Star Formation

Star Formation
To Appear in ARAA, vol. 50
Preprint typeset using LATEX style emulateapj v. 08/22/09
Robert C. Kennicutt, Jr.
Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, United Kingdom
arXiv:1204.3552v2 [astro-ph.GA] 22 Jun 2012
Neal J. Evans II
The University of Texas at Austin, Department of Astronomy, 2515 Speedway, Stop C1400 Austin, TX 78712-1205, USA
European Southern Observatory, Casilla 19001, Santiago 19, Chile
To Appear in ARAA, vol. 50
We review progress over the past decade in observations of large-scale star formation, with a focus
on the interface between extragalactic and Galactic studies. Methods of measuring gas contents and
star formation rates are discussed, and updated prescriptions for calculating star formation rates are
provided. We review relations between star formation and gas on scales ranging from entire galaxies
to individual molecular clouds.
Subject headings: star formation, galaxies, Milky Way
1.1. Introduction
Star formation encompasses the origins of stars and
planetary systems, but it is also a principal agent of
galaxy formation and evolution, and hence a subject at
the roots of astrophysics on its largest scales.
The past decade has witnessed an unprecedented
stream of new observational information on star formation on all scales, thanks in no small part to new facilities such as the Galaxy Evolution Explorer (GALEX),
the Spitzer Space Telescope, the Herschel Space Observatory, the introduction of powerful new instruments on
the Hubble Space Telescope (HST), and a host of groundbased optical, infrared, submillimeter, and radio telescopes. These new observations are providing a detailed
reconstruction of the key evolutionary phases and physical processes that lead to the formation of individual
stars in interstellar clouds, while at the same time extending the reach of integrated measurements of star formation rates (SFRs) to the most distant galaxies known.
The new data have also stimulated a parallel renaissance
in theoretical investigation and numerical modelling of
the star formation process, on scales ranging from individual protostellar and protoplanetary systems to the
scales of molecular clouds and star clusters, entire galaxies and ensembles of galaxies, even to the first objects,
which are thought to have reionized the Universe and
seeded today’s stellar populations and Hubble sequence
of galaxies.
This immense expansion of the subject, both in terms
of the volume of results and the range of physical scales
explored, may help to explain one of its idiosyncracies,
namely the relative isolation between the community
studying individual star-forming regions and stars in the
Milky Way (usually abbreviated hereafter as MW, but
sometimes referred to as “the Galaxy”), and the largely
extragalactic community that attempts to characterise
the star formation process on galactic and cosmologiElectronic address: [email protected]
Electronic address: [email protected]
cal scales. Some aspects of this separation have been
understandable. The key physical processes that determine how molecular clouds contract and fragment into
clumps and cores and finally clusters and individual stars
can be probed up close only in the Galaxy, and much of
the progress in this subject has come from in-depth case
studies of individual star-forming regions. Such detailed
observations have been impossible to obtain for even relatively nearby galaxies. Instead the extragalactic branch
of the subject has focused on the collective effects of star
formation, integrated over entire star-forming regions, or
often over entire galaxies. It is this collective conversion
of baryons from interstellar gas to stars and the emergent radiation and mechanical energy from the stellar
populations that is most relevant to the formation and
evolution of galaxies. As a result, much of our empirical
knowledge of star formation on these scales consists of
scaling laws and other parametric descriptions, in place
of a rigorous, physically-based characterization. Improving our knowledge of large-scale star formation and its
attendant feedback processes is essential to understanding the birth and evolution of galaxies.
Over the past several years, it has become increasingly
clear that many of the key processes influencing star formation on all of these scales lie at the interface between
the scales within individual molecular clouds and those of
galactic disks. It is now clear that the large scale SFR is
determined by a hierarchy of physical processes spanning
a vast range of physical scales: the accretion of gas onto
disks from satellite objects and the intergalactic medium
(Mpc); the cooling of this gas to form a cool neutral phase
(kpc); the formation of molecular clouds (∼ 10 − 100 pc);
the fragmentation and accretion of this molecular gas to
form progressively denser structures such as clumps (∼ 1
pc) and cores (∼ 0.1 pc); and the subsequent contraction
of the cores to form stars (R⊙ ) and planets (∼ AU). The
first and last of these processes operate on galactic (or
extragalactic) and local cloud scales, respectively, but
the others occur at the boundaries between these scales,
and the coupling between processes is not yet well understood. Indeed it is possible that different physical pro-
Kennicutt and Evans
cesses provide the “critical path” to star formation in different interstellar and galactic environments. Whatever
the answer to these challenging questions, however, Nature is strongly signalling that we need a unified approach
to understanding star formation, one which incorporates
observational and astrophysical constraints on star formation efficiencies, mass functions, etc. from small-scale
studies along with a much deeper understanding of the
processes that trigger and regulate the formation of starforming clouds on galactic scales, which, in turn, set the
boundary conditions for star formation within clouds.
This review makes a modest attempt to present a consolidated view of large-scale star formation, one which incorporates our new understanding of the star formation
within clouds and the ensemble properties of star formation in our own MW into our more limited but broader
understanding of star formation in external galaxies. As
will become clear, the subject itself is growing and transforming rapidly, so our goal is to present a progress report in what remains an exciting but relatively immature
field. Nevertheless a number of factors make this a timely
occasion for such a review. The advent of powerful multiwavelength observations has transformed this subject in
fundamental ways since the last large observational review of the galaxy-scale aspects (Kennicutt 1998a), hereafter denoted K98. Reviews have covered various observational aspects of star formation within the MW (Evans
1999; Bergin & Tafalla 2007; Zinnecker & Yorke 2007),
but the most comprehensive reviews have been theoretically based (Shu et al. 1987; McKee & Ostriker 2007).
We will take an observational perspective, with emphasis on the interface between local and galactic scales. We
focus on nearby galaxies and the MW, bringing in results from more distant galaxies only as they bear on the
issues under discussion.
The remainder of this article is organized as follows.
In the next subsection, we list some definitions and conventions that will be used throughout the paper. All
observations in this subject rest on quantitative diagnostics of gas properties and star formation rates on various
physical scales, and we review the current state of these
diagnostics (§2, §3). In §4, we review those properties of
Galactic star-forming regions which are most relevant for
comparison to other galaxy-wide studies. In §5, we review the star-forming properties of galaxies on the large
scale, including the MW; much of this section is effectively an update of the more extended review presented
in K98. Section 6 updates our knowledge of relations between star formation and gas (e.g., the Schmidt law) and
local tests of these relations. The review concludes in §7
with our attempted synthesis of what has been learned
from the confluence of local and global studies and a look
ahead to future prospects.
We list in §1.3 some key questions in the field. Some
have been or will be addressed by other reviews. Some
are best answered by observations of other galaxies; some
can only be addressed by observations of local starforming regions in the MW. For each question we list
sections in this review where we review the progress to
date in answering them, but many remain largely unanswered and are referred to the last section of this review
on future prospects.
Space limitations prevent us from citing even a fair
fraction of the important papers in this subject, so we
instead cite useful examples and refer the reader to the
richer lists of papers that are cited there.
1.2. Definitions and Conventions
Here we define some terms and symbols that will be
used throughout the review.
The term “cloud” refers to a structure in the interstellar medium (ISM) separated from its surroundings by the
rapid change of some property, such as pressure, surface
density, or chemical state. Clouds have complex structure, but theorists have identified two relevant structures:
clumps are the birthplaces of clusters; cores are the birthplaces of individual or binary stars (e.g., McKee & Ostriker 2007). The observational equivalents have been
discussed (e.g., Table 1 in Bergin & Tafalla 2007), and
cores reviewed (di Francesco et al. 2007; Ward-Thompson
et al. 2007a), and we discuss them further in §2.2.
