et al. 2005; Jogee et al. 2009), it has been assessed whether the morphological
census derived from GEMS/STAGES would change significantly if carried out
data a factor of 5 deeper from the GOODS project (testing sensitivity to surface
brightness limits), or if carried out at F850LP (always rest-frame optical at
these redshifts). We found that the population does not show significantly
different morphologies between our (comparatively) shallow F606W data and
the deeper/redder imaging data from GOODS (see Fig. 5 in Jogee et al. 2009).
7
This bias might also be present in the case of studies looking for signs of interactions in the host
galaxies of AGNs, attempting to assess whether the AGN activity is preceded by a merger.
SFR ENHANCEMENT IN GALAXY INTERACTIONS
39
Method
An independent visual inspection of the galaxy sample has been carried out
by four classifiers, A.R.R., E.F.B., R.E.S. and D.H.M. in order to identify
morphological signatures of major gravitational interactions. Each classifier
assigned every one of the ∼2500 sample members to one of the three following
groups:
1. Non-major interactions: The bulk of galaxies in this bin show no
signatures of gravitational interactions. Asymmetric, irregular galaxies
with patchy star formation triggered by internal processes lie in this
category.
A small fraction of galaxies in this bin show a clearly
recognizable morphology (e.g. spiral structure) but also signatures of
an interaction (such as tidal tails, or warped, thick or lopsided disks)
but have no clear interaction companion; note that these objects could
be interacting systems where the companion is now reasonably distant
and/or faint and more difficult to identify. The tidal enhancement of SF
from such systems will not be missed by putting them in this bin; rather, it
will be measured statistically and robustly from the two point correlation
function analysis. Minor mergers and interactions (interactions where the
secondary is believed, on the basis of luminosity ratio, to be less than 1/4
of the mass of the primary) also belong to this category.
2. Major close interactions: Close pairs resolved in HST imaging but not in
ground-based COMBO-17 data, consisting of two galaxies with mass ratios
between 1:1 and 1:4 based on relative luminosity, and clear signatures
of tidal interaction such as tidal tails, bridges or common envelope (see
Fig. 2.2). From now on I shall refer to objects classified in this group as
”very close pairs”.
3. Major merger remnants: Objects that are believed to be the coalesced
product of a recent major merger between two individual galaxies.
Signposts of major merger remnants include a highly-disturbed ’train
wreck’ morphology, double nuclei of similar luminosity, tidal tails of
similar length, or spheroidal remnants with large-scale tidal debris (see
Fig. 2.3). Galaxies with clear signs of past merging but a prominent disk
(e.g., highly asymmetric spiral arms or one tidal tail) were deemed to be
minor merger remnants and were assigned into the group 1. Naturally
there is some uncertainty and subjectivity in the assignment of this class,
40
CHAPTER 2
in particular; such uncertainty is taken into account in my analysis by
the Monte Carlo sampling of all four classifications in order to properly
estimate the dispersion in the opinions of the individual classifiers (see
below).
Table 2.1 Results from the morphological classification
Lower mass limit
1010 M⊙
2 × 1010 M⊙
Sample size
2551
1749
Group 1
Group 2
Group 3
2380 ± 37 ± 49 106 ± 7 ± 10 72 ± 7 ± 8
1640 ± 32 ± 40 69 ± 6 ± 8 44 ± 5 ± 7
Note. — Galaxy and interaction sample. Group 1: Isolated objects and minor interactions. Group
2: Extremely close pairs (rP < 15 kpc). Group 3: Merger remnants. The first error bar represents
classifier-to-classifier scatter while the second one represents Poisson noise.
I then assign the objects in the groups 2 and 3 (very close pairs with
morphological signatures of interaction and merger remnants respectively) to a
small projected separation and treat every one of them as a galaxy pair in order
to combine them with the correlation function analysis result for pairs with
separations > 2”. All objects in Group 2 (extremely close pairs with projected
separations < 15 kpc as measured by centroids in HST imaging) are assigned
to a separation of 10 kpc and all objects in Group 3 (merger remnants) are
assigned to a separation of 0 kpc. I have checked for duplicate pairs in both the
visually selected sample and the COMBO-17 catalog in order to avoid repeated
pairs. Galaxies in group 1 are already included in the two point correlation
function analysis, and any SF triggered by major interactions or early-stage
major merging is accounted for by that method. As I have four different
classifications for every object (one given by each human classifier), I randomly
assign one of them, calculate the average value of the weight I are using and
repeat the process a number of times. As by definition objects in groups 2 and
3 are considered to be a galaxy pair by themselves, I remove in every Monte
Carlo realization the objects assigned to those groups before I run the weighted
correlation function. This approach presents two clear advantages: a) the
resultant bootstrapping error not only represents the statistical dispersion but
also the different criteria of the four human classifiers, and b) the morphology
of every object is weighted with the four classifications given. This means that
objects with discrepant classifications are not just assigned to one category
when I calculate the SFR (or specific SFR) enhancement; rather, any dispersion
in classifications is naturally accounted for (e.g. minor/major criteria). The
SFR ENHANCEMENT IN GALAXY INTERACTIONS
41
numbers of such systems and their uncertainties, estimated from the classifierto-classifier scatter, are given in Table 2.1.
2.3
Results
I are now in a position to quantify the triggering of star formation in galaxy
interactions and mergers in the redshift interval 0.4 < z < 0.8, in the cases where
each galaxy has M∗ > 1010 M⊙ and the pair has a stellar mass ratio between
1:1 and 1:4. My primary analysis is based on a marked cross-correlation
between star-forming galaxies, as defined in §3, and all galaxies in the sample.
For morphologically-selected very close pairs or interactions (unresolved by
COMBO-17), I also require them to be blue or detected by Spitzer to be
considered as part of the star-forming sample8 , with a mass of M∗ > 2 × 1010 M⊙ .
I perform two analyses in this chapter: the cross-correlation of star-formers
as primary galaxies with all galaxies as secondaries (my default case), and
the autocorrelation of star-forming galaxies. While the first analysis is a
rather more direct attack on the question of interest, I show results from
the autocorrelation of star-forming galaxies to illustrate the effects of making
different sample choices on the final results.
2.3.1
Enhancement in the Star Formation Activity
My main results are shown in Fig. 2.4, which shows the enhancement of the
specific star formation rate (SSFR) in pairs as a function of their projected
separation. As explained in §2.1.3 I use UV+IR SFRs for the objects detected
in 24 µm and only UV SFRs for those undetected. For the whole sample, 38% of
the galaxies where detected by Spitzer above the 83µm limit, while if I restrict to
the groups 2 and 3 in my morphological classification I find a detected fraction
of 60%. Fig. 2.4 shows a clear enhancement in the SSFR for projected pair
separations rP < 40 kpc. It could be argued that the SSFR is a better measure
of the SF enhancement than the SFR-weighted estimator, because the strong
scaling of SFR with galaxy mass is factored out. The figure shows both the
cross-correlation between star-forming primaries and all secondaries (SF–All,
8
All galaxies, irrespective of their color or IR flux, were classified; the star-forming galaxies are simply
a subsample of this larger sample.
42
CHAPTER 2
Figure 2.2 Objects classified in group 2: Major close interactions. The presence of two
galaxies and signs of interaction are required. The classifier believes the mass ratio is
between 1:1 and 1:4. At this stage of the interaction, dry mergers are still recognizable as
seen in panels at top center, bottom center and bottom right. The black bar at the bottom
of every panel shows a proper distance of 20 kpc at the redshift of the object. Some of
the objects classified in this group were also separated as two galaxies in the ground-based
catalog and treated in consequence.
SFR ENHANCEMENT IN GALAXY INTERACTIONS
43
Figure 2.3 Objects classified in group 3: Major merger remnants.The black bar at the
bottom of every panel shows a proper distance of 20 kpc at the redshift of the object
44
CHAPTER 2
Figure 2.4 Pair specific SFR enhancement as function of the projected separation between
two galaxies. The two smallest radii bins are derived from morphologically-selected very
close pairs (shown with rP ∼ 10 kpc) and merger remnants (shown with rP = 0);
enhancements at larger radii are determined using weighted two-point correlation functions.
A statistically significant enhancement is present in galaxy pairs and mergers below 40 kpc
in both the cross–correlation between star forming galaxies as primaries and all galaxies as
secondaries (black filled symbols) and the autocorrelation of star–forming galaxies (empty
diamonds). Error bars have been calculated by bootstrapping.
solid line) and the star-forming galaxy autocorrelation (SF–SF, dotted line).
The two bins at rp ≤ 15 kpc are calculated from morphologically-selected very
close pairs (rp = 10 kpc) and merger remnants (rP = 0). All the errors in ESSF R
have been computed by bootstrap resampling. This approach allows us to treat
both the morphologically-selected objects and the galaxy pairs exactly in the
same way, having as a result a coherent display of the error bars.
There are two reasons why this excess in ESSF R in close pairs and remnants
is likely a sign that interactions induce additional star formation, rather than
being due to a correlation with some other unidentified quantity: a) It is well
known from simulations (Mihos & Hernquist 1996b; Di Matteo et al. 2007; Cox
et al. 2008) that a burst of star formation is expected in the collisions of gasrich galaxies, and b) the observed effect is in the opposite sense of the usual
SFR ENHANCEMENT IN GALAXY INTERACTIONS
45
SFR–density relation (e.g., Balogh et al. 2002), which says that galaxies in
dense environments (where preferentially close galaxy pairs tend to be found,
as shown in Barton et al. 2007) have, on average, weaker star formation activity
than galaxies in less dense regions.
Even when I consider my morphological classification and further Monte Carlo
resampling method to be very robust, potential classification errors could
act in two different directions. Interacting systems misidentified as noninteracting will be diluted into the background star formation as single galaxies
contributing to pairs at random separations. While this SF should be lost to the
interacting bin, the effect on the average SFR would be minimal. On the other
hand, isolated galaxies misidentified as interacting systems because of internal
instabilities or stochastic star formation would act to reduce the enhancement.
As mentioned before, the SFR for the objects undetected at 24 µm has been
calculated based only on the UV. In the 24µm detected objects, I have found
no clear trend in both the UV vs. UV+TIR SFRs and in the TIR/TUV vs.
optical dust attenuation but found instead a constant correction factor with
a large scatter (4.1 ± 2.4 as estimated from the relation between TIR/TUV vs
optical attenuation.) I have checked the effects of such a dust-correction of the
UV-only SFRs: the results differ in all bins by ¡10%, comparable to or smaller
than other sources of systematic uncertainty.
Yet, in order to understand the degree of obscuration in galaxy interactions I
have repeated my analysis including only UV–derived SFRs, this is, excluding
the TIR component in Eq. 2.2 for 24µm detections. The result of this analysis
is shown in Fig. 2.5. The enhancement in the unobscured SSFR measured
for close pairs (rP < 40 kpc) in this case is dramatically smaller than the
enhancement including the dust-obscured (IR-derived) star formation rate.
This is more apparent in the very close pairs and merger remnants, where
the excess in the SSFR even disappears completely in the case of the SF–
SF autocorrelation (E(rP < 15kpc) ≃ 1). This implies that most of the
directly triggered star formation is dust obscured, in good agreement with the
expectations from Mihos & Hernquist (1994, 1996b), Di Matteo et al. (2007),
Cox et al. (2008) and the detailed models by Jonsson et al. (2006). In these
simulations most of the star formation is triggered in the central regions of the
galaxy after the cold gas has been funneled to the inner kpc.
This scenario is also supported by my measurement of the mean ratio between
the total SFR and the UV-derived, which gives an idea of the degree of dust-
46
CHAPTER 2
Figure 2.5 Same as Fig. 2.4 but tracing only unobscured (UV-derived) star formation. The
unobscured SSFR enhancement found in galaxy pairs with separations rP < 40 kpc and
mergers remnants is dramatically reduced with respect to the case in which the obscured
star formation is taken into account (Fig. 2.4).
obscuration (SF RIR+U V /SF RU V ). I find 6.64 ± 0.66 in the case of the merger
remnants (Group 3 in §2.2.2) and 6.63 ± 0.64 in the case of the very close pairs
(group 2), compared to 3.15 ± 0.53 for all objects in the sample.
Star formation rate vs. specific star formation rate
To study the fraction of the global star formation directly triggered by galaxy–
galaxy interactions the enhancement in the SFR (rather than in the SSFR) is
a better quantity to consider.