We will generally explicitly use “surface density” or
“volume density”, but symbols with Σ will refer to surface density, N will refer to column density, and symbols
with n or ρ will refer to number or mass volume density, respectively. The surface density of H I gas is represented by ΣHI if He is not included and by Σ(atomic)
if He is included. The surface density of molecular gas
is symbolized by ΣH2 , which generally does not include
He, or Σmol , which generally does include He. For MW
observations, He is almost always included in mass and
density estimates, and Σmol may be determined by extinction or emission by dust (§2.3) or by observations
of CO isotopologues (§2.4). When applied to an individual cloud or clump, we refer to it as Σ(cloud) or
Σ(clump). For extragalactic work, ΣH2 or Σmol are almost always derived from CO observations, and inclusion of He is less universal. In the extragalactic context,
Σmol is best interpreted as related to a filling factor of
molecular clouds until Σmol ∼ 100 M⊙ pc−2 , where the
area filling factor of molecular gas may become unity
(§2.4). Above this point, the meaning may change substantially. The total gas surface density, with He, is
Σgas = Σmol + µΣHI , where µ is the mean molecular
weight per H atom; µ = 1.41 for MW abundances (Kauffmann et al. 2008), though a value of 1.36 is commonly
The conversion from CO intensity (usually in the
J = 1 → 0 rotational transition) to column density of H2 ,
not including He, is denoted X(CO), and the conversion
from CO luminosity to mass, which usually includes the
mass of He, is denoted αCO .
The term “dense gas” refers generally to gas above
some threshold of surface density, as determined by extinction or dust continuum emission, or of volume density, as indicated by emission from molecular lines that
trace densities higher than does CO. While not precisely
defined, suggestions include criteria of a threshold surface
density, such as Σmol > 125 M⊙ pc−2 (Goldsmith et al.
2008; Lada et al. 2010; Heiderman et al. 2010), a volume
density criterion (typically n > 104 cm−3 ) (e.g., Lada
1992), and detection of a line from certain molecules,
such as HCN. The surface and volume density criteria
roughly agree in nearby clouds (Lada et al. 2012) but
may not in other environments.
The star formation rate is symbolized by SFR or Ṁ∗ ,
often with units of M⊙ yr−1 or M⊙ Myr−1 , and its
Star Formation
meaning depends on how much averaging over time and
space is involved. The surface density of star formation rate, Σ(SFR), has the same averaging issues. The
efficiency of star formation is symbolized by ǫ when it
means M⋆ /(M⋆ + Mcloud ), as it usually does in Galactic studies. For extragalactic studies, one usually means
Ṁ∗ /Mgas , which we symbolize by ǫ′ . The depletion time,
tdep = 1/ǫ′ . Another time often used is the “dynamical”
time, tdyn , which can refer to the free-fall time (tf f ), the
crossing time (tcross ), or the galaxy orbital time (torb ).
In recent years, it also has become common to compare
galaxies in terms of their SFR per unit galaxy mass, or
“specific star formation rate” (SSFR). The SSFR scales
directly with the stellar birthrate parameter b, the ratio of the SFR today to the average past SFR over the
age of the galaxy, and thus provides a useful means for
characterizing the star formation history of a galaxy.
The far-infrared luminosity has a number of definitions, and consistency is important in converting them
to Ṁ∗ . A commonly used definition integrates the dust
emission over the wavelength range 3–1100 µm (Dale &
Helou 2002), and following those authors we refer to this
as the total-infrared or TIR luminosity. Note however
that other definitions based on a narrower wavelength
band or even single-band infrared measurements are often used in the literature.
We refer to mass functions with the following conventions. Mass functions are often approximated by power
laws in logM :
dN/dlogM ∝ M −γ ,
In particular, the initial mass function (IMF) of stars is
often expressed by equation 1 with a subscript to indicate
stars (e.g., M∗ ).
Structures in gas are usually characterized by distributions versus mass, rather than logarithmic mass:
dN/dM ∝ M −α ,
for which α = γ + 1. Terminology in this area is wildly
inconsistent. To add to the confusion, some references
use cumulative distributions, which decrease the index
in a power law by 1.
The luminosities and masses of galaxies are well represented by an exponentially truncated power-law function
(Schechter 1976):
Φ(L) = (Φ∗ /L∗ )(L/L∗ )α e(−L/L
The parameter α denotes the slope of the power-law function at low luminosities, and L∗ represents the luminosity above which the number of galaxies declines sharply.
For the relatively shallow slopes (α) which are typical of
present-day galaxies, L∗ also coincides roughly with the
peak contribution to the total light of the galaxy population. As discussed in §5.2, the Schechter function also
provides a good fit to the distribution function of total
SFRs of galaxies, with the characteristic SFR in the exponential designated as SFR∗ , in analogy to L∗ above.
The term “starburst galaxy” was introduced by Weedman et al. (1981), but nowadays the term is applied to a
diverse array of galaxy populations. The common property of the present-day populations of starbursts is a SFR
out of equilibrium, much higher than the long-term average SFR of the system. No universally accepted quantitative definition exists, however. Some of the more commonly applied criteria are SFRs that cannot be sustained
for longer than a small fraction (e.g., ≤ 10%) of the
Hubble time, i.e., with gas consumption timescales of
less than ≪1 Gyr, or galaxies with disk-averaged SFR
surface densities Σ(SFR) ≥ 0.1 M⊙ yr−1 kpc−2 (§5.2).
Throughout this review we will use the term “quiescent
star-forming galaxies” merely to characterize the nonstarbursting galaxy population. Note that these local criteria for identifying starbursts are not particularly useful
for high-redshift galaxies; a young galaxy forming stars
at a constant SFR might more resemble a present-day
starburst galaxy than a normal galaxy today.
1.3. Questions
1. How should we interpret observations of the main
molecular diagnostic lines (e.g., CO, HCN) and
millimeter-wave dust emission? How does this interpretation change as a function of metallicity,
surface density, location within a galaxy, and star
formation environment? (§2.4, §5.1, §7.3)
2. How does the structure of the ISM, the structure
of star-forming clouds, and the star formation itself
change as a function of metallicity, surface density,
location within a galaxy, and star formation environment? (§2.4, §5, §7.3).
3. How do the mass spectra of molecular clouds and
dense clumps in clouds vary between galaxies and
within a galaxy? (§2.5, §5.1, §7.3)
4. How constant is the IMF, and how are star formation rate measurements affected by possible
changes in the IMF or by incomplete sampling of
the IMF? (§2.5, §3.3, §4.2, §6.4)
5. What are the limits of applicability of current star
formation rate tracers? How are current measurements biased by dust attenuation or the absence of dust, and how accurately can the effects of
dust be removed? How do different tracers depend
on metallicity, and what stellar mass ranges and
timescales do they probe? (§3)
6. How long do molecular clouds live and how can we
best measure lifetimes? Do these lifetimes change
systematically as functions of cloud mass, location
in a galaxy, or some other parameter? (§4.3, §7.3)
7. Do local observations provide any evidence for bimodality in modes of star formation, for example
distributed versus clustered, low-mass versus highmass star formation? (§4, §7.3)
8. On the scale of molecular clouds, what are the
star formation efficiencies [ǫ = M⋆ /(M⋆ + Mcloud)],
and star formation rates per unit mass (ǫ′ =
Ṁ∗ /Mcloud ), and do these efficiencies vary systematically as functions of cloud mass or other parameters? (§4, §7.3)
Kennicutt and Evans
9. How do spatial sampling and averaging affect the
observed form of the star formation relations expressed in terms of total, molecular, or dense gas
surface densities? How well do Ṁ∗ diagnostics used
in extragalactic studies work on finer scales within
a galaxy? (§3.9, §6, §6.4, §7.3)
10. Are there breakpoints or thresholds where either
tracers or star formation change their character?
(§2, §3, §7)
2.1. ISM Basics
The interstellar medium (ISM) is a complex environment encompassing a very wide range of properties
(e.g., McKee & Ostriker 1977; Cox 2005). In the Milky
Way, about half the volume is filled by a hot ionized
medium (HIM) with n < 0.01 cm−3 and TK > 105 K,
and half is filled by some combination of warm ionized
medium (WIM) and warm neutral medium (WNM), with
n ∼ 0.1 − 1 cm−3 and TK of several thousand K (Cox
2005). The neutral gas is subject to a thermal instability that predicts segregation into the warm neutral and
cold neutral media (CNM), the latter with n > 10 cm−3
and TK < 100 K (Field et al. 1969). The existence of
the CNM is clearly revealed by emission in the hyperfine transition of H I, with median temperature about 70
K, determined by comparison of emission to absorption
spectra (Heiles & Troland 2003). However, the strict
segregation into cold and warm stable phases is not supported by observations suggesting that about 48% of the
WNM may lie in the thermally unstable phase (Heiles &
Troland 2003). Finally, the molecular clouds represent
the coldest (TK ∼ 10 K in the absence of star formation), densest (n > 30 cm−3 ) part of the ISM. We focus on the cold (TK < 100 K) phases here, as they are
the only plausible sites of star formation. The warmer
phases provide the raw material for the cold phases, perhaps through “cold” flows from the intergalactic medium
(Dekel & Birnboim 2006). In the language of this review,
such flows would be “warm.”
In the next section, we introduce some terminology
used for the molecular gas as a precursor to the following
discussion of the methods for tracing it. We then discuss
the use of dust as a tracer (§2.3) before discussing the
gas tracers themselves (§2.4).
2.2. Clouds and Their Structures
The CNM defined in the preceding section presents a
wide array of structures, with a rich nomenclature, but
we focus here on the objects referred to as clouds, invoking a kind of condensation process. This name is perhaps
even more appropriate to the molecular gas, which corresponds to a change in chemical state.
The molecular cloud boundary is usually defined by
the detection, above some threshold, of emission from
the lower rotational transitions of CO. Alternatively, a
certain level of extinction of background stars is often
used. In confused regions, velocity coherence can be
used to separate clouds at different distances along the
line of sight. However, molecular clouds are surrounded
by atomic envelopes and a transition region in which
the hydrogen is primarily molecular, but the carbon is
mostly atomic (van Dishoeck & Black 1988). These
regions are known as PDRs, which stands either for
Photo-Dissociation Regions, or Photon-Dominated Regions (Hollenbach & Tielens 1997). More recently, they
have been referred to as “dark gas.”
The structure of molecular clouds is complex, leading
to considerable nomenclatural chaos. Cloud projected
boundaries, defined by either dust or CO emission or
extinction, can be characterized by a fractal dimension
around 1.5 (Falgarone et al. 1991; Scalo 1990; Stutzki
et al. 1998), suggesting an intrinsic 3-D dimension of 2.4.
When mapped with sufficient sensitivity and dynamic
range, clouds are highly structured, with filaments the
dominant morphological theme; denser, rounder cores
are often found within the filaments (e.g., André et al.
2010; Men’shchikov et al. 2010; Molinari et al. 2010).
The probability distribution function of surface densities, as mapped by extinction, can be fitted to a lognormal function for low extinctions, AV ≤ 2 − 5 mag
(Lombardi et al. 2010), with a power law tail to higher
extinctions, at least in some clouds. In fact, it is the
clouds with the power-law tails that have active star formation (Kainulainen et al. 2009). Further studies indicate that the power-law tail begins at Σmol ∼ 40 − 80
M⊙ pc−2 , and that the material in the power-law tail lies
in unbound clumps with mean density about 103 cm−3
(Kainulainen et al. 2011).
Within large clouds, and especially within the filaments, there may be small cores, which are much less
massive but much denser. Theoretically, these are the
sites of formation of individual stars, either single or
binary (Williams et al. 2000). Their properties have
been reviewed by di Francesco et al. (2007) and WardThompson et al. (2007a). Those cores without evidence
of ongoing star formation are called starless cores, and
the subset of those that are gravitationally bound are
called prestellar cores. Distinguishing these two requires
a good mass estimate, independent of the virial theorem,
and observations of lines that trace the kinematics. A
sharp decrease in turbulence may provide an alternative
way to distinguish a prestellar core from its surroundings
(Pineda et al. 2010a).
While clouds and cores are reasonably well defined,
intermediate structures are more problematic. Theoretically, one needs to name the entity that forms a cluster.
Since large clouds can form multiple (or no) clusters, another name is needed. Williams et al. (2000) established
the name “clump” for this structure. The premise was
that this region should also be gravitationally bound, at
least until the stars dissipate the remaining gas. Finding
an observable correlative has been a problem (§2.5).
Finally, one must note that this hierarchy of structure
is based on relatively large clouds. There are also many
small clouds (Clemens & Barvainis 1988), some of which
are their own clumps and/or cores. The suggestion by
Bok & Reilly (1947) that these could be the sites of star
formation was seminal.
2.3. Dust as an ISM Tracer
In the Milky Way, roughly 1% of the ISM is found in
solid form, primarily silicates and carbonaceous material
(Draine 2003) (see also a very useful website1 ). Dust
Star Formation
grain sizes range from 0.35 nm to around 1 µm, with evidence for grain growth in molecular clouds. The column
density of dust can be measured by studying either the
reddening (using colors) or the extinction of starlight,
using star counts referenced to an unobscured field. The
relation between extinction (e.g., AV ) and reddening
[e.g., E(B − V )] is generally parameterized by RV =
AV /E(B − V ). In the diffuse medium, the reddening has
been calibrated against atomic and molecular gas to obtain N (H I)+2N (H2 ) = 5.8 × 1021 cm−2 E(B−V )(mag),
not including helium (Bohlin et al. 1978). For RV = 3.1,
this relation translates to N (H I)+2N (H2 ) = 1.87 × 1021
cm−2 AV (mag). This relation depends on metallicity,
with coefficients larger by factors of about 4 for the LMC
and 9 for the SMC (Weingartner & Draine 2001).
The relation derived for diffuse gas is often applied in
molecular clouds, but grain growth flattens the extinction curve, leading to larger values of RV , and a much
flatter curve in the infrared (Flaherty et al. 2007; Chapman et al. 2009). More appropriate conversions can be
found in the curves for RV = 5.5 in the website referenced above. There is evidence of continued grain growth
in denser regions, which particularly affects the opacity
at longer wavelengths, such as the mm/submm regions
(Shirley et al. 2011).
Reddening and extinction of starlight provided early
evidence of the existence of interstellar clouds (Barnard
1908). Lynds (1962) provided the mostly widely used
catalog of “dark clouds” based on star counts, up to
AV ∼ 6 mag, at which point the clouds were effectively
opaque at visible wavelengths. The availability of infrared photometry for large numbers of background stars
from 2MASS, ISO, and Spitzer toward nearby clouds has
allowed extinction measurements up to AV ∼ 40 mag.
These have proved very useful in characterizing cloud
structure and in checking the gas tracers discussed in
§2.4. Extinction mapping with sufficiently high spatial
resolution can identify cores (e.g., Alves et al. 2007), but
many are not gravitationally bound (Lada et al. 2008),
and they are likely to dissipate.
At wavelengths with strong, diffuse Galactic background emission, such as the mid-infrared, dust absorption against the continuum can be used in a way parallel to extinction maps (e.g., Bacmann et al. 2000; Stutz
et al. 2007). The main uncertainties in deriving the gas
column density are the dust opacity in the mid-infrared
and the fraction of foreground emission.
The energy absorbed by dust at short wavelengths is
emitted at longer wavelengths, from infrared to millimeter, with a spectrum determined by the grain temperature and the opacity as a function of wavelength. At
wavelengths around 1 mm, the emission is almost always
optically thin and close to the Rayleigh-Jeans limit for
modest temperatures. (For Td = 20K, masses, densities,
etc. derived in the Rayleigh-Jeans limit at λ = 1 mm
must be multiplied by 1.5). Thus, the millimeter-wave
continuum emission provides a good tracer of dust (and
gas, with knowledge of the dust opacity) column density
and mass.