I show in Fig. 2.6 the enhancement in the SFR (ESF R(rp )) as a function of the
projected pair separation. For the cross–correlation function (my default case)
the enhancement in the SFR is similar to the one found in the SSFR at all
separations except for the merger remnants (rp = 0), in which the excess above
the whole population is ∼ 50% lower. The SFR–weighted autocorrelation of
star forming galaxies matches that of the SSFR–weighted one for rp < 40 kpc
but differs beyond: ESF R = 1.25 for 40 < rP < 180 kpc. While most of these
points in Fig. 2.6 are individually compatible with the error bars shown in
Fig. 2.4, taken together they represent a ∼ 2σ significant difference between
SFR ENHANCEMENT IN GALAXY INTERACTIONS
47
ESSF R and ESF R for the entire region 40 < rp < 180 kpc.
Figure 2.6 SFR enhancement in galaxy interactions. The two smallest radii bins are derived
from morphologically-selected extremely close pairs (rP ∼ 10 kpc) and merger remnants
(shown with rP = 0); enhancements at larger radii are determined using weighted twopoint correlation functions. There is a clear enhancement at rP < 40 kpc for the crosscorrelation analysis (black-filled symbols) which is compatible with ESSF R (Fig. 2.4) except
for the merger remnants, where the excess is ∼50% lower. The autocorrelation of star
forming galaxies (empty symbols) presents an unexpected behavior, showing a very mild
enhancement at rP < 180 kpc.
A potential driver of the SFR enhancement in the regime 40 < rP < 180 kpc is
the fact that more massive galaxies tend to be both more clustered and have
higher SFR (Noeske et al. 2007); this could translate into a weak enhancement
in the SFR in galaxy pairs living in dense environments (see Barton et al.
2007 for a thorough discussion on the relation between galaxy pairs and
environment) which will not be present in the SSFR, because the normalization
by galaxy mass factors out this dependence. To test the relevance of this
systematic effect, I randomized the SFRs among galaxies of similar mass 500
times in the sample and repeated the analysis. I show the results of this exercise
in Fig. 2.7, where I can see a tail of enhancement with a behavior similar to
the one seen in Fig. 2.6. I believe that a combination of the density–mass–
SFR relation plus noise is driving ESF R > 1 (autocorrelation) between 40 and
180 kpc.
It is clear that most of this extra enhancement at large separations is driven
48
CHAPTER 2
Figure 2.7 SFR enhancement measured after randomizing the SFR between galaxies of
similar stellar mass. A mild enhancement is found out to separations of ∼ 160 kpc. I show
the points corresponding to the SF-SF autocorrelation at distances > 15 kpc, where no
morphological information is used.
by the relation between SFR and clustering properties of massive galaxies, but
there is yet another possible source of uncertainty: If one galaxy turns out
to be in the same group or cluster where a galaxy interaction is taking place,
some of the enhancement will be ‘lifted’ and shifted to larger separations. In
Chapter 3 I will develop a toy model in order to check for this effect.
Accordingly to the results I show in Fig. 2.7, I consider only the enhancement
at rP < 40 kpc as produced by major merging in what follows, and use the
differences between the SFR and SSFR enhancement on < 40 kpc scales as a
measure of systematic uncertainty. Under those assumptions, I find a weak
enhancement of star formation at rP < 40 kpc of ǫ = 1.50 ± 0.25 in the SF–SF
autocorrelation and ǫ = 1.80 ± 0.30 in the SF–All cross-correlation. These values
have been computed as the average of the enhancement in the bins rP < 40 kpc
together in ESSF R and ESF R . These (conservative) error bars include both the
statistical uncertainties and the systematics driving the differences between the
SFR and the SSFR.
SFR ENHANCEMENT IN GALAXY INTERACTIONS
49
Further Uncertainties
As I have briefly mentioned in §2.1, there are some uncertainties which need to
be estimated in the process of calculating the enhancement in the SF activity.
Here I try to estimate the impact of the stellar-mass and IR SED selection
uncertainties. Through this section I will focus in my default case, the SF-All
cross-correlation.
Random errors in stellar masses in Borch et al. (2006) are < 0.1 dex (with 0.3
dex in cases with large starbursts (Bell & de Jong 2001)) on a galaxy-by-galaxy
basis, and systematic errors non related to the choice of an universally-applied
stellar IMF are 0.1 dex. In addition, M/L ratios in starbursting galaxies can
be biased to produce unrealistic high stellar masses(Bell & de Jong 2001).
Those effects would have certain impact in the calculation of the SSFR, and
thus, in the enhancement of that quantity. In order to estimate how those
mass uncertainties affect my results, I have run two additional Monte Carlo
shufflings. In Fig. 2.8 I show the result of this exercise. I have randomly
added a gaussian error with σ = 0.1 dex to the stellar masses of all galaxies and
repeated the process 500 times, finding an average output value similar to the
one presented in Fig. 2.4 but with larger errors. The impact of the new errors
on the average enhancement (taking into account also the enhancement in the
SFR, as I did in the previous section) is negligible.
In order to estimate the uncertainties introduced by systematics in the M/L
ratio of starbursts, I have performed a similar exercise but using an error which
includes a systematic shift down of 0.1 dex, σ = 0.2 dex and a tail to the lower
masses defined by an inverted lognormal distribution. I have applied this new
error to objects with SF R > 16M⊙ yr −1, which roughly corresponds to twice the
average SFR in my sample of star forming galaxies, and the symmetric error
described above to galaxies with SF R < 16M⊙ yr −1 . The result (dash-dotted in
Fig. 2.8) shows some extra enhancement in this case, which leads to an average
enhancement in the SF activity ǫ = 1.85±0.35, barely changing the result already
found.
Another potential source of uncertainty is the stellar masses of pairs of galaxies
not resolved in the ground-based photometry catalog (i.e., my very close pairs
group). In order to test the impact of this underdeblending on the galaxy
masses, I take U and V rest-frame fluxes of galaxies widely separated, add
them together and check what stellar mass would result in the case of applying
the Borch et al. (2006) method to a galaxy with exactly the same color as
50
CHAPTER 2
Figure 2.8 Enhancement in the SSFR including estimates for the errors in the stellar
masses. Dotted line: Gaussian error with σ = 0.1 dex. Dash-dotted line: Non star forming
galaxies with gaussian error with σ = 0.1 dex and starburst galaxies (SF R > 16M⊙ yr −1)
with errors following an inverted lognormal distribution to produce a tail to the lower
masses, with a shift of 0.1 dex also to the lower masses and σ = 0.2 dex. Solid line:
Enhancement in the SSFR as in Fig.2.4, for comparison.
the combination of the two galaxies, and compare with the sum of the two
original masses. I find that for pairs of galaxies of all kinds (all-all, SF-SF and
SF-all) there is a < 0.01 dex offset and 0.08 dex scatter between the two sets
of masses. I.e., masses from combined luminosities are the same as the sum
of the individual masses to 0.08 dex, what means that my stellar masses are
extremely robust against underdeblending issues.
Together with the stellar-masses, the main source of uncertainty in my analysis
is the conversion between observed 24µm and TIR in the process of obtaining
the SFRs. Zheng et al. (2007b) have demonstrated that the Sbc template used
here is an appropriate choice for this dataset at all IR luminosities, but in
order to find an absolute upper limit for the final results I will show in §2.4.2 I
estimate the different results I would obtain if considering an Arp220 template
in some cases.
I find that at a given 24µm flux, the use of an Arp220 template gives a TIR
luminosity which is higher than that derived using a Sbc template by a factor
of 2. I apply this factor of 2 correction to the TIR luminosity of all the galaxies
that I define as starburst for this purpose (SF R > 16M⊙ yr −1) and show the
SFR ENHANCEMENT IN GALAXY INTERACTIONS
51
Figure 2.9 Impact on the SSFR enhancement when using an Arp220 template in the
conversion between observed 24 µm and TIR luminosity for certain objects. Red line:
Extreme case in which I apply an Arp220 template to all interacting systems (and Sbc
template to everything else). Green line: Arp220 template applied to objects with SF R >
16M⊙ yr −1 (and Sbc template to everything else). Black line: Same as in Fig. 2.4, for
comparison. Red and green lines include the asymmetric stellar mass errors applied in
Fig. 2.8.
result as the green line in Fig. 2.9. The enhancement found in this case is
ǫ = 2.1 ± 0.4, consistent with, by higher than the ǫ = 1.8 ± 0.3 found in §2.3.1.
I also want to test the extreme case in which the IR SED of all galaxies
undergoing an interaction follows an Arp220 SED, independently of their level
of SFR. This is clearly an unrealistic case as I know that some of my galaxies in
close pairs and remnants have SFRs as low as 4-5M⊙ yr −1 (factor of 10 less SFR
than Arp220), and I know also that the average IR SED of z ∼ 0.6 galaxies
with SF Rs ≥ 10M⊙ yr −1 is similar to the Sbc template adopted here (Zheng
et al. 2007a), but it is useful in the sense that it provides a strong upper limit
beyond the uncertainties of my data and method. The result found in this case
can be seen as the red line in Fig. 2.9. Clearly, a much stronger enhancement
is present as a consequence of this overestimation of the TIR luminosity, that
leads, when taken together with the SFR enhancement calculated in the same
way, to ǫ = 3.1 ± 0.6.
52
2.3.2
CHAPTER 2
How important are mergers in triggering dust-obscured
starbursts?
I have demonstrated that when averaged over all events and all event phases
there is a relatively modest SFR enhancement from major galaxy merging
and interactions. It is of interest to constrain how the distribution of SFRs
differs between the non-interacting and interacting galaxies. Here I present a
preliminary result on one aspect of the issue, namely the fraction of infraredluminous galaxies that are in close pairs rp < 40 kpc or were visually classified
as merging systems.
Figure 2.10 The fraction of systems in close projected pairs rp < 40 kpc or in visually
identified mergers as function of the total IR luminosity of all 24µm detected galaxies in
the sample. The merger fraction is ∼ 20% from my luminosity limit of 6 × 1010 L⊙ to
3 × 1011 L⊙ . Higher than this luminosity, the merger fraction begins to grow to 55% just
below 1012 L⊙ .
In Fig. 2.10 I show how the fraction of galaxies that are either in close
pairs (rp < 40 kpc) or in morphologically-classified merger remnants varies
as a function of their total IR luminosity. This fraction is constant (∼20%)
for 6 × 1010 L⊙ < LT IR < 3 × 1011 L⊙ . At higher luminosities, the merger
fraction increases as a function of the IR luminosity, reaching 55% just below
LT IR = 1012 L⊙ . The lower IR limit of 6 × 1010 L⊙ was chosen to ensure a flux of
83µJy over the entire redshift range. The increase in merger fraction at high
IR luminosity is in accord with previous results at both low and intermediate
redshift (e.g., Sanders et al. 1988). This suggests that merging and interactions
are an important trigger of intense, dust-obscured star formation. Apparently,
SFR ENHANCEMENT IN GALAXY INTERACTIONS
53
high IR luminosities are difficult to reach without an interaction.
A key point, however, is that not all mergers have high IR luminosity. While
mergers can produce enormous SFRs, and also LT IR > 1012 L⊙ is best reached
by merging, the typical SFR enhancement in mergers is modest.
2.4
Discussion
I have assembled a unique data set for galaxies at 0.4 < z < 0.8 that
combines redshifts, stellar masses, SFRs and HST morphologies to explore
the role of major mergers and interactions in boosting the SFR. In practice, I
have combined projected correlation-function and morphological techniques to
estimate the average enhancement of star formation in star-forming galaxies
with M∗ > 1010 M⊙ and 0.4 < z < 0.8, where the average is taken over most
merging phases and all mergers. I find a SF enhancement by a modest factor
of ∼ 1.8 for separations of < 40 kpc in both the SFR and the SSFR. How does
this compare with previous observations and models? What implications does
this mild enhancement have on the contribution of major mergers to the cosmic
SF history?