As a by-product of studies of the CMB, COBE,
WMAP, and Planck produce large-scale maps of
mm/submm emission from the Milky Way. With Planck,
the angular resolution reaches θ = 4.7′ at 1.4 mm in
an all-sky map of dust temperature and optical depth
(Planck Collaboration et al. 2011b). Mean dust temperature increases from Td = 14 − 15 K in the outer Galaxy
to 19 K around the Galactic center. A catalog of cold
clumps with Td = 7 − 17 K, mostly within 2 kpc of the
Sun, many with surprisingly low column densities, also
resulted from analysis of Planck data (Planck Collaboration et al. 2011c). Herschel surveys will be providing
higher resolution [25′′ at 350 µm (Griffin et al. 2010) and
6′′ at 70 µm (Poglitsch et al. 2010)] images of the nearby
clouds (André et al. 2010), the Galactic Plane (Molinari
et al. 2010), and many other galaxies (e.g., Skibba et al.
2011; Wuyts et al. 2011). Still higher resolution is available at λ ≥ 350 µm from ground-based telescopes at
dry sites. Galactic plane surveys at wavelengths near 1
mm have been carried out in both hemispheres (Aguirre
et al. 2011; Schuller et al. 2009). Once these are put on
a common footing, we should have maps of the Galactic plane with resolution of 20′′ to 30′′ . Deeper surveys of nearby clouds (Ward-Thompson et al. 2007b),
the Galactic Plane, and extragalactic fields are planned
with SCUBA-2.
While studies from ground-based telescopes offer
higher resolution, the need to remove atmospheric fluctuations leads to loss of sensitivity to structures larger
than typically about half the array footprint on the sky
(Aguirre et al. 2011). While the large-scale emission is
lost, the combination of sensitivity to a minimum column
density and a maximum size makes these surveys effectively select structures of a certain mean volume density.
In nearby clouds, these correspond to dense cores (Enoch
et al. 2009). For Galactic plane surveys, sources mainly
correspond to clumps but can be whole clouds at the
largest distances (Dunham et al. 2011b).
2.4. Gas Tracers
One troublesome aspect of extragalactic studies has
been the determination of the amount and properties of
the gas. We discuss first the atomic phase, then the
molecular phase, and finally tracers of dense gas.
2.4.1. The Cold Atomic Phase
The cold, neutral atomic phase is traced by the hyperfine transition of hydrogen, occuring at 21 cm in the rest
frame. This transition reaches optical depth of unity at
N (H I) = 4.57 × 1020 cm−2 (Tspin /100K)(σv /1km s−1 ),
where Tspin is the excitation temperature, usually equal
to the kinetic temperature, TK , and σv is the velocity
dispersion (eq. 8.11 in Draine 2011). For dust in the
diffuse ISM of the Milky Way, this column density corresponds to AV = 0.24 mag, and optical depth effects
can be quite important. The warm, neutral phase is difficult to study, as lines become broad and weak, but it
has been detected (Kulkarni & Heiles 1988). A detailed
analysis of both CNM and WNM can be found in Heiles
& Troland (2003).R
With I(H I) = Sν dv (Jy km s−1 ),
M (H I)/M⊙ = 2.343 × 105 (1 + z)−1 (DL /Mpc)2 I(H I),
not including helium (eq. 8.21 in Draine 2011, but note
errata regarding (1 + z) factor, which was in the numer-
Kennicutt and Evans
ator in the 2011 edition). A coefficient of 2.356 × 105 is
in common use among H I observers (e.g., Walter et al.
2008; Catinella et al. 2010; Giovanelli et al. 2005; Meyer
et al. 2004), usually traced to Roberts (1975). The difference is almost certainly caused by a newer value for
the Einstein A value in Draine (2011).
2.4.2. Molecular Gas
The most abundant molecule is H2 , but its spectrum
is not a good tracer of the mass in molecular clouds.
The primary reason is not, as often stated, the fact that
it lacks a dipole moment, but instead the low mass of
the molecule. The effect of low mass is that the rotational transitions require quite high temperatures to
excite, making the bulk of the H2 in typical clouds invisible. Continuum optical depth at the mid-infrared wavelengths of these lines is also an impediment. The observed rotational H2 lines originate in surfaces of clouds,
probing 1% to 30% of the gas in a survey of galaxies (e.g.,
Roussel et al. 2007).
Carbon monoxide (CO) is the most commonly used
tracer of molecular gas because its lines are the strongest
and therefore easiest to observe. These advantages are
accompanied by various drawbacks, which MW observations may help to illuminate. Essentially, CO emission
traces column density of molecular gas only over a very
limited dynamic range. At the low end, CO requires protection from photodissociation and some minimum density to excite it, so it does not trace all the molecular
(in the sense that hydrogen is in H2 ) gas, especially if
metallicity is low. At the high end, emission from CO
saturates at modest column densities. A more complete
review by A. Bolatto of the use of CO to trace molecular gas is scheduled for a future ARAA, so we briefly
highlight the issues here.
CO becomes optically thick at very low total column
densities. Using CO intensity to estimate the column
density of a cloud is akin to using the presence of a brick
wall to estimate the depth of the building behind it. The
isotopologues of CO (13 CO and C18 O) provide lower optical depths, but at the cost of weaker lines. To use these,
one needs to know the isotope ratios; these are fairly well
known in the Milky Way (Wilson & Rood 1994), but they
may differ substantially in other galaxies. In addition,
the commonly observed lower transitions of CO are very
easily thermalized (Tex = TK ) making them insensitive
to the presence of dense gas.
The common practice in studies of MW clouds is to
use a combination of CO and 13 CO to estimate optical
depth and hence CO column density (N (CO)). One can
then correlate N (CO) or its isotopes against extinction
to determine a conversion factor (Dickman 1978; Frerking et al. 1982). A recent, careful study of CO and 13 CO
toward the Taurus molecular cloud shows that N (CO)
traces AV up to 10 mag in some regions but only up to 4
mag in other regions, and other issues cause problems below AV = 3 mag (Pineda et al. 2010b). Freeze-out of CO
and conversion to CO2 ice causes further complications
in cold regions of high column density (Lee et al. 2003;
Pontoppidan et al. 2008; Whittet et al. 2007), but other
issues likely dominate the interpretational uncertainties
for most extragalactic CO observations.
Since studies of other galaxies generally have only CO
observations available, the common practice has been to
relate H2 column densityR (N (H2 )) to the integrated intensity of CO [I(CO) = T dv (K km s−1 )] via the infamous “X-factor”: N (H2 )= X(CO)I(CO). For example,
Kennicutt (1998b) used X(CO) = 2.8 × 1020 cm−2 (K
km s−1 )−1 .
Pineda et al. (2010b) find X(CO) = 2.0 × 1020 cm−2
(K km s−1 )−1 in the parts of the cloud where both CO
and 13 CO are detected along individual sight lines. CO
does emit beyond the area where 13 CO is detectable and
even, at a low level, beyond the usual detection threshold for CO. Stacking analysis of positions beyond the
usual boundary of the Taurus cloud suggest a factor
of two additional mass in this transition region (Goldsmith et al. 2008). Such low intensity, but large area,
emission could contribute substantially to observations
of distant regions in our galaxy and in other galaxies.
For the outer parts of clouds, where only CO is detected, and only by stacking analysis, X(CO) is six times
higher (Pineda et al. 2010b). Even though about a quarter of the total mass is in this outer region, they argue
that the best single value to use is X(CO) = 2.3 × 1020
cm−2 (K km s−1 )−1 , similar to values commonly adopted
in extragalactic studies. When possible, we will use
X(CO) = 2.3 × 1020 cm−2 (K km s−1 )−1 for this paper.
In contrast, Liszt et al. (2010) argue that X(CO) stays
the same even in diffuse gas. If they are right, much of
the integrated CO emission from some parts of galaxies
could arise in diffuse, unbound gas.
Comparing to extinction measures in two nearby
clouds extending up to AV = 40 mag, Heiderman et al.