2.4.1
Comparison with previous observations
My analysis is most directly comparable to estimates of star formation rate
enhancement in galaxy close pairs by Li et al. (2008) using the SDSS at z ∼ 0.1
because of the similarities between our methods. Using a cross-correlation
between star-forming and all galaxies, they found an enhancement of ≃ 1.45
for an average galaxy mass of hlog(M∗ /M⊙ )i = 10.6 within a radius of 15 to
∼ 35 − 40 kpc. In Fig. 4.2, I show the comparison between their presentepoch measurements and mine (average galaxy mass ∼ 1010.5 M⊙ , SF–all crosscorrelation) revealing reasonable quantitative agreement. Both the projected
separation scale (. 40 kpc) and the overall amplitude at small projections
(×1.5 − 2) agree. The enhancement found here also agrees (given the error
bars) with the enhancement found at 0.75 < z < 1.1 in Lin et al. (2007). My
results are similar to those at both z = 0.1 and at z = 1, despite the factors of
several difference between the typical star formation rates of galaxies between
z = 1 and z = 0 (see, e.g., Zheng et al. 2007a). This is interesting, and points to
54
CHAPTER 2
Figure 2.11 Comparison between the enhancement found in this work (black filled points)
and the one found in Li et al. (2008) at z ≃ 0.1 (open diamonds). In both cases, a crosscorrelation SF–all is shown. Both works show a statistically significant enhancement of the
SSFR at rP < 40 kpc.
a picture in which at least the average enhancement of star formation in galaxy
interactions appears to be independent of the ‘pre-existing’ star formation in
the population.
Lin et al. (2007) also measured an enhancement in the TIR emission in galaxy
pairs and mergers in the 0.4 < z < 0.75 range. They find that the infrared
luminosity of close pairs with both members selected to be blue is 1.8 ± 0.4
times that of control pairs, similar to my value 1.75 ± 0.18 for close pairs in the
bin 15kpc < rP < 40kpc from the SF-SF autocorrelation. For late-phase mergers,
they measure 2.1 ± 0.4, marginally consistent with my 1.54 ± 0.08 from the SFSF autocorrelation at rP = 0 kpc. Slight differences in that number may be
attributed to differences in the ’merger’ classification. For example, many of
the remnants that I include in this study may not be detected by automated
methods based on the intensity-weighted Gini-M20 or asymmetry parameters.
As shown in recent work (Jogee et al. 2009; Miller et al. 2008), automated
methods based on CAS asymmetry parameters tend to capture only a fraction
(typically 50% to 70%) of the visually-identified merger remnants and often
pick up a dominant number of non-interacting galaxies that have small-scale
asymmetries associated with dust and star formation.
SFR ENHANCEMENT IN GALAXY INTERACTIONS
55
In related work (Jogee et al. 2009), we recently estimated the overall merging
rate and also addressed the SFR enhancement at 0.24 < z < 0.8. For the
subsample of systems with M∗ > 2.5 × 1010 M⊙ I find that the average SFR of late
stage mergers with mass ratio between 1:1 and 1:10 (both major and minor
mergers) are only enhanced by a modest factor (1.5-2 from their Fig. 15) with
respect to non-interacting galaxies. There are three differences that make it
difficult to perform an exact comparison between our works: a) In the present
study I try to isolate the contribution from major interactions (mass ratio
1:1 to 1:4) while in Jogee et al. (2009) I focused on both major and minor
interactions (mass ratio from 1:1 to 1:10). b) The normalization is slightly
different because in the present work I compare the SFR in mergers with the
SFR in the pair of progenitors, while in Jogee et al. (2009) we compare with
the SFR of individual galaxies with mass similar to the interacting system. As
the average SFR is a function of the galaxy stellar mass, 2×SFRM >1010 ,progenitor 6=
SFRM >2×1010 ,descendant . c) In the present work I attempt to target both early and
late phases of the interaction, while in Jogee et al. (2009) we focus on the later
phase. Nonetheless, it is encouraging that the two studies agree qualitatively
in finding a modest enhancement in the average SFR in galaxy interactions.
Taken together, I argue that my results are consistent with those of previous
works. I have used a bigger sample of galaxies with both HST/ACS and
Spitzer/MIPS coverage than previous works at z ≥ 0.4 and I tried to trace
the SFR enhancement in all the stages of the interaction with a consistent
treatment of ground-based selected galaxy pairs and morphologically-selected
pairs and remnants. I view it as extremely encouraging that where the works
are the most robust (close pairs), the results are highly consistent (comparing
my work with Li et al. 2008 and the pairs from Lin et al. 2007). It is clear that
robustly assessing the star formation enhancement in advanced-stage mergers,
identifiable using only high-resolution data and morphological techniques, is
considerably more challenging. The results for advanced-stage mergers are
therefore less well-constrained, but are nonetheless all consistent with a modest
but significant enhancement in SFR.
2.4.2
What fraction of star formation is triggered by major
interactions?
I can now combine my estimates for the SFR enhancement, the fraction of
galaxies in projected close pairs, the average SFR, and the amount of SFR
56
CHAPTER 2
in recognizable merger remnants to quantify what fraction of star formation
at 0.4 < z < 0.8 is directly triggered by major interactions. I will not include
systematics such as the uncertainty in conversion of 24µm to total IR, or
the effect of the 24µm flux limit, but I will consider the systematics driving
the difference between the SSFR enhancement and the SFR enhancement. I
make the cross-correlation between star forming galaxies as primaries and all
galaxies as secondaries my default case because it includes the residual SFR
in red galaxies and also traces the SF enhancement in disk galaxies during the
encounter with a non star forming galaxy. I will also show the values obtained
for the SF-SF autocorrelation. I use the values 1.80±0.30 and 1.50±0.25 found in
§ 2.3.1 in rP < 40 kpc systems, for the cross-correlation and the autocorrelation
respectively.
The fraction of galaxies in close physical pairs within a separation rf can be
derived using the following approximation (Patton et al. 2000; Masjedi et al.
2006; Bell et al. 2006b):
P (r < rf ) =
4πn γ 3−γ
r r .
3−γ 0 f
(2.7)
Here P (r < rf ) is the fraction of galaxies in the parent sample in pairs with
real separations of r < rf , n is the number density of galaxies satisfying the
pair selection criteria, and r0 and γ are the parameters of the power-law realspace correlation function of the parent sample, subjected to the pair selection
criteria (i.e., I use a stellar mass ratio of 1:1 to 1:4 as a requirement for a pair
to enter into the correlation function).
Note that because in this chapter I typically impose criteria for matching and
forming pairs (e.g., a mass ratio between 1:1 and 4:1), the number density n
used is not the number density of the larger parent sample nparent . The number
of possible pairs at any projected separation range is lower than in the case in
which no mass ratio criteria is imposed because many pairs with mass ratios
beyond the allowed limit are automatically rejected. As the fraction of galaxies
in close physical pairs is directly related to the number density of galaxies n,
this parameter has to be fine-tuned in order to get the right fraction. The
number density used in Eq. 2.7 has to be corrected for the effect that the
mass ratio criteria introduces on the total number of potential pairs. Then,
the number density of the larger parent sample nparent is not used here, instead
I use n = nparent Npairs /[0.5Nparent (Nparent − 1)], where Npairs is the number of pairs
that can be formed in the parent sample given the matching criteria, and Nparent
SFR ENHANCEMENT IN GALAXY INTERACTIONS
57
is the number of galaxies in the parent sample (N(N − 1)/2 is the expression
for the number of possible pairs in the case of simply pairing up the parent
sample).
I tested this approximation using the semi-analytic galaxy catalog of De Lucia
et al. (2006), derived from the Millennium N-body simulation. At z ∼ 0.6 these
simulations matched well the stellar mass function and correlation function
of M∗ > 1010 M⊙ galaxies. I find that at r < 50 kpc Equation 2.7 is a good
approximation to the actual fraction of galaxies in close pairs in the simulation;
at larger separation Equation 2.7 is increasingly incorrect.
From fits to the projected two-point cross-correlation function of my sample, I
determine r0 = 1.8 ± 0.2 Mpc, γ = 2.2 ± 0.1 for the real-space correlation function,
and n = 0.0152 galaxies per cubic Mpc9 ; the latter gives a sample of Ngal =
nV = 1913 galaxies in the volume probed by this study. This yields P (r <
40 kpc) = 0.06 ± 0.01 (i.e., 6% of sample galaxies are in close pairs with real-space
separations < 40 kpc). With this real-space two-point correlation function,
75±10% of all projected close pairs should be real close physical pairs10 (Eq.
6 of Bell et al. 2006b and confirmed using the Millennium Simulation at the
redshift of interest). Thus the fraction of objects in projected close pairs will
be fpair,proj = 0.06/0.75 = 0.08 ± 0.02. This fraction includes projections due to
real structures like clusters or filaments, but not the purely random projections
due to redshift uncertainties which would be present if I would just count the
galaxies in projected close pairs in my catalogue.
When considering all pairs at all separations in my sample with M∗ > 1010 M⊙ ,
mass ratios between 1 : 1 and 1 : 4, and primary galaxies with 24µm fluxes
> 83µ Jy and/or blue, the average SFR is hSF Ritypical,pair = 13.2 ± 0.6M⊙ yr−1 . The
total SFR in the Nrem = 38 ± 5 recognizable merger remnants is SF Rremnants =
753 ± 97M⊙ yr−1 . Thus, I can calculate the fraction of SFR occuring in pairs with
separations < 40 kpc:
Ngal fpair,proj 0.5ǫ hSF Ritypical,pair + SF Rremnants
= 20 ± 3%
Ngal 0.5 hSF Ritypical,pair
(2.8)
for the SF–All correlation. A similar analysis with the SF–SF correlation yields
9
The correlation function is calculated in proper coordinates, because the process of interest is galaxy
merging and close pairs of galaxies have completely decoupled from the Hubble flow.
10
This is only valid after removing the effect introduced by purely random projections with the correlation
function method.
58
CHAPTER 2
16 ± 3%. What I have done in the numerator of Eq. 2.8 is to take the typical
SFR in my pairs and divide by two in order to get the typical SFR of a galaxy
contributing to such pairs. This number is different from the typical SFR in my
galaxy sample for two reasons: first, I have imposed a mass–ratio criterion (only
allow pairs with mass ratios between 1:1 and 1:4), which makes the averaged
SFR in all pairs to be slightly biased high respect random pairs without any
mass ratio criterion, and second, the fact that I force the primary galaxy to be
a star former (in the case of the cross-correlation) has a similar effect. Then
I have multiplied it by the enhancement ǫ in order to take into account the
excess SFR triggered by major interactions and introduced the factor Ngal to
account for all the SFR occuring in those galaxies. A key piece of Eq. 2.8 is
the different treatment of merger remnants. The correlation function can tell
us what is the fraction with separations between rP = 40 kpc and rP = 0 kpc but
I have defined merger remnants as objects which have already coalesced, so if
we think in terms of the duration of the interaction instead of the separation
between the galaxies, these objects would be beyond the reach of the correlation
function, and have to be treated separately. In the denominator I have only
divided by the total SFR occuring in all the galaxies contributing to any pair
I can form with the already mentioned criteria. The difference between this
factor and the total SFR calculated simply adding up the SFR of all galaxies in
the sample is 5% and is a consequence of the few galaxies which are not paired
with any other galaxy in the sample.
Yet, the fraction of the total SFR that occurs in pairs and remnants with
< 40 kpc separation does not immediately characterize the SFR triggered by
interactions, because ∼ 12% of SF should happen at rP < 40 kpc anyway, as I
show below. Only the excess star formation in pairs and remnants should be
atributed to triggering by interactions:
Ngal fpair,proj 0.5(ǫ − 1) hSF Ritypical,pair + (SF Rremnants − Nrem hSF Ritypical,pair )
= 8 ± 3%.
Ngal 0.5 hSF Ritypical,pair
(2.9)
Again, a similar analysis for the SF–SF autocorrelation yields 5 ± 3%. These
values for the excess are 12% lower than those in Eq. 2.8 due to the total
number of interacting systems, which is higher than the 8% of galaxies in close
pairs mentioned before because it includes the merger remnants that are not
taken into account by the correlation function method.
Taking all this together, this analysis shows that only ∼ 8% of the star formation
at 0.4 < z < 0.8 is triggered by major mergers/interactions. This may seem in
SFR ENHANCEMENT IN GALAXY INTERACTIONS
59
disagreement with previous results from ’morphological’ studies. I therefore
compare my results with those of Bell et al. (2005) and Wolf et al. (2005), who
found that ∼ 30% of the global SFR at z = 0.7 is taking place in morphologically
perturbed systems and with Jogee et al. (2009), where we find a similar result
at 0.24 < z < 0.8.
Both Bell et al. (2005) and Wolf et al. (2005) performed a study of the total SFR
occuring in visually-classified interacting galaxies in a thin redshift slice 0.65 <
z < 0.75 without imposing a lower mass limit (only an apparent magnitude
limit). That is the key difference between those earlier works and mine. I
impose a mass cut in this chapter of 1010 M⊙ and 2 × 1010 M⊙ for galaxies and
visually-classified interactions respectively. E.g. the fraction of SFR in galaxies
with M∗ > 1 − 2 × 1010 M⊙ that Bell et al. (2005) and Wolf et al. (2005) identified
as interacting/peculiar is 15-21%, compared to 20% in Eq. 2.8. Only 1/6 of
the star formation in the interacting/peculiar galaxies from Bell et al. (2005)
and Wolf et al. (2005) occurs in what I would designate as merger remnants,
with the other 5/6 occuring in galaxy pairs. Jogee et al. (2009) argued that
30% of star formation was in systems that they classified as major or minor
interactions, with mass limits different from those used in this work. This value
is an upper limit to the fraction of star formation in major mergers where each
galaxy has mass > 1010 M⊙ , both because of the effect of mass limits, and because
minor mergers host much of the star formation in systems that they classified
to be interacting. Accounting for these differences, my result is in qualitative
agreement with theirs.
However, the key difference is that neither Bell et al. (2005), Wolf et al. (2005)
nor Jogee et al. (2009) try to quantify the excess of SF in interacting systems,
as I do in going from Eq. 2.8 to Eq. 2.9. In summary, my new results here
pose no inconsistency with earlier studies, but refine them by quantifying the
physically more relevant quantity of SF excess.
I have presented the average enhancement in SFR caused by major mergers of
galaxies with masses above 1010 M⊙ at 0.4 < z < 0.8, deriving that approximately
8% of the SF in the volume is directly triggered by major merging. As I have
mentioned before, the SFR enhancement ǫ seems to be roughly independent
of the quiescent SFR ground level present in the galaxy population, that is,
insensitive to the drop in the SFR density of the Universe since z=1. If
this is true, it means that the fraction of star formation directly triggered
by galaxy interactions (given a mass cut) would depend only on the number of
galaxies undergoing interactions. Using the evolution of pair fraction found in
60
CHAPTER 2
Kartaltepe et al. (2007) I can infer a directly-triggered SF fraction of 1-2% in
the local Universe, as well as a fraction of 14-18% at z=1. On the other hand,
assuming no evolution in the pair fraction would keep the merger–triggered
fraction at 8% between z = 0 and z = 1. These numbers have to be taken
extremely carefully by the reader, as I present here only a crude extrapolation
of my results to different redshifts in order to get an idea of the importance of
the merger-driven star formation in the Universe.
There are a number of limitations of my result that should be borne in mind.
First, I can only include star formation rates > 5 M⊙ yr−1 for z ∼ 0.6 galaxies.
Therefore, my estimates of the SF contribution from merging may be an upper
limit because the merger-driven boost in SFR will cause more objects to satisfy
this criterion. Second, there are uncertainties in the conversion of 24µm to
total IR, which could influence the excess star formation in close pairs or
mergers by ∼ 30% (Papovich & Bell 2002; Zheng et al. 2007b); this could be
addressed once longer-wavelength, deep Herschel PACS observations become
available. I can only calculate an absolute upper limit by using the value of the
enhancement found in the extreme case in which the 24µm to TIR conversion
in all the interactions, independently of their luminosity, is calculated using
an Arp220 template. Using as input ǫ = 3.1 ± 0.6 for Eq. 2.9 I would find a
directly triggered fraction of 19 ± 5%, consistent with an scenario in which the
underlying level of SF is basically negligible and most of the new stars are
being formed in the burst mode. Third, it is conceivable that some enhanced
star formation occurs in very late-stage merger remnants that were no longer
recognized as remnants and hence were not included in this census. This is
both a practical (classification) and conceptual issue: when does one declare
a merger remnant a normal galaxy again? Nonetheless, despite these points,
the analysis presented here has made it very clear that only a small fraction
of star formation in galaxies with M∗ > 1010 M⊙ at 0.4 < z < 0.8 is triggered by
major interactions/mergers.
2.4.3
Comparison with theoretical expectations
Star formation enhancement in mergers has been studied extensively with
hydrodynamical N-body simulations (e.g., Barnes & Hernquist 1991; Mihos
& Hernquist 1994, 1996b; Springel 2000; Cox et al. 2006, 2008; Di Matteo
et al. 2007). However, large-scale cosmological simulations lack the dynamic
range to resolve the internal dynamics of galaxies, crucial for modeling the
SFR ENHANCEMENT IN GALAXY INTERACTIONS
61
gas inflows and the associated enhancement in star formation. Therefore, the
majority of these studies (except Tissera et al. 2002) have been of binary galaxy
mergers with idealized initial conditions, typically bulgeless or late-type disks.
In most studies, the properties of these progenitor disks are chosen to be
representative of present-day, relatively massive spiral galaxies such as the
Milky Way. These studies have shown that the burst efficiency in mergers is
sensitive to parameters such as merger mass ratio and orbit, and progenitor
gas fraction and bulge content. Therefore, any attempt to use these results
in an ensemble comparison must somehow convolve these dependencies with
a redshift dependent, cosmologically motivated distribution function for these
quantities. In addition, Cox et al. (2006) have shown that star formation
enhancement in mergers can also depend on the treatment of supernova
feedback in the simulations. Furthermore, the detailed star formation history
during the course of a merger, particularly in the late stages, may depend on
the presence of an accreting supermassive black hole (Di Matteo et al. 2005).
Let us consider the results from representative examples of such binary merger
simulations, by Cox et al. (2008), who studied a broad range of merger mass
ratios, gas fractions, and progenitor B/T ratios, as well as exploring the effects
of two different SN feedback recipes. The 1:1 merger of two “Milky Way”like progenitors (shown in their Figure 12) shows an average factor of ∼ 1.5
enhancement in SF over about 2.5 Gyr, and a larger enhancement of a factor
of 2–10 for a shorter period of about 0.6 Gyr. The overall average enhancement
over the whole merger is about a factor of 2.5, depending on the precise
timescale one averages over. Very large enhancements (∼ 5 − 10) occur over
a very short timescale, . 100 Myr. This particular simulation represents the
largest expected SF enhancement, as the burst efficiency increases strongly
towards equal merger mass ratio. For mergers with 1:2.3 mass ratio (Figure
10 of Cox et al. 2008), there is an enhancement of a factor of ∼ 1.5 for 2.5–3
Gyr, and of 2.5 for about 0.6 Gyr. It is also interesting to note that the star
formation rate in the late stages of the merger, when the galaxy still appears
morphologically disturbed (see Fig. 7 of Cox et al. 2008) is depressed with respect
to the isolated case. A diverse set of progenitor morphologies, ranging from
ellipticals to late-type spirals, was studied by Di Matteo et al. (2007). Overall,
their results are qualitatively similar to those from Cox et al. (2008).
The simulations discussed so far aimed to reflect progenitor disks with gas
fractions, sizes, and morphologies typical of relatively massive, low-redshift
late-type spirals such as the Milky Way: gas fraction fg ∼ 0.2; B/T ∼ 0.2; scale
62
CHAPTER 2
length rd ∼ 3 kpc. However, Hopkins et al. (2009) show that the burst efficiency
is strong function of progenitor gas fraction, in the sense that higher gas fraction
progenitors have weaker fractional enhancements. The burst efficiency is a factor
of eight lower for a gas fraction of 90 % than for the canonically-used value
of 20%. It is worth noting here that I find the same level of SF enhancement
in major mergers at z ∼ 0.6 and z ∼ 0.1, where the gas fractions of the two
samples are expected to be rather different (see §2.4.1). Whether or not this is
quantitatively at odds with the expectations of Hopkins et al. (2009) remains
to be seen. On the other hand, recent results from Di Matteo et al. (2008)
show no difference between the strength or duration of tidally-triggered bursts
of star formation in local Universe and their higher redshifts counterparts, in
good agreement with the present study.
To place results in a cosmological context, Somerville et al. (2008) used the
results from a large suite of hydrodynamic merger simulations (Cox et al.
2006; Robertson et al. 2006) to parameterize the dependence of burst efficiency
and timescale on merger mass ratio, gas fraction, progenitor circular velocity,
redshift, and the assumed effective equation of state. They implemented these
scalings within a cosmological semi-analytic merger tree model. I applied
my selection criteria to mock catalogs from Somerville et al. (2008), by
comparing the fraction of SFR produced in the triggered mode in galaxies
with M∗ > 2 × 1010 M⊙ in my redshift range which suffered a major merger in the
last 500 Myr with the total SFR occuring in galaxies M∗ > 1010 M⊙ . I found that
approximately 7% of the SFR in the volume is produced in the burst mode
triggered by major mergers. This is in excellent agreement with the 8 ± 3% of
the overall SFR being directly triggered by major interactions I showed in the
previous section.
2.5
Conclusions
To quantify the average effect of major mergers on SFRs in galaxies, I have
studied the enhancement of SF caused by major mergers between galaxies
with M∗ > 1010 M⊙ at 0.4 < z < 0.8. I combined redshifts and stellar masses
from COMBO-17 with high-resolution imaging based on HST/ACS data for
two fields (ECDFS/GEMS and A901/STAGES) and with star formation rates
that draw on UV and deep 24µm data from Spitzer to form a sample a factor of
two larger than previous studies in this redshift range. I then applied robust
SFR ENHANCEMENT IN GALAXY INTERACTIONS
63
two-point correlation function techniques, supplemented by morphologicallyclassified very close pairs and merger remnants to identify interacting galaxies.
My main findings are as follows:
1. Major mergers and interactions between star-forming massive galaxies
trigger, on average, a mild enhancement in the SFR in pairs separated by
projected distances rP < 40 kpc; I find an enhancement of ǫ = 1.80 ± 0.30
considering the SF-All cross-correlation, where only one galaxy in the
pair is required to be forming stars. For a similar analysis using the
autocorrelation of star forming galaxies I find ǫ = 1.50 ± 0.25.
2. My results agree well with previous studies of SF enhancement using
close pairs at z < 1. In particular, the behavior of SF enhancement at
z = 0.1, z = 0.6 and z = 1 appear to be rather similar, indicating that the
average SFR enhancement in galaxy interactions is independent of the
‘pre-existing’ SFR in the population.
3. I combine my estimate of the average SFR enhancements in major mergers
with the global SFR to show that overall, 8±3% of the total star formation
at these epochs is directly triggered by major interactions. I conclude that
major mergers are an insignificant factor in stellar mass growth at z < 1.
4. Major interactions do, however, play a key role in triggering the most
intense dust-obscured starbursts: I find that the majority of galaxies with
IR-luminosities in excess of 3 × 1011 L⊙ are visually classified as ongoing
mergers or found in projected pairs within < 40 kpc separation. This is
not in disagreement with the small average SFR enhancement if the most
intense SF bursts last only ∼ 100 Myr.
5. My results for the SF enhancement appear to be in qualitative agreement
with the extensive suite of hydrodynamical simulations by Di Matteo et al.
(2007, 2008) and Cox et al. (2008), who produce both intense, short-lived
bursts of SF in some interactions, but yet produce average enhancements
of only 25-50% averaged over the ∼ 2 Gyr timescale taken to complete
the merger. Furthermore, I find excellent agreement between the fraction
of the total SFR directly triggered by major merging measured here and
the 7% calculated from mock catalogues obtained from Somerville et al.
(2008).
Chapter 3
Systematic Errors in Weighted 2–point
Correlation Functions
Correlation functions (2-point and higher order ones) have proved to be
powerful statistical tools in order to address the study of the galaxy clustering
(e.g. Peebles & Groth 1976; Groth & Peebles 1977; Peebles 1980; Davis
& Peebles 1983) and are still widely used in both local (Connolly et al.