(2010) found considerable variations from region to region, with I(CO) totally insensitive to increased extinction in many regions. Nonetheless, when averaged over
the whole cloud, the standard X(CO) would cause errors
in mass estimates of ±50%, systematically overestimating the mass for Σmol < 150 M⊙ pc−2 and underestimating for Σmol > 200 M⊙ pc−2 . Simulations of turbulent
gas with molecule formation also suggest that I(CO) can
be a very poor tracer of AV (Glover et al. 2010). Overall,
the picture at this point is that measuring the extent of
the brick wall will not tell you anything about particularly deep or dense extensions of the building, but if the
buildings are similar, the extent of the wall is a rough
guide to the total mass of the building (cf. Shetty et al.
Following that thought, the luminosity of CO
J = 1 → 0 is often used as a measure of cloud mass,
with the linewidth reflecting the virial theorem in a
crude sense. In most extragalactic studies, individual
clouds are not resolved, and the luminosity of CO is
essentially a cloud counting technique (Dickman et al.
1986). Again, this idea works only if the objects being counted have rather uniform properties. In this approach, M = αCO L(CO). For the standard value for
X(CO) discussed above (X(CO) = 2.3 × 1020 cm−2 (K
km s−1 )−1 ) αCO = 3.6 M⊙ (K km s−1 pc2 )−1 without helium, and αCO = 4.6 M⊙ (K km s−1 pc2 )−1 with correction for helium.
The effects of cloud temperature, density, metallicity,
etc. on mass estimation from CO were discussed by Maloney & Black (1988), who concluded that large variations
in the conversion factor are likely. Ignoring metallicity ef-
Star Formation
fects, they would predict X(CO) ∝ n0.5 TK −1 , where n is
the mean density in the cloud. Shetty et al. (2011b) find
a weaker dependence on TK , X(CO) ∝ TK −0.5 . These
scalings rests on some arguments that may not apply in
other galaxies. Further modeling with different metallicities (Shetty et al. 2011a; Feldmann et al. 2012) has
begun to provide some perspective on the range of behaviors likely in other galaxies.
There is observational evidence for changes in αCO in
centers of galaxies. In the MW central region, Oka et al.
(1998) suggest a value for X(CO) a factor of 10 lower
than in the MW disk. The value of αCO appears to
decrease by factors of 2-5 in nearby galaxy nuclei (e.g.,
Meier & Turner 2004; Meier et al. 2008), and by a factor
of about 5-6 in local ULIRGs (Downes & Solomon 1998;
Downes et al. 1993), and probably by a similar factor in
high-redshift, molecule-rich galaxies (Solomon & Vanden
Bout 2005).
A compilation of measurements indicates that αCO decreases from the usually assumed value with increasing
surface density of gas once Σmol > 100 M⊙ pc−2 (Fig. 1,
Tacconi et al. 2008). This Σmol corresponds to AV ∼ 10
mag, about the point where CO fails to trace column
density in Galactic clouds, and the point where the beam
on another galaxy might be filled with CO-emitting gas.
Variation in αCO has a direct bearing on interpretation
of starbursts (§6), and it is highly unlikely that αCO is
simply bimodal over the full range of star forming environments. Indeed, Narayanan et al. (2012) use a grid
of model galaxies to infer a smooth function of I(CO):
αCO = min[6.3, 10.7 × I(CO)
]Z ′−0.65 , where Z ′ is
the metallicity divided by the solar value.
Other methods have been used to trace gas indirectly, including gamma-ray emission and dust emission. Gamma-rays from decay of pions produced from
high-energy cosmic rays interacting with baryons in the
ISM directly trace all the matter if one knows the cosmic ray flux (e.g., Bloemen 1989). Recent analysis of
gamma-ray data from Fermi have inferred a low value
for X(CO) of (0.87 ± 0.05) × 1020 cm−2 (K km s−1 )−1
in the solar neighborhood (Abdo et al. 2010). This value
is a factor of three lower than other estimates and early
results from dust emission, using Planck, which found
X(CO) = (2.54±0.13) × 1020 cm−2 (K km s−1 )−1 for the
solar neighborhood. (Planck Collaboration et al. 2011b).
Abdo et al. (2010) also inferred the existence of “dark
gas”, which is not traced by either H I or CO, surrounding the CO-emitting region in the nearby Gould
Belt clouds, with mass of about half of that traced by
CO. Planck Collaboration et al. (2011b) have also indicated the existence of “dark gas” with mass 28% of the
atomic gas and 118% of the CO-emitting gas in the solar
neighborhood. The dark gas appears around AV = 0.4
mag, and is presumably the CO-poor, but H2 -containing,
outer parts of clouds (e.g., Wolfire et al. 2010), which can
be seen in [CII] emission at 158 µm and in fluorescent H2
emission at 2 µm (e.g., Pak et al. 1998). It is dark only
if one restricts attention to H I and CO. At low metallicities, the layer of C+ grows, and a given CO luminosity
implies a larger overall cloud (see Fig. 14 in Pak et al.
1998). However, Planck Collaboration et al. (2011b) also
suggest that the dark gas may include some gas that is
primarily atomic, but not traced by H I emission, owing
to optical depth effects.
Dust emission is now being used as a tracer of gas for
other galaxies. Maps of H I gas are used to break the
degeneracy between the gas to dust ratio δgdr and α′CO
in the following equation:
δgdr Σdust = α′CO I(CO) + ΣHI .
Leroy et al. (2011) minimize the variation in δgdr to find
the best fit to α′CO in several nearby galaxies. They
determine Σdust from Spitzer images of 160 µm emission, with the dust temperature (or equivalently the external radiation field) constrained by shorter wavelength
far-infrared emission. This method should measure everything with substantial dust that is not H I, so includes the so-called “dark molecular gas.” They find that
α′CO = 3 − 9 M⊙ pc−2 (K km s−1 )−1 , similar to values based on MW studies, for galaxies with metallicities down to 12+[O/H]∼ 8.4, below which α′CO increases
sharply to values like 70. Their method does not address
the column density within clouds, but only the average
surface density on scales larger than clouds. For galaxies
not too different from the MW, the standard α′CO will
roughly give molecular gas masses, but in galaxies with
lower metallicity, the effects can be large. An extreme
is the SMC, where α′CO ∼ 220 M⊙ pc−2 (K km s−1 )−1
(Bolatto et al. 2011). Maps of dust emission at longer
wavelengths should decrease the sensitivity to dust temperature.
2.4.3. Dense Gas Tracers
Lines other than CO J = 1 → 0 generally trace warmer
(e.g., higher J CO lines) and/or denser (e.g., HCN,
CS, ...) gas. Wu et al. (2010a) showed that the line
luminosities of commonly used tracers (CS J = 2 → 1,
J = 5 → 4, and J = 7 → 6; HCN J = 1 → 0, J = 3 → 2)
correlate well with the virial mass of dense gas; indeed
most follow relations that are close to linear. Since these
lines are optically thick, the linear correlation is somewhat surprising, but it presumably has an explanation
similar to the cloud-counting argument offered above for
CO. Collectively, we refer to these lines as “dense gas
tracers”, but the effective densities increase with J and
vary among species (see Evans 1999; Reiter et al. 2011b
for definitions and tables of effective and critical densities). As an example for HCN J = 1 → 0,
log(L′HCN1−0 ) = 1.04 × log(MVir (RHCN1−0 )) − 1.35 (7)
from a robust estimation fit to data on dense clumps in
the MW (Wu et al. 2010a). The line luminosities of other
dense gas tracers also show strong correlations with both
virial mass (Wu et al. 2010a) and the mass derived from
dust continuum observations (Reiter et al. 2011b).
These tracers of dense gas are of course subject to
the same caveats about sensitivity to physical conditions,
such as metallicity, volume density, turbulence, etc., as
discussed above for CO. In fact, the other molecules
are more sensitive to photodissociation than is CO, so
they will be even more dependent on metallicity (e.g.,
Rosolowsky et al. 2011). Dense gas tracers should become much more widely used in the ALMA era, but caution is needed to avoid the kind of over-simplification
that has tarnished the reputation of CO. Observations
of multiple transitions and rare isotopes, along with realistic models, will help (e.g., Garcı́a-Burillo et al. 2012).
Kennicutt and Evans
2.4.4. Summary
What do extragalactic observations of molecular tracers actually measure? None are actually tracing the
surface density of a smooth medium, with the possible exception of the most extreme starbursts. The luminosity of CO is a measure of the number of emitting structures times the mean luminosity per structure.
Dense gas tracers work in a similar way, but select gas
above a higher density threshold than does CO. For CO
J = 1 → 0, the structure is the CO emitting part of a
cloud, which shrinks as metallicity decreases. For dense
gas tracers, the structure is the part of a cloud dense
enough to produce significant emission, something like a
clump if conditions are like the MW, but even more sensitive to metallicity. Using a conversion factor, one gets
a “mass” in those structures.
Estimates of the conversion factors for CO vary by factors of 3 for the solar neighborhood and at least an order of magnitude at low metallicity and by at least half
an order of magnitude for our own Galactic Center and
for extreme systems like ULIRGs. Dividing by the area
of the galaxy or the beam, one gets “Σmol ”, which really should be thought of as an area filling factor of the
structures being probed times some crude estimate of
the mass per structure. That estimate depends on conditions in the structures, such as density, temperature,
and abundance and on the external radiation field and
the metallicity. Once the L(CO) translates to surface
densities above that of individual clouds (Σmol >∼ 100
M⊙ pc−2 ), the interpretation may change as the area filling factor can now exceed unity. Large ranges of velocity
in other galaxies (if not exactly face-on) allow I(CO) to
still count clouds above this threshold, but the clouds
may no longer be identical. The full range of inferred
molecular surface densities in other galaxies inferred from
CO, assuming a constant conversion factor, is a factor of
103 (§6); given that CO traces Σmol only over a factor
of 10 at best in well-studied clouds in the MW (Pineda
et al. 2010b; Heiderman et al. 2010), this seems a dangerous extrapolation.
2.5. Mass Functions of Stars, Clusters, and Gas
The mass functions of the structures in molecular
clouds (§2.2) are of considerable interest in relation to
the origin of the mass functions of clusters (clumps) and
stars (cores). Salpeter (1955) fit the initial mass function (IMF) of stars to a power law in logM∗ with exponent γ∗ = 1.35, or α∗ = 2.35 (see §1.2 for definitions). More recent determinations over a wider range of
masses, including brown dwarfs, indicate a clear flattening at lower masses, either as broken power laws (Kroupa
et al. 1993) or a log-normal distribution (Miller & Scalo
1979; Chabrier 2003). A detailed study of the IMF in the
nearest massive young cluster, Orion, with stars from 0.1
to 50 M⊙ with a mean age of 2 Myr, shows a peak between 0.1 and 0.3 M⊙ , depending on evolutionary models, and a deficit of brown dwarfs relative to the field IMF
(Da Rio et al. 2012). Steeper IMFs in massive elliptical
galaxies have been suggested by van Dokkum & Conroy (2011). Zinnecker & Yorke (2007) summarize the
evidence for a real (not statistical) cut-off in the IMF
around 150 M⊙ for star formation in the MW and Mag-
ellanic Clouds. Variations in the IMF with environment
are plausible, but convincing evidence for variation remains elusive (Bastian et al. 2010).
The masses of embedded young clusters (Lada &
Lada 2003), OB associations (McKee & Williams 1997),
and massive open clusters (Elmegreen & Efremov 1997;
Zhang & Fall 1999), follow a similar relation with
γcluster ∼ 1. Studies of clusters in nearby galaxies have
also found γcluster = 1 ± 0.1, with a possible upper mass
cutoff or turn-over around 1 − 2 × 106 M⊙ (Gieles et al.
2006), perhaps dependent on the galaxy (but see Chandar et al. 2011). In contrast, the most massive known
open clusters in the MW appear to have a mass of
(6 − 8) × 104 M⊙ (Portegies Zwart et al. 2010; Davies
et al. 2011; Homeier & Alves 2005).
The mass functions of clusters and stars are presumably related to the mass functions of their progenitors,
clouds or clumps, and cores. For comparison to structures in clouds, we will use the distributions versus mass,
rather than logarithmic mass, so our points of comparison will be α∗ = 2.3 and αcluster = 2. From surveys of
emission from CO J = 1 → 0 in the outer galaxy, where
confusion is less problematic, Heyer et al. (2001) found
a size distribution of clouds, dN/dr ∝ r−3.2±0.1 , with no
sign of a break from the power-law form from 3 to 60 pc.
The mass function, using the definition in equation 2, was
fitted by αcloud = 1.8±0.03 over the range 700 to 1 × 106
M⊙ . Complementary surveys of the inner Galaxy found
αcloud = 1.5 up to Mmax = 106.5 M⊙ (Rosolowsky 2005).
The upper cut-off around 3-6 × 106 M⊙ appears to be
real, despite issues of blending of clouds (Williams &
McKee 1997; Rosolowsky 2005). Using 13 CO J = 1 → 0,
which selects somewhat denser parts of clouds, RomanDuval et al. (2010) found α13 CO = 1.75 ± 0.23 for
Mcloud > 105 M⊙ . Clumps within clouds, identified
by mapping 13 CO or C18 O, have a similar value for
αclump = 1.4 − 1.8 (Kramer et al. 1998). All results agree
that most clouds are small, but, unlike stars or clusters,
most mass is in the largest clouds (αcloud < 2).
Studies of molecular cloud properties in other galaxies
have been recently reviewed (Fukui & Kawamura 2010;
Blitz et al. 2007). Mass functions of clouds in nearby
galaxies appear to show some differences, though systematic effects introduce substantial uncertainty (Wong
et al. 2011; Sheth et al. 2008). Evidence for a higher
value of αcloud has been found for the LMC (Fukui et al.
2001; Wong et al. 2011) and M33 (Engargiola et al. 2003;
Rosolowsky 2005). Most intriguingly, the mass function
appears to be steeper in the interarm regions of M51
than in the spiral arms (E. Schinnerer and A. Hughes,
personal communication), possibly caused by the aggregation of clouds into larger structures within arms and
disaggregation as they leave the arms (Koda et al. 2009).
Much work has been done recently on the mass function of cores, and Herschel surveys of nearby clouds will
illuminate this topic (e.g., André et al. 2010). At this
point, it seems that the mass function of cores is clearly
steeper than that of clouds, much closer to that of stars
(Motte et al. 1998; Enoch et al. 2008; Sadavoy et al.
2010). A turnover in the mass function appears at a
mass about 3-4 times that seen in the stellar IMF (Alves
et al. 2007; Enoch et al. 2008). The similarity of αcore
to α∗ supports the idea that the cores are the immediate
Star Formation
precursors of stars and that the mass function of stars
is set by the mass function of cores. In this picture, the
offset of the turnover implies that about 0.2 to 0.3 of
the core mass winds up in the star, consistent with simulations that include envelope clearing by outflows (e.g.,
Dunham et al. 2010). Various objections and caveats to
this appealing picture have been registered (e.g., Swift
& Williams 2008; Reid et al. 2010; Clark et al. 2007;
Hatchell & Fuller 2008).
Note that no such tempting similarity exists between
the mass function of clusters and the mass function of
clumps defined by 13 CO maps, questioning whether that
observational definition properly fits the theoretical concept of a clump as a cluster-forming entity. Structures
marked by stronger emission in 13 CO or C18 O (Rathborne et al. 2009) are not always clearly bound gravitationally. Ground and space-based imaging of submillimeter emission by dust (e.g., Men’shchikov et al. 2010) offer
promise in this area, but information on velocity structure will also be needed. The data so far suggest that
the structure is primarily filamentary, more like that of
clouds than that of cores. CS, HCN and other tracers of
much denser gas (§2.4), along with dust continuum emission (§2.3) have identified what might be called “dense
clumps”, which do appear to have a mass function similar to that of clusters (Shirley et al. 2003; Beltrán et al.