2002; Eisenstein et al. 2005; Masjedi et al. 2006) and high-redshift Universe
(Giavalisco et al. 1998; Blain et al. 2004). Study of the two point correlation
function have matured to the point that one can study how galaxies populate
dark matter halos in detail (e.g., Zehavi et al. 2004), the typical halo masses
of galaxy populations as a function of redshift (e.g., Lyman breaks - Giavalisco
et al. 1998), the relative clustering of different populations (e.g., the tendency
of AGN to cluster like the massive galaxy population as a whole; Li et al.
2006b), and the use of clustering measures on the smallest scale to constrain
the merger history of galaxies (e.g., Patton et al. 2000, Bell et al. 2006b).
Furthermore, the correlation function method allows me not only to study the
clustering of the galaxies themselves, but also how some of their properties
are clustered. Weighted correlation functions (Boerner et al. 1989) or in a
general sense, marked statistics (Beisbart & Kerscher 2000; Gottlöber et al.
2002; Faltenbacher et al. 2002; Skibba et al. 2006) have been widely used in
the last ten years in order to study how observables depend on the separation
between galaxies. In particular, weighted correlation functions are frequently
used to study the dependence of star formation rate (SFR) on separation
between galaxies, in great part to explore the influence of galaxy interactions
on enhancing a galaxy pair’s SFR (e.g., Li et al. 2006 or Chapter 2 in this
thesis).
The goal of this chapter is to explore the application of weighted correlation
65
66
CHAPTER 3
functions to study the variation of SFR in galaxy pairs as a function of
separation, but the results can be extrapolated to other observables like color,
morphologies, mass, etc. I briefly introduce weighted 2 point correlation
functions in § 3.1. I then construct a toy model with which I study the
behavior of the inferred weighted quantities relative to the input behavior
(§ 3.2). This toy model is primarily to illustrate some general features of
how weighted correlation functions recover input behavior, and I stress that
the framework discussed in this work applies generally to any application of
weighted correlation function analysis, while noting that I choose to present a
case that is most directly analagous to the study of SFR enhancement in close
pairs of galaxies. I show the results of this analysis in § 3.3. In § 3.4, I briefly
compare with observational results of SF enhancement derived using the Sloan
Digital Sky Survey (Li et al. 2008). In § 3.5, I present my conclusions. When
necessary, I have assumed H0 = 70 km s−1, Ωm0 = 0.3, ΩΛ0 = 0.7.
3.1
Background
In this chapter, I explore the possible artifacts that the use of a marked
correlation function could introduce when studying the clustering of galaxy
properties. A full explanation of the methodology followed in this work has
been already presented in Chapter 2, and is similar to the methodology adopted
by Skibba et al. (2006) and Li et al. (2008); I summarize here the basics of the
method.
The 2–point correlation function ξ(r) is the excess probability of finding a galaxy
at a given distance r from another galaxy:
dP = n[1 + ξ(r)]dV,
(3.1)
where dP is the probability of finding a galaxy in volume element dV at a
distance r from a galaxy, and n is the galaxy number density. A simple
estimator of the unweighted correlation function is ξ(r) ≃ DD/RR − 1, where
DD is the histogram of separations between galaxies and RR is the histogram
of separations between galaxies in a randomly-distributed catalog. In a similar
way, one can estimate the weighted correlation function as W (r) ≃ P P/P PR − 1,
where P P is the weighted histogram of real galaxies and P PR the weighted
histogram of separations from the catalog with randomized coordinates.
SYSTEMATIC ERRORS IN WEIGHTED 2–POINT CORRELATION FUNCTIONS 67
I choose to use an additive weighting scheme (the weight of the pair is the sum
of the weights of individual galaxies) for concreteness (Chapter 2), while noting
that a multiplicative weighting would yield a qualitatively similar result. Then,
I can define the ‘mark’ E(r) as the excess clustering of the weighted correlation
function compared to the unweighted correlation function:
E(r) =
3.2
1 + W (r)
.
1 + ξ(r)
(3.2)
An idealized experiment
I use De Lucia et al. (2006) catalog at z = 0 derived from the Millenium
simulation (Springel et al. 2005) in order to study how the enhancement
in a physical quantity caused by a galaxy–galaxy interaction (e.g., a SF
enhancement) would be recovered by weighted 2–point correlation function
techniques. I manually assign a weight (I refer to it as the mark) to every
galaxy in the sample, giving a mark=1 to galaxies which are not closer than
rc = 35 kpc to any other galaxy and mark= ǫ (with ǫ > 1) to those galaxies
which are in close, 3D pairs with separation r < rc kpc. For concreteness, I
consider simulated galaxies with stellar masses M∗ > 2.5 × 1010 M⊙ , noting that
the conclusions reached in this work are generally applicable, in a qualitative
sense.
I now examine how the marks of galaxy pairs relate to the actual behavior
of the enhancement as a function of separation from their nearest neighbor.
The mark is estimated by dividing the weighted correlation function by its
unweighted counterpart, and recall that the correlation function relates every
galaxy to every other galaxy in the sample 1 . The weight is additive, ans since
every galaxy with a companion closer than rc has weight ǫ, the mark of a close
pair is 2ǫ. Yet, the galaxies in this close pair will be matched also to every other
galaxy in the sample. Therefore, when a galaxy in the same group or cluster at
a distance r > rc from the enhanced pair is matched with a galaxy in the pair,
the mark of that pair will be ǫ + 1 (1 being the default weight of non-enhanced
galaxies). I see that a pair with r > rc will show an enhancement when, in
reality, there is no physical interaction-induced enhancement at that radius.
As that third galaxy will be matched with both galaxies in the neighbor close
1
Even in the case in which some criteria for pair-matching are imposed, like line-of-sight constraints,
mass ratio, etc., one particular galaxy will be matched with many secondaries at very different separations.
68
CHAPTER 3
pair, two pairs with mark=ǫ + 1 will be contributed. Furthermore, imagine
now that there is another real close pair of galaxies placed at several Mpc
from the first close pair, in which both galaxies will also have mark=ǫ. From
matching all those 4 galaxies, the final product will be 6 galaxy pairs displaying
mark=2ǫ. This will clearly affect both the normalization of the mark and the
recovered value for the enhancement, producing a tail of false enhancement
in the regions where more companions would be found (representing dense
regions of the Universe) and decreasing the enhancement found at r < rc .
3.3
Results
I show this effect in Fig. 3.1. Clearly, a relatively weak tail of enhancement
is recovered out to large separations. The amplitude of this tail has a radial
dependence, as close pairs of galaxies tend to be found in dense regions of the
Universe (Barton et al. 2007), where more neighbors are available. As the
magnitude of this tail depends on the distribution of neighbors as a function
of the separation it will be more relevant for galaxy samples in which the
clustering is stronger (e.g., massive galaxies, or non star-forming galaxies).
Also visible in Fig. 3.1 is the dilution of the recovered enhancement compared
with the actual enhancement ǫ for pairs with r < rc ; E(r < rc ), is lower than the
”real” enhancement ǫ by a factor which increases with ǫ. This effect is better
seen in Fig.3.2, where I show the relative discrepancy between E(r < rc ) and
ǫ, as a function of ǫ. In this idealized case, this discrepancy can be exactly
recovered by accounting carefully for the different pairs formed by galaxies in
the sample. The relationship between E(r < rc ) and ǫ is:
E(r < rc ) =
ǫ Np,tot
,
Wcp,max Ncp,max + Wmp Nmp + Wf p Nf p
(3.3)
where Np,tot is the total number of pairs which can be formed from the galaxy
sample2 , Ncp,max is the total number of pairs which can be formed with galaxies
belonging to close pairs3 ,Wcp,max is the weight associated with those pairs, Npm
is the number of pairs in which only one galaxy belongs to a close pair, Wmp is
the weight associated with them, and Wf p and Np,f ar are respectively the weight
2
When performing an autocorrelation, the total number of unique pairs would be N (N − 1)/2, N being
the number of galaxies in the sample.
3
This is not the same as the number of close pairs, as I already explained.
SYSTEMATIC ERRORS IN WEIGHTED 2–POINT CORRELATION FUNCTIONS 69
Figure 3.1 Apparent enhancement as a function of distance and ”real” enhancement ǫ
(which acts only at r < rc kpc) computed for a sample with a minimum stellar mass of
2.5 × 1010 M⊙ and different values of ǫ. The vertical dotted line shows the separation rc (35
kpc in this case). A tail of artifial enhancement extending to large separations is produced
as an artifact of the weighted correlation function method. The enhancement recovered
in the close pairs r < rc kpc is reduced respect to ǫ and the level of reduction is a strong
function of ǫ (see text and Fig 3.2 for more details).
and the number of pairs in which none of the galaxies belongs to a close pair.
In the particular case of an additive weight, this expression reduces to:
E(r < rc ) =
(f 2
2ǫ
,
+ f )(ǫ − 1) + 2
(3.4)
where f is the fraction of galaxies in close pairs. The degree of clustering
of the sample is reflected in the value of f , so this expression is valid under
different clustering conditions. For the purposes of this work, I calculate f
directly from the mock catalogue, but real galaxy surveys lack of accurate 3D
information. In principle f can be calculated from the 2-point correlation
function by integrating Eq.3.1 out to the distance one considers a pair to be
close (rc ). If the correlation function is parametrized as a power law ξ(r) =
(r/r0 )−γ , then:
Z
rc
n[1 + ξ(r)]dV
P (r < rc ) = f =
0
(3.5)
70
CHAPTER 3
Figure 3.2 Relative error in E(r < rC ), the enhancement recovered by the marked
correlation function in close pairs as a function of the ”real” enhancement ǫ in those
pairs. For this example I have used, as in Fig. 3.1 a lower mass cut of 2.5 × 1010 M⊙ .
Diamonds: Recovered values from the method. Solid line: Expected value using the
proper normalization shown in Eq. 3.4. The error when the intrinsic enhancement is small
is modest; when ǫ < 4 then the discrepancy between E(r < rc ) and ǫ is < 10%.
f≃
4πn γ 3−γ
r r .
3−γ 0 c
(3.6)
In a work in preparation, I explore the validity of Eqn. 3.6, finding that it is a
reasonable approximation for rc < 50 kpc for realistic degrees of clustering, but
that Eqn. 3.6 is increasingly inaccurate for larger rc or stronger clustering.
It is worth noting that in the above example I have studied the simple
case in which the enhancement is present only in close galaxy pairs, with
the enhancement represented by a step function. When applying weighted
correlation functions to more complex problems, like those involving clustering
of the mass or color, the function describing the behavior of the weight on
separation would be much more complex. In that case, an expression for the
behavior of the weight as a function of separation will have to be derived
on a case-by-case basis and matched with the data. Yet, even in that more
complex case, the underlying problem is very similar: the magnitude of any
radial dependence in properties will be diluted and smeared out in radius by
the use of weighted 2 point correlation function methods.
SYSTEMATIC ERRORS IN WEIGHTED 2–POINT CORRELATION FUNCTIONS 71
3.4
An example application to observations
In order to test the relevance of this analysis to the real Universe, I compare my
predictions with a well-established phenomenon: the enhancement of the star
formation rate (SFR) in galaxy interactions. This observable has two obvious
advantages. Firstly, appart from ny results in the previous chapter there are
a number of works in which this enhancement has been studied (Barton et al.
2000; Lambas et al. 2003; Li et al. 2008) Second, the SFR is expected to
be enhanced only at scales at which galaxy-galaxy interactions are relevant;
beyond that scale star formation is not only not expected to be enhanced, but
should be depressed because of the well known SFR-density anticorrelation
(e.g., Balogh et al. 2002). From the above mentioned works I choose to
compare with Li et al. (2008) for three reasons: a) they use marked statistics,
b) their large sample allowed an accurate estimate of enhancement to be made,
and c) SDSS clustering has been shown to be similar to the one present in the
De Lucia et al. (2006) mock catalogue from the Millenium Simulation in the
local Universe (Springel et al. 2005).
Figure 3.3 Specific SFR enhancement in (massive) galaxy pairs as function of the projected
separation as measured by Li et al. (2008) (diamonds) and my prediction including the tail
of artificial enhancement out to several hundred kiloparsecs (solid line). In this example a
value of ǫ = 1.8 has been used. The galaxy sample has been selected to be consistent with
the massive sample in Li et al. (2008).
Real galaxy surveys, even spectroscopic surveys, have no access to the real
space separation of galaxies. Li et al. (2008) used a projected correlation
function w(rP ) to circumvent this difficulty, where the projected correlation
72
CHAPTER 3
function is related to the 3D correlation function via:
Z ∞
w(rp ) =
ξ([rp2 + π 2 ]1/2 )dπ,
(3.7)
−∞
where π is the coordinate along the line of sight, and rp is the projected
separation transverse to the line of sight. I use for this exercise galaxies
more massive than 3 × 1010 M⊙ in order to match the selection criteria in Li
et al. (2008). Moreover, they did not use an additive weight but used the
SSFR of the primary galaxy as the weight of the pair. I also use such a
scheme here to perform my weighted analysis in the simulation. Li et al.
(2008) calculated the cross-correlation between a subsample of galaxies which
are forming stars (primaries) and all the galaxies in the sample (secondaries).
As I lack of such information I run a correlation using all the galaxies as
both primaries and secondaries. I choose to model the data with a constant
enhancement ǫ = 1.8 at r < rc , with rc = 35 kpc. I also neglect any environmental
suppression of star formation at separations r > rc (Barton et al. 2000; Balogh
et al. 2002). These are clearly oversimplifications, as the real dependence of
enhancement (and suppression at large radii) on separation will be considerably
more complex. Yet, this simple model suffices to illustrate the recovered
enhancement signature expected from a model in which SF is enhanced only
at small radii.
Notwithstanding these limitations, I compare the results of my simple model
with the data in Fig. 3.3. Strikingly, I find that the tail of enhanced SF out
to ∼200kpc seen in the data may, in great part, be a reflection of the use of
marked correlation functions statistics to explore the radial dependence of SF
enhancement in galaxies. This has direct relevance in the interpretation of the
results from Li et al. (2008). If one argued that the enhancement at ∼ 100 kpc
(or much of it) was real, one would need to fulfil two criteria to produce such an
effect. Firstly, assuming that the triggering event is the first pass, one would
need an enhancement lifetime of at least 300Myr (longer than the internal
dynamical time) for typical orbital velocities of 300km/s or less. Secondly, a
significant fraction of the secondaries would need to have near-radial orbits in
order to produce such an enhancement. If, as I suggest instead, the enhanced
SF at ∼ 100 kpc is an artifact of the use of the 2 point correlation function, then
one would argue that enhancement happens only for close pairs and shorter
interaction-induced SF timescales and a greater diversity of orbits would be
permitted. While developing a model that realistically reproduces the data is
beyond the scope of this thesis, one can clearly see that this effect needs to be
SYSTEMATIC ERRORS IN WEIGHTED 2–POINT CORRELATION FUNCTIONS 73
accounted for in order to robustly interpret the behavior of marked correlation
functions.
3.5
Conclusions
Weighted correlation functions are an increasingly important tool for understanding how galaxy properties depend on their separation from each other.
I use a mock galaxy sample drawn from the Millenium simulation, assigning
weights using a simple prescription to illustrate and explore how well a weighted
correlation function recovers the true radial dependence of the input weights.
I find that the use of a weighted correlation function results in a dilution of
the magnitude of any radial dependence of properties and a smearing out of
that radial dependence in radius, compared to the input behavior. I present a
quantitative discussion of the dilution in the magnitude of radial dependence in
properties in the special case of a constant enhancement ǫ for pairs separated by
r < rc . In this particular case the matching of one member of an enhanced pair
with an unenhanced galaxy in the same group gives an artificial enhancement
∼ 0.1ǫ out to large radii < 5rc , and matches of one member of an enhanced pair
with a member of another very distant enhanced pair pulls down the value
of the recovered enhancement, with the discrepancy between the input and
recovered enhancement being a function of the fraction of galaxies in close pairs
and the value of the input enhancement. This systematic error is < 10% for
enhancements ǫ < 4, but precision measurements should account for this effect.
I compare these results with observations of SFR enhancement from the SDSS
Li et al. (2008), finding very similar behavior — a significant enhancement
at radii < 40 kpc and a weak enhancement out to more than 150 kpc, lending
credibility to the notion that weak enhancement in SFR seen out to large radii
is an artifact of the use of weighted correlation function statistics. While I
explored a particular case in this chapter, it is easy to see that the phenomenon
is general.
Given this difference between input weights and those recovered by the
weighted 2 point correlation function, one might ask if one shouldn’t use a
different method to explore radial trends in observables. I would argue that
most different methods boil down to weighted 2 point correlation functions
implicitly anyway, and that one is stuck at least at the qualitative level with the
differences between input and recovered weights that I have discussed above.
74
CHAPTER 3
For example, partnering projected pairs into different ’pairs’ (i.e., not matching
every galaxy with every other galaxy) suffers from two drawbacks: this is
still a projected analysis, and many projected close pairs will be separated by
significant distances along the line of sight; and second, one may choose the
wrong galaxy to partner with, a particularly acute issue for triplets or groups of
galaxies. One can see that such a method will suffer from a similar supression
of enhancement from the inclusion of non-pairs in the pair sample; of course,
radial smearing is not possible in such a case, as there is only one radial bin.
I conclude that those wishing to quantitatively analyze weighted correlation
functions (or related observables) will need to account carefully for this effect
using an analysis of simulated mock catalogs.
Chapter 4
The Merger–Driven Evolution of Massive
Red Galaxies
In the introduction of this thesis (Chapter 1) I have mentioned that galaxy
mergers are expected to be one of the main modes of massive galaxy growth in
a hierarchical Universe. Now I focus on the impact of mergers on the build–up
of massive red galaxies.
While the stellar populations of such massive red galaxies were already formed
at redshift z > 1, these galaxies are expected to continue their mass–assembly
at later times by the addition of stellar mass through merging. A factor ∼
2 − 3 evolution in number density has been observed around the knee of the
luminosity function (LF) of red galaxies at ∼ 1011 M⊙ since z = 1 (Bell et al.
2004; Faber et al. 2007; Brown et al. 2007), but studies of much more massive
galaxies have found results compatible with no evolution in that redshift range
when accounting for passive luminosity evolution (Cimatti et al. 2006; Cool
et al. 2008).
The goal of this chapter is to estimate the impact of galaxy mergers on the
evolution of massive, red galaxies from z = 1 to the present day. The main
challenge in observational studies of merger statistics is the identification of
such systems. Galaxy mergers are found either in an early phase of the
interaction, when the two galaxies have not yet coalesced and are found in
a close pair (Patton et al. 2000; Le Fèvre et al. 2000; Lin et al. 2004, 2008; Bell
et al. 2006b; Kartaltepe et al. 2007), or in a later phase, when they display
signatures of gravitational interaction and are just prior to or after coalescence
(Abraham et al. 1996; Conselice et al. 2003; Lotz et al. 2004; Bell et al. 2005;
McIntosh et al. 2008; Jogee et al. 2009). A wide range of results have been
found for the merger fraction evolution, parameterized as (1 + z)m , with m
ranging from 0 to 4 (e.g., Patton et al. 2000; Le Fèvre et al. 2000; Lin et al.
75
76
CHAPTER 4
2004; Kartaltepe et al. 2007).
Here, I use robust 2–point correlation function techniques on a sample of
galaxies with 0.2 < z < 1.2 with masses in excess of 5 × 1010 M⊙ selected from
the COSMOS and COMBO–17 surveys to quantify the merger rate of massive
galaxies and its evolution. I augment the statistical significance of my analysis
by using an estimate of the pair fraction found in Sloan Digital Sky Survey
(SDSS) at z ∼ 0.1. The total volume probed by this study at intermediate
redshifts is at least 4 times larger than any previous mass–selected study on
the evolution of the merger fraction, and reduces dramatically the systematic
uncertainties related to cosmic variance by the use of four independent fields.
Then I compare the inferred galaxy merger rate with the observed number
density evolution of massive (M∗ > 1011 M⊙ ), red galaxies from z ∼ 1 to the
present day, which I obtain by converting Brown et al. (2007) LFs to stellar–
mass functions. I assume H0 = 70 km/s, Ωm = 0.3 and ΩΛ = 0.7.
4.1
Sample and method
The bulk of my sample is drawn from the ∼2 sq. degree COSMOS survey
(Scoville et al. 2007). I use photometric redshifts calculated from 30-band
photometry by Ilbert et al. (2009); comparison with spectroscopic redshifts
shows excellent accuracy. I use those redshifts to derive rest-frame quantities
and stellar masses by using the observed broad-band photometry in conjunction
with a non-evolving template library derived using Pégase stellar population
model (see Fioc & Rocca-Volmerange 1999) and a Chabrier (2003) stellar initial
mass function (IMF). The use of a Kroupa et al. (1993) or a Kroupa (2001)
IMF would yield similar stellar masses to within ∼ 10%. The reddest templates
are produced through single exponentially–declining star formation episodes,
intermediate templates also have a low-level constant star formation rate (SFR)
and the bluer templates have superimposed a recent burst of star formation.
A full description of the stellar masses will be provided in a future paper;
comparison with Pannella et al. (2009) masses shows agreement at the 0.1 dex
level.
To combat the sample variance of a single 2 sq. degree field, I augment
the COSMOS sample with a sample drawn from three widely-separated 0.25
sq. degree fields from COMBO-17. COMBO–17 photo-z’s, colors and stellar
masses have been extensively described in Wolf et al. (2003),Wolf et al. (2004),
THE MERGER–DRIVEN EVOLUTION OF MASSIVE RED GALAXIES
77
Borch et al. (2006) and Gray et al. (2009). Given the different depths of the
two surveys I only include galaxies from the COMBO-17 catalog at z < 0.8,
where it is complete for my mass limit. The final sample comprises ∼ 18000
galaxies with M∗ ≥ 5 × 1010 M⊙ over an area of ∼ 2.75 sq. deg. in the redshift
range 0.2 < z < 1.2.
I use the fraction of galaxies with a companion closer than 30 kpc (close pairs)
as a proxy for the merger fraction, as those systems are very likely to merge
in a few hundred Myr1 . As redshift errors translate into line-of-sight (l.o.s.)
distance uncertainties of the order of ∼ 50 − 100 Mpc I use projected 2-point
correlation functions (2pcf) to find the number of projected close pairs and
then deproject into the 3D space.
The projected correlation function w(rP ) is the integral along the line of sight
of the real-space correlation function:
w(rp ) =
Z
∞
ξ([rp2 + π 2 ]1/2 )dπ,
(4.1)
−∞
where rp is the distance between the two galaxies projected on the plane of sky
and π the line-of-sight separation. A convenient and simple estimator of the
2pcf at small scales is w(rp ) = ∆(DD/RR − 1) (e.g. Bell et al. 2006b), where ∆ is
the path length being integrated over, DD(rP ) is the histogram of separations
between real galaxies and RR(rP ) is the histogram of separations between
galaxies in a randomly-distributed catalog. As shown in the literature (e.g.
Davis & Peebles 1983; Li et al. 2006a), the real-space 2pcf can be reasonably
well fit by a power-law. Assuming ξ(r) = (r/r0 )−γ , then w(rp ) = Cr0γ r01−γ , with
√
C π{Γ[(γ − 1)/2]/Γ(γ/2)}. I fit the latter expression to my data to find the
parameters γ and r0 and use them in the real-space 2pcf to find the fraction of
galaxies in close pairs.
As I wish to preserve S/N I did not integrate along the entire l.o.s. when
calculating w(rP ). Instead I allowed galaxies to form a pair only if the redshift
√
difference was smaller than σpair = 2 × σz , with σz being the redshift error
of the primary galaxy. As the photo-z errors follow a Gaussian distribution
with width σz (Wolf et al. 2003, 2004) a fraction of the pairs would be missing
by simply imposing the l.o.s. criteria. Thus, following Bell et al. (2006b) the
fraction of galaxy pairs is
1
As the lower mass limit of my sample is 5 × 1010 M⊙ , I am automatically selecting both members of
the pair to be above that mass.
78
CHAPTER 4
f=
Z
σpair
−σpair
√
1
2
2
e−z /2σz dz.
2πσz
(4.2)
Then, w(rP ) is multiplied by 1/f in order to account for missing pairs; in my
case a correction factor of 1.19.