2006; Reid & Wilson 2005),
The comparison of mass functions supports the idea
(McKee & Ostriker 2007) that cores are the progenitors
of stars and dense clumps are the progenitors of clusters,
with clouds less directly related. Upper limits to the
mass function of clumps would then predict upper limits
to the mass function of clusters, unless nearby clumps
result in merging of clusters. Because most clouds and
many clumps are more massive than the most massive
stars, it is less obvious that an upper limit to stellar
masses results from a limit on cloud or clump masses. If
clump masses are limited and if the mass of the most massive star to form depends causally (not just statistically)
on the mass of the clump or cloud, the integrated galactic IMF (IGIMF) can be steepened (Kroupa & Weidner
2003; Weidner & Kroupa 2006). We discuss the second
requirement in §4.2 and consequences of this controversial idea in §3.3 and §6.4.
The influx of new observations over the past decade
has led to major improvements in the calibration and
validation of diagnostic methods for measuring SFRs in
galaxies. Whereas measuring uncertainties of factors of
two or larger in SFRs were commonplace ten years ago,
new diagnostics based on multi-wavelength data are reducing these internal uncertainties by up to an order of
magnitude in many instances. These techniques have
also reduced the impact of many systematic errors, in
particular uncertainties due to dust attenuation, though
others such as the IMF (§2.5) remain important limiting
A detailed discussion of SFR diagnostics and their calibrations was given in K98, and here we highlight progress
made since that review was published. In §3.8, we compile updated calibrations for the most commonly used
indices, based on updated evolutionary synthesis models
and IMF compared to K98. The new challenges which
come with spatially-resolved measurements of galaxies
are discussed in §3.9.
3.1. Star Counting and CMD Analysis
The most direct way to measure star formation rates is
to count the number of identifiable stars of a certain age.
Ideally, one would have reliable masses and ages for each
star and the mean star formation rate would be given by
hṀ∗ i =
N (M∗ , t∗ )M∗ /t∗
M∗ =Ml
where N (M∗ , t∗ ) is the number of stars in a mass bin
characterized by mass M∗ and a lifetime bin (the time
since formation) characterized by t∗ , and the star formation rate would be averaged over the longest value of t∗ in
the sum. In practice, complete information is not available, and one needs to limit the allowed lifetimes to find
the star formation rate over a certain period. In particular, for nearby clouds in the MW, nearly complete lists of
young stellar objects (YSOs) with infrared excesses are
available. If one assumes that the YSOs sample the IMF
in a typical way, one can derive the mean mass of stars
(hM∗ i), and the equation becomes
hṀ∗ i = N (Y SOs)hM∗ i/texcess .
With currently favored IMFs, hM∗ i = 0.5 M⊙ . The main
source of uncertainty is in texcess , the duration of an
infrared excess (§4.1).
For young clusters one can determine mean ages from
fitting isochrones to a color-magnitude diagram, and
measure Ṁ∗ assuming coeval formation as long as some
stars have not yet reached the main sequence. Some clusters have measurements of stars down to very low masses
(e.g., the Orion Nebula Cluster, Hillenbrand 1997), but
most need corrections for unseen low-mass stars. For
older clusters one can derive the total mass, but not (directly) the duration of star formation, which has to be
In principle similar techniques can be applied on a
galaxy-wide basis. Beyond the Magellanic Clouds, current instruments cannot resolve individual YSOs in most
regions, and as a result most studies of SFRs in galaxies are based either on measurements of massive O-type
and/or Wolf-Rayet stars (see K98) or on measurements
of the entire color-magnitude diagram (CMD). Considerable progress has been made recently in using spatiallyresolved mapping of CMDs to reconstruct spatially and
age-resolved maps of star formation in nearby galaxies.
Many of these use the distribution of blue helium-burning
stars in the CMD (e.g., Dohm-Palmer et al. 2002), but
more recent analyses fit the entire upper CMDs to synthetic stellar populations to derive estimates of spatially
resolved stellar age distributions with formal uncertainties (e.g., Dolphin 2002; Weisz et al. 2008). This technique does not have sufficient age resolution to determine
accurate SFRs for ages less than ∼10 Myr, but when applied to high quality datasets such as those which can be
obtained with HST, they can provide sufficient age resolution to constrain the temporal behaviors and changes in
the spatial distributions of formation over the past 100
Kennicutt and Evans
Myr or longer (e.g., Weisz et al. 2008; Williams et al.
3.2. Ultraviolet Continuum Measurements: The
Impact of GALEX
The near-ultraviolet emission of galaxies longward of
the Lyman-continuum break directly traces the photospheric emission of young stars and hence is one of the
most direct tracers of the recent SFR. For a conventional
IMF, the peak contribution to the integrated UV luminosity of a young star cluster arises from stars with
masses of several solar masses. Consequently this emission traces stars formed over the past 10–200 Myr, with
shorter timescales at the shortest wavelengths (see Table
For extragalactic studies, this subject has been revolutionised by the launch of the Galaxy Evolution Explorer
(GALEX) mission (Martin et al. 2005a). It imaged approximately two thirds of the sky in far-ultraviolet (FUV;
155 nm) and near-ultraviolet (NUV; 230 nm) channels to
limiting source fluxes mAB ∼ 20.5, and obtained deeper
full-orbit or multi-orbit imaging (mAB ≥ 23) for selected
galaxies and fields such as those in the Sloan Digital
Sky Survey (SDSS). The spatial resolution (4.5′′ to 6′′
FWHM) of the imager makes it an especially powerful
instrument for integrated measurements of distant galaxies and resolved mapping of the nearest external galaxies.
Although most scientific applications of GALEX data to
date have arisen from its imaging surveys, a series of
spectroscopic surveys and pointed observations of varying depths were carried out as well (Martin et al. 2005a).
The main impacts of GALEX for this subject are summarized in §5. Broadly speaking its largest impacts were
in providing integrated UV fluxes (and hence SFR estimates) for hundreds of thousands of galaxies, and in
exploiting the dark sky from space at these wavelengths
to reveal star formation at low surface brightnesses and
intensities across a wide range of galactic environments.
Other spaceborne instruments have also provided important datasets in this wavelength region, including the
XMM Optical Monitor (Mason et al. 2001) and the Swift
UV/Optical Telescope (Roming et al. 2005). Although
these instruments were primarily designed for follow-up
of X-ray and gamma-ray observations, they also have
been used to image nearby and distant galaxies, with
the advantage of higher spatial resolution (∼1′′ FWHM).
Several important studies have also been published over
the past decade from observations made with the Ultraviolet Imaging Telescope on the ASTRO missions (Stecher
et al. 1997; Marcum et al. 2001). The Hubble Space
Telescope continues to be a steady source of observations (mainly in the NUV) for targeted regions in nearby
The primary disadvantage of the ultraviolet is its severe sensitivity to interstellar dust attenuation. The
availability of new data from GALEX and other facilities has stimulated a fresh look at this problem. If the
intrinsic color of the emitting stellar population is known
a priori, the FUV–NUV color or the UV spectral slope
(usually denoted β) can be used to estimate the dust
attenuation, and numerous calibrations have been published (e.g., Calzetti et al. 1994; Kong et al. 2004; Seibert
et al. 2005; Johnson et al. 2007; Salim et al. 2007; Treyer
et al. 2007; Hao et al. 2011). The accuracy of these pre-
scriptions rests heavily on the presumed (but uncertain)
intrinsic colors, the shape of the dust extinction curve,
and the complicated effects of geometry and scattering
when averaging over a large physical region (e.g., Gordon
et al. 2001).