Given the 3D correlation function ξ(r), the differential probability of finding
a galaxy occupying a volume δV at a distance r of another galaxy is δP =
n[1 + ξ(r)]δV , where n is the number density of secondary galaxies. Then, by a
simple integration of this expression, I obtain the probability of a galaxy being
within a distance rf of any other galaxy (Patton et al. 2000; Bell et al. 2006b;
Masjedi et al. 2006):
P (r ≤ rf ) =
Z
rf
n[1 + ξ(r)]dV
(4.3)
0
Because ξ(r) = (r/r0 )−γ and ξ(r) ≫ 1 at the small scales, I obtain:
P (r ≤ rf ) = fpair =
4πn γ 3−γ
r r ,
3−γ 0 f
(4.4)
where fpair is the fraction of galaxies in close pairs. As galaxy interactions
are completely decoupled from the Hubble flow, I calculate probabilities as a
function of the proper (physical) separation between the two galaxies. Errors
in the correlation function are calculated by means of bootstrap resampling.
4.2
Results and discussion
In Fig. 4.1 I show the fraction of massive galaxies found in pairs with separations
r < 30 kpc as a function of z. To augment the data at z ∼ 0.1, I calculate the
SDSS close pair fraction using γ and r0 given by Li et al. (2006a). I adjust
their r0 by ∼ 5% (an empirical adjustment based on the COSMOS+COMBO17 sample) to account for different lower mass limits and binning. I also use
the number density of galaxies fulfilling my mass criteria, adopting the g-band
selected stellar-mass function in Bell et al. (2003) after correcting for stellar
IMF and H0 .
I perform an error-weighted least-squares fit of the form F (z) = f (0) × (1 +
THE MERGER–DRIVEN EVOLUTION OF MASSIVE RED GALAXIES
79
Table 4.1 3D correlation function parameters and close pair fractions
z
0.2 < z ≤ 0.4a
0.4 < z ≤ 0.6a
0.6 < z ≤ 0.8a
0.8 < z ≤ 1.0b
1.0 < z ≤ 1.2b
a
b
γ
2.03 ± 0.05
2.06 ± 0.04
1.94 ± 0.04
1.93 ± 0.03
1.96 ± 0.03
r0
3.50 ± 0.50
3.60 ± 0.50
3.80 ± 0.30
2.85 ± 0.25
2.55 ± 0.20
fpair (¡ 30 kpc)
0.0171 ± 0.0050
0.0238 ± 0.0043
0.0241 ± 0.0038
0.0277 ± 0.0031
0.0315 ± 0.0030
Combined COSMOS+COMBO–17 sample
COSMOS–only sample
Figure 4.1 Fraction of M∗ > 5 × 1010 M⊙ galaxies in close (3D) pairs (r < 30 kpc) as a
function of redshift. Diamonds: Pair fraction found using only the COSMOS catalog. Black
circles: Pair fraction found when adding galaxies from the COMBO–17 survey at z < 0.8
(I do not include galaxies from the COMBO–17 catalog in the two higher z bins). Star:
Pair fraction from SDSS. The line shows the best fit to a real space pair fraction evolution
with shape F (z) = f (0) × (1 + z)m , with f (0) = 0.0130 ± 0.0019 and m = 1.21 ± 0.25 (fit
to all black-filled points: star, circles and diamonds). Dashed line: Predicted fraction of
galaxies above M∗ > 5 × 1010 M⊙ involved in mergers, from the Somerville et al. (2008)
model.
80
CHAPTER 4
z)m to the filled points in Fig. 4.1, i.e., the SDSS pair fraction, the combined
COSMOS+COMBO–17 pair fraction at 0.2 < z < 0.8 and the COSMOS pair
fraction at 0.8 < z < 1.2. I find f (0) = 0.0130 ± 0.0019 and m = 1.21 ± 0.25. These
associated uncertainties are at the same level as the systematic uncertainties
in the overall M/L scale and its evolution since z = 1.
In my correlation function I do not impose an specific mass ratio criteria, but
given the shape of the mass function above M∗ > 5 × 1010 M⊙ , I expect most of
the mergers to be majors; i.e., with mass rations between 1:1 and 1:4. I find
between 70 and 90 percent of the purely projected close pairs have such a mass
ratio.
Galaxies from the COSMOS survey represent 70% of my sample in the bins
ranging from z = 0.2 to z = 0.8, however, the addition of COMBO–17 galaxies
helps to decrease the sample variance. From the work by Moster et al. (in
prep), I estimate that the sample variance is reduced by a factor of ∼ 30% by
including the three ∼ 0.25 sq. deg independent fields from COMBO–17. This
effect is clearly seen in Fig. 4.1. Considering only galaxies from COSMOS,
there is an abrupt transition between z = 0.7 and z = 0.9, which is smoothed by
the inclusion of COMBO–17 galaxies.
In Fig. 4.1 I include the close pair fractions found using mock catalogs from
the Somerville et al. (2008) semi-analytic model (SAM). There is qualitative
agreement between the slow evolution and overall normalization between
models and observations, and given the difficulty that all models have in
matching the shape of the stellar mass function in detail (which affects both
the numerator and denominator of the close pair fraction; De Lucia et al. 2006;
Somerville et al. 2008), I find this match encouraging. Predictions from other
SAMs tend to agree reasonably well with Somerville et al. (2008) as shown in
Fig. 11 of Jogee et al. (2009; see also Guo & White 2008).
4.2.1
Comparison with previous works
Very few studies of close pair fraction evolution use mass-limited samples. Bell
et al. (2006b) used COMBO–17 data (0.75 sq. deg., the same catalog I use here
to complement my COSMOS catalog) to find a fraction of galaxies in close
major pairs (r < 30 kpc) of 2.8% for galaxies more massive than 3 × 1010 M⊙
at 0.4 < z < 0.8, in excellent agreement with my result despite the slightly
different mass limit. They also performed an autocorrelation of all galaxies
THE MERGER–DRIVEN EVOLUTION OF MASSIVE RED GALAXIES
81
Figure 4.2 Evolution of the number of galaxies in close pairs. The estimate for major pair
fraction of galaxies M > 3 × 1010 M⊙ from Bell et al. (2006b) is shown as empty squares.
The results from Bundy et al. (2009) are represented by the asterisks. The point by Xu
et al. (2004) is shown as the grey diamond. McIntosh et al. (2008) is shown as the grey
star.
with M∗ > 2.5 × 1010 M⊙ finding a pair fraction of ∼ 5%. This mismatch in
pair fraction is entirely a consequence of the lower mass limit of the sample;
adopting in my analysis instead a mass limit of M∗ > 2.5 × 1010 M⊙ I recover
a pair fraction of ∼ 5%. The main driver of this higher pair fraction is that
∼ 50% of pairs in a sample limited to have M∗ > 2.5 × 1010 M⊙ have mass ratios
between 1:4 and 1:10; i.e., the major merger fraction is similar, but the close
pair fraction is boosted by a considerable contribution from minors.
Recently, Bundy et al. (2009) found a higher pair fraction by studying a sample
of galaxy pairs from the GOODS fields (total area ∼ 0.36 sq. deg.). In Fig. 4.2 I
show their results for the mass range > 3×1010 M⊙ after converting their fraction
of pairs to the fraction of galaxies in pairs. I cannot explain why their results
are so different from mine. I also show the estimate from Xu et al. (2004),
who used a combined sample from the 2MASS and 2dFGRS surveys, after
converting their results to my IMF and H0 , and the result from McIntosh et al.
82
CHAPTER 4
(2008), who measured the pair fraction in galaxy groups. I further correct the
pair fractions found by Xu et al. (2004) and Bundy et al. (2009) down by 30%
to account for pairs in their analyses that are genuinely associated with each
other (so are not random projections), have projected separations of < 30 kpc
but are separated by more than 30kpc in real space (i.e., galaxies in groups
that are projected along the line of sight; Bell et al. 2006b)2 .
I can not compare my measurements with morphological studies of merger
fractions because of uncertainties with the nature of the progenitors, and
selection effects related to orbital parameters, galaxy structure and gas
fractions. It is also hazardous to compare with close pair measurements
based on luminosity-selected samples. Lin et al. (2008) used a sample of
galaxies with B-band magnitudes (corrected for passive luminosity evolution)
−21 < MB < −19. For red galaxies, this is roughly compatible with my
mass–selected sample, but it includes many low-mass blue galaxies, which
makes a comparison impossible because their clustering properties are very
different. Furthermore, as merging can enhance the star formation activity
(see Chapter 2), selecting galaxies in rest-frame blue bands is biased in favor
of mergers, as such a selection would recover merging systems with lower mass
given the decreased M/L ratio induced by the interaction. All of these effects
will be more pronounced in gas–rich galaxies, and gas fractions were likely
higher in the past, leading to a redshift dependent bias.
Kartaltepe et al. (2007) derived the evolution of the pair fraction from a
luminosity-selected sample from a similar dataset as analyzed in this chapter.
Their very different result (they find m = 3.1 ± 0.1) is caused at least in
part by the difference between mass– and luminosity–selected samples, as
described above. In addition, they identify pairs in both the ground-based
and HST/ACS-based catalogues. Because their sample is selected by groundbased luminosity, very close pairs that are only resolved by ACS can be as
bright as a single galaxy in a more widely separated pair that is resolved in the
ground-based imaging. This artificially raises that close pair fraction, especially
at high redshift.
2
This effect is present also in pair fractions determined from spectroscopic redshifts as long as a
deprojection to the 3D space is not performed.
THE MERGER–DRIVEN EVOLUTION OF MASSIVE RED GALAXIES
4.2.2
83
The impact of galaxy merging on the creation of red M∗ >
1011M⊙ galaxies.
My measured fraction of M∗ > 5 × 1010 M⊙ galaxies in close pairs as a function
of redshift constrains the impact that merging-induced mass assembly has on
the creation rate of M∗ > 1011 M⊙ systems.
As only ∼ 6% of my galaxies with a projected companion at r < 30 kpc has a
second companion at such separation, I assume that the number of close pairs is
simply one half of the number of galaxies in close pairs. The fraction of newly
created M∗ > 1011 M⊙ galaxies due to merging is frem = Ncp /N11 , where Ncp is the
number of close pairs of galaxies above 5 × 1010 M⊙ each and N11 is the total
number of galaxies with stellar masses in excess of 1011 M⊙ .
Following Patton & Atfield (2008) or Bell et al. (2006b), the merger timescale
for galaxy pairs at this separation is approximately τ = 0.5 Gyrs, so I compute
the creation rate of newly assembled galaxies, Rrem , as Rrem = frem /τ . I integrate
the merger rate over cosmic time finding that, on average, present day galaxies
with stellar masses larger than 1011 M⊙ have undergone 0.5 (0.7) mergers since
z = 0.6 (1.2) from interactions between galaxies more massive than 5 × 1010 M⊙ .
Now I want to address the question whether my observed merger rate evolution
can explain the observed number density evolution of M∗ > 1011 M⊙ red galaxies.
I assume that mergers of massive galaxies quench the star formation activity
and the remnants will be red systems in order to compare with the number
density evolution of red galaxies.
I convert the evolution of the B-band luminosity function of red galaxies as
measured by Brown et al. (2007) to the evolution in the number density
of galaxies more massive than 1011 M⊙ . For this conversion I use the typical
stellar mass-to-light ratio of nearby red galaxies (M/LB = 3.4 ± 0.6, e.g., Bell
et al. 2003; Kauffmann et al. 2003) and apply a correction to account for its
evolution with redshift, derived from the evolution of the fundamental plane
zero point (∆ log(M/LB ) = 0.555 ± 0.042., van Dokkum & van der Marel 2007).
I repeat the process 10000 times allowing the luminosity function parameters,
as well as the M/LB constraints, to vary randomly within their uncertainties.
I estimate the final uncertainty by estimating the typical dispersion of those
10000 realizations.
In Fig. 4.3 I show the observed evolution on the number density of massive, red
84
CHAPTER 4
Figure 4.3 Number density evolution of red galaxies with M∗ > 1011 M⊙ . Filled points
represents the observed evolution by Brown et al. (2007) (see text for details). The solid
line shows the expected growth implied by my measurement of the close pair fraction.
galaxies together with the evolution implied by my merger rate measurement.
I stress that both measurements are completely independent except for the fact
that I use the observed density at z ∼ 0.9 as the zeropoint where I anchor the
evolution predicted by my close pair fractions. I find that mergers of massive
galaxies can explain the evolution in the observed number density of massive,
red galaxies since z = 1. I have used τ = 0.5 Gyrs, but using the τ ∼ 1 Gyr
timescale from Kitzbichler & White (2008) yields a somewhat slower evolution
that is still compatible within the error bars.
There are two caveats I would like to mention. Firstly, given the nature of my
method, some of the progenitor galaxies have masses above 1011 M⊙ , so strictly
speaking they are not newly formed massive galaxies. Second, because I adopt a
lower mass limit of 5 × 1010 M⊙ , I underestimate the number of major mergers
that could lead to the formation of a massive galaxy. For example, a pair with
individual masses M∗ = 6 × 1010 M⊙ and M∗ = 4 × 1010 M⊙ would not make it
into my pair sample but would produce a major merger remnant of 1011 M⊙ .
Assuming that the merging population has a composition similar to my overall
THE MERGER–DRIVEN EVOLUTION OF MASSIVE RED GALAXIES
85
sample, I estimate that this latter lower mass limit issue has an impact a factor
∼ 2 larger on the creation of > 1011 M⊙ galaxies than the overestimate caused
by double counting already massive red galaxies (i.e., for each pair in which a
progenitor was already above my mass limit I have ∼ 2 pairs which will form
a massive remnant that I am not counting because of my mass limit). Thus,
if anything, I underestimate the real creation rate of massive galaxies induced
by merging.
4.3
Conclusions
I have studied the impact of galaxy mergers on the evolution of massive red
galaxies by using 2pcfs to measure the fraction of galaxies in close pairs from
a sample of ∼ 18000 galaxies more massive than 5 × 1010 M⊙ drawn from the
COSMOS and COMBO–17 surveys and a pair fraction estimate from SDSS.
I have also used constraints from the observed evolution of the fundamental
plane to calculate the number density evolution of > 1011 M⊙ red galaxies from
Brown et al. (2007) LFs. My main findings are:
• The fraction of galaxies in close pairs evolves as F (z) = (0.0130±0.0019)×(1+
z)1.21±0.25 . When assuming a merging timescale of τ = 0.5 Gyr it implies that
galaxies more massive than 1011 M⊙ have undergone, on average, 0.5(0.7)
major mergers since z = 0.6(1.2).
• The evolution implied by this merger rate is sufficient to explain the
observed number density evolution of red galaxies with masses above
1011 M⊙ . This result, together with the recent finding by van der Wel
et al. (2009) that all massive quiescent galaxies in the local Universe have
been formed by mergers, points to a scenario in which mergers are the
dominant mechanism responsible for the formation of the red sequence
above such stellar mass.
Chapter 5
Conclusions
In this thesis I have studied the impact of major galaxy mergers on the
evolution of galaxies over the last ∼ 8 Gyrs. I have used ground–based and
space–based photometry from the UV to the MIR to constrain, specifically,
how mergers influence the creation of new stars in the Universe and how much
they contribute to the assembly of stellar mass in massive, elliptical galaxies
from already formed stars. I also had to develop statistical tools which will
improve the reliability of future studies on the clustering of physical properties
of galaxies.
In Chapter 2 I have made use of COMBO–17 survey redshifts and stellar
masses, together with 24µm photometry from Spitzer in order to study the SF
enhancement induced by galaxy interactions. This study has produced three
main results: a) When averaged over all interactions and all phases of the
interaction, the star formation activity is enhanced by a factor of 1.8 ± 0.3; b)
Most of the interactions do not induce a ULIRG phase, but nevertheless, it
seems that in order to reach the highest levels of SFR observed, interactions
are required; and c) Over the redshift range 0.4 < z < 0.8, roughly 20% of the
star formation density is found in major interacting systems, but only a 8 ± 3%
of such star formation is directly triggered by the interaction.
While working on the already mentioned problem of the SFR enhancement in
galaxy interactions I found that the statistical tool I was using, the weighted
2-point correlation function, could introduce a bias in the shape of the recover
enhancement. In Chapter 3 I used the Millennium Simulation in order to
estimate the magnitude of the bias that the use of such a tool would introduce
on my results. My findings were that the nature of the 2-point analysis, in
which every point is matched with every other point, was causing that galaxies
close to a physical close pair were inheriting a fraction of the enhancement
87
88
CHAPTER 5
even if a causal relation does not exist. My simulations show that in those
cases where the enhancement is relatively small (< 4), the overall uncertainty
is negligible. On the other hand, studies of physical properties which strongly
correlate with galaxy clustering should correct for this bias.
In Chapter 4 I have addressed one of the big open questions in modern studies
of galaxy evolution, this is, the contribution from galaxy mergers to the buildup of the red sequence at large stellar masses. I have used catalogs from
the COSMOS and COMBO–17 surveys in order to estimate the merger rate
evolution from z = 0 to z = 1.2 and constrain the implications for the formation
of red galaxies with stellar masses larger than 1011 M⊙ . I found that the fraction
of M∗ ≥ 5 × 1010 M⊙ galaxies found in close pairs at separations r < 30 kpc
evolves as F (z) = (0.0130 ± 0.0019) × (1 + z)1.21±0.25 . By assuming a pair timescale
of τ = 0.5 Gyr this pair fraction implies that, on average, galaxies more massive
than 1011 M⊙ have undergone 0.5(0.7) major mergers since redshift 0.6(1.2).
I have also used the luminosity functions of red galaxies in the rest-frame B
band from Brown et al. (2007) to measure the number density evolution of M∗ >
1011 M⊙ red galaxies. I transformed those luminosity functions to mass functions
by using constraints on the M/LB ratio evolution from the fundamental plane
of elliptical galaxies from z = 1 to z = 0 (van Dokkum & van der Marel 2007)
and a normalization of such ratio in the local Universe from SDSS (Bell et al.
2003; Kauffmann et al. 2003). I found that the number density of massive red
galaxies has increased by a factor of ∼ 4 since z = 1 and that the merger rate of
massive galaxies can, under the assumption that all merger remnants will be
red galaxies, explain such evolution.
Overall, this thesis has helped to understand the role that galaxy mergers
play in the big picture of galaxy evolution in the last 8 gyrs. Cosmologically
speaking, major mergers are not an important factor in the formation of new
stars since z = 1, since less than 10% of the star formation has a causal
relation with such events. On the other hand, I have argued that major galaxy
interactions play a crucial role in in the build–up of stellar mass in massive red
galaxies. These two results, which could seem mutually exclusive at first sight
are rather complementary, i.e., major mergers are irrelevant for the generation
of new stellar mass in the Universe, but they cause the reorganization of
the already existent stellar mass transforming disks into bulges and adding–up
galaxies to form more massive systems.
Ten or fifteen years ago we started to witness the high redshift Universe and
CONCLUSIONS
89
realized that the galaxy populations looked somehow different at different
times. Nowadays, it is clear that the global properties of galaxies not only
depend on the age of the Universe at which we observe them but also on the
environment in which the galaxy is found. Galaxies in dense environments
have, on average, different global properties (morphology, SF activity, color,
etc.) than galaxies in the field and that might have some impact in the global
evolution of galaxy populations. As an example, I have shown how galaxy
mergers drive the evolution of the massive end of the red sequence but we
do not know if the merger rate is dominated by galaxies in groups/clusters or
by galaxies in the field. Furthermore, we still do not have a definitive answer
to the question of what is driving the decline of the cosmic star formation
density, neither we know what quenches the star formation and force galaxies
to migrate from the blue cloud to the red sequence.
I have argued that mergers move galaxies in the mass axis of the color–mass
diagram, but more detailed studies are needed in order to understand if the
new formed very massive galaxies are assembled from a population of already
red galaxies on the red sequence or from the quenching of the star formation
in mergers involving blue galaxies. For example, mergers have been predicted
to trigger nuclear activity by driving large amounts of gas to the very central
region of the galaxy, where the supermassive black hole is expected to lie,
but not conclusive observational evidence has been found so far. Given the
relations linking the mass of the black hole with some properties of the galaxies,
coevolution is expected. I believe that it is not a minor problem for us as a
community that we have failed to confirm or refute such scenario.
We also need to understand what is driving the quenching in the lower mass
galaxies since z = 1. Mergers do certainly account for a fraction of the quenched
systems, but in the regime of M∗ < 1011 M⊙ galaxies, Ram-pressure stripping and
other environmental mechanisms are expected to play also an important role,
so does the gradual depletion of available gas. All these questions need to be
answered in order to understand the last 8 Gyrs of galaxy evolution.
But, indeed, the Universe does extend beyond z = 1. We are at the beginning
of the era in which NIR instrumentation has become sensitive enough to start
large galaxy surveys at z > 1, or in other words, we are starting to harvest
the desert. For example, massive elliptical galaxies at z ∼ 2 were 5 times
smaller than present day galaxies of equivalent stellar mass. Arguments in favor
and against mergers driving the evolution in the mass–size relation have been
published in the last two years, but I believe that we do not fully understand
90
CHAPTER 5
the process behind such an evolution. Another major breakthrough in the
last years has been the realization of the importance that the so-called clumpy
disk galaxies could have on galaxy evolution. The clumpiness of those disks is
expected to be related to massive flows of cold gas from the cosmic web. We do
not know what dominates the star formation density at z > 1 but we do know
that clumpy galaxies were relatively common at z > 1 and very rare at lower
redshifts. If the decline of the cosmic SFR since z ∼ 1 turns out to be related
with the absence of cold inflows, the study of these galaxies could provide a
huge step in the direction of understanding the star formation properties of
the Universe.
It is clear, then, that the knowledge about galaxy evolution has advanced at a
incredible rate over the last 15 years, but there are still many issues to be solved
before we can claim a profound comprehension of the field. In the next 10–20
years, thanks to powerful new instrumentation, we will collect new information
which will greatly help to reach a better understanding of our Universe.
The most exciting fact is that we might not have yet asked ourselves the
questions that we will answer over the next two decades.
Acknowledgements
I would like to thank all the people who have helped me in some way during
my thesis.
First of all, Eric Bell, my thesis advisor. He has not only guided me through
these years of research, saved my scientific life when the political side of
research was exceeding the limits of what I can take and been extremely patient
when I did come down to his office every second day with my newest crazy idea
about how to unveil the mysteries of the Universe, but also taught me what
might be the most important thing I have learned about Astronomy: There
are millions of questions out there to be answered, but only some are worth a
good astronomer’s time.
Arjen van der Wel is a postdoc at MPIA who has been helping me a great deal
during the last year of this thesis. He did not have any formal responsibility
on me but he has been extremely helpful for the development of this thesis,
to the point that I am not sure if I would have made it on time without him.
Thanks for that.
Hans–Walter Rix, Alejo Martı́nez Sansigre, Yolanda Sestayo de la Cerra, Dan
McIntosh, Isabel Franco Rico, Ros Skelton and Christine Ruhland have also
played an important role in the development of my research.
Christian Fendt, Ingrid Apfel and Heide Seifert for performing with exquisite
91
92
ACKNOWLEDGEMENTS
efficiency their work and helping in so many different issues during these years.
Uli Hiller and Marco Piroth. Every institute or university would be lucky to
have such great professionals and so willing-to-help technicians.
On the personal side, my wife Yolanda deserves the biggest acknowledgement
of all, because she has been the other half of the fine–tuned researcher–parental
machine we have formed in our little family. I remember how we used to discuss
about our thesis when we got to Heidelberg, later during the pregnancy and
more recently while we were playing with Silvia on the carpet. We have gone
through very hard times being so far from our families and now that we are
so close to the end I cannot believe we have made it. Thanks for all those
moments.
I take the opportunity to apologize to my wife for my (many and frequent)
jokes on “How can you know that if you haven’t detected one single highenergy neutrino so far?”
My parents, M. Dolores and Octavio, are responsible for half of what I am. I
can only admire the great efforts they have made to create the basis on which
we (my two brothers and myself) are building our lives. This thesis, as little
thing as it might be, is evidence for how well you have done your job. Thanks
for everything.
Silvia will be one day old enough to read these words. I want her to know that
in spite of the many sleepless nights, her temper when she looses the pacifier
and the permanent attention she requires because of her tendency to run faster
than what her short legs permit, she has been the light at the end of the tunnel,
the air that we deeply breathe when we had to run the final sprint.
She is my North Star.
Aday Robaina Rapisarda.
Heidelberg, 30th October 2009
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