The abundance of high quality far-infrared observations of nearby galaxies has made it possible to test how
well the UV colors correlate with independent estimates
of the dust attenuation from the IR/UV flux ratios. Earlier observations of bright starburst galaxies suggest a
tight relation between the logarithmic IR/UV ratio (often termed the “IRX”) and UV color (e.g., Meurer et al.
1999), and indeed this “IRX–β relation” provided the
primary means for calibrating the color versus attenuation relation. Subsequent observations of a wider range
of galaxies, however, has revealed a much larger scatter
in the relation (e.g., Boquien et al. 2012). When galaxies
of all types are considered, the scatter in actual FUV attenuations for a fixed FUV–NUV color can easily be two
orders of magnitude. Even when the comparison is restricted to galaxies with intrinsically high SFRs (as might
be observed at high redshift), the uncertainties can easily
reach an order of magnitude. As a result, more weight
is being applied to alternative estimates of attenuation
corrections and SFRs based on combinations of UV with
IR measurements (§3.7).
3.3. Emission-Line Tracers
The remaining SFR indicators to be discussed here rely
on measuring starlight that has been reprocessed by interstellar gas or dust, or on tracers related to the death
of massive stars. The most widely applied of these are
the optical and near-infrared emission lines from ionized
gas surrounding massive young stars. For a conventional
IMF, these lines trace stars with masses greater than
∼15 M⊙ , with the peak contribution from stars in the
range 30–40 M⊙ . As such, the lines (and likewise the
free-free radio continuum) represent a nearly instantaneous measure of the SFR, tracing stars with lifetimes of
∼3–10 Myr (Table 1).
The application of Hα and other emission line SFR
tracers has expanded dramatically in the last decade,
through very large spectroscopic surveys of samples of local and distant galaxies, narrow-band emission-line imaging surveys, and large imaging surveys of nearby galaxies designed to study spatial variations in the SFR. Advances in near-infrared instrumentation have also led to
the first systematic surveys in the Paschen and Brackett
series lines, as well as for Hα observed at high redshifts.
Results from several of these surveys are discussed and
referenced in §5.
The Hα emission line remains the indicator of choice
for observations of local and distant galaxies alike, but
for moderate redshifts, the bluer visible lines have been
applied, in particular the [O II] forbidden line doublet
at 372.7 nm. This feature is subject to severe systematic
uncertainties from dust attenuation and excitation variations in galaxies. K98 published a single SFR calibration
for the line, but subsequent analyses (e.g., Jansen et al.
2001; Kewley et al. 2004; Moustakas et al. 2006) have
shown that the systematic effects must be removed or at
least calibrated to first order for reliable measurements.
Even then, the uncertainties in the [O II]-based SFRs are
much larger than for Hα.
Star Formation
Over the past decade, increasing attention has been
given to measurements of the redshifted Lyα line (λrest
= 121.6 nm) as a tracer of star-forming galaxies, especially at high redshifts where it provides unique sensitivity to both low-mass star-forming galaxies and intergalactic gas clouds or “blobs” (e.g., Ouchi et al. 2009,
2010). The strength of the line (8.7 times stronger than
Hα for Case B recombination) makes it an attractive
tracer in principle, but in realistic ISM environments the
line is subject to strong quenching from the combination
of resonant trapping and eventual absorption by dust,
usually quantified in terms of a Lyα escape fraction. As
a result Lyα surveys to date have been mainly used for
identifying large samples of distant star-forming galaxies.
Applying the line as a quantitative SFR tracer requires
an accurate measurement of the escape fraction. Several ongoing studies are quantifying this parameter by
comparing Lyα fluxes of galaxies with independent SFR
tracers such as Hα or the UV continuum (e.g., Atek et al.
2009; Scarlata et al. 2009; Blanc et al. 2011; Hayes et al.
2011). These show that the escape fraction varies wildly
between galaxies with a range of more than two orders of
magnitude (order 0.01 to 1), but also increases systematically with redshift. It is possible that Lyα will prove to
be a powerful SFR tracer for the highest-redshift objects,
but in view of the large scatter and systematic uncertainties associated with its use we have chosen not to include
a SFR calibration of the line in this review.
Other workers have investigated the efficacy of the infrared fine-structure cooling lines, which arise in H II
regions or PDRs, as quantitative SFR tracers. Ho &
Keto (2007) compiled data from ISO and Spitzer on the
[Ne II]12.8 µm and [Ne III]15.6 µm lines, and found that
the sum of the line fluxes correlates well with hydrogen
recombination line fluxes, with a scatter of ∼0.3 dex.
In a similar vein, Boselli et al. (2002) and RodriguezFernandez et al. (2006) have investigated the applicability of the [C II]158 µm line as a SFR measure. They
found good general correspondance between the [C II] luminosity and other measures of the SFR such as ionized
gas and dust emission, but the scatter in the relationships is at least a factor of ten. Even larger variations in
L[CII] /LIR were found in a more diverse sample of starforming galaxies by Malhotra et al. (1997). The availability of a rich new set of [C II] observations from Herschel,
combined with the detection of redshifted [C II] emission
in submillimeter galaxies (SMGs) from ground-based instruments, has sparked a resurgence of interest in this
The largest systematic errors affecting Hα-based SFRs
are dust attenuation and sensitivity to the population of
the upper IMF in regions with low absolute SFRs. For
regions with modest attenuations the ratios of Balmer
recombination lines (Balmer decrement) can be used to
correct for dust, and this method has been applied in
a number of large spectrophotometric surveys of nearby
galaxies (e.g., Kewley et al. 2002; Brinchmann et al. 2004;
Moustakas et al. 2006). The Balmer decrements offer
only approximate corrections for attenuation because of
variations on scales smaller than the resolution. These
variations may lead to an underestimate of the extinction because lines of sight with low extinction are more
heavily weighted within the beam. This problem can
be addressed partly by adopting a reddening law which
compensates in part for these departures from a pure
foreground scheme geometry (e.g., Charlot & Fall 2000).
The attenuation of the emission lines is found to be systematically higher than that of the continuum starlight
at the same wavelengths (e.g., Calzetti et al. 1994), which
presumably reflects the higher concentrations of dust in
the young star-forming regions.
As is the case with UV-based SFRs, the availability
of far-infrared maps and luminosities for nearby galaxies
has also made it possible to calibrate multi-wavelength
methods for applying dust attenuation corrections to
these measurements (§3.7). They reveal that the Balmer
decrement provides reasonably accurate attenuation corrections in normal galaxies, where attenuations are modest (typically 0–1 mag at Hα), and care is taken to correct the emission-line fluxes for underlying stellar absorption. The Balmer decrement method for estimating dust
attenuation breaks down badly, however in circumnuclear starbursts or other dusty galaxies (e.g., Moustakas
et al. 2006). With the advent of large-format integralfield spectrographs there is promise of applying Balmer
decrement measurements on a spatially-resolved basis in
galaxies (e.g., Blanc 2010; Sánchez et al. 2012).
The accuracy of SFRs derived from emission lines will
also degrade in regions where the SFR is so low that
one enters the regime of small number statistics in the
population of massive ionizing stars. If the IMF itself
were completely blind to the SFR, we would expect such
effects to become apparent below Hα luminosities of order 1038 ergs s−1 , or SFRs of order 0.001 M⊙ yr−1 (e.g.,
Cerviño et al. 2003). At the very least, this effect will
produce a much larger scatter in ionizing flux per unit
SFR in this regime. In low-SFR regions, this sampling
noise can be exacerbated by the short lifetimes of the
ionizing stars, producing large temporal fluctuations in
Hα emission even for a fixed longer-term SFR. As a result, other tracers (e.g., FUV emission) tend to provide
more accurate and sensitive measurements of the SFR at
low star formation levels.
Can these effects cause systematic errors in the SFRs?
Pflamm-Altenburg et al. (2007, 2009) have investigated
the effect of an IGIMF (§2.5) on SFR tracers, and shown
that the systematic depletion of massive stars in low-SFR
environments could cause Hα to substantially underestimate the actual SFR. Interestingly a systematic deficit
of Hα emission in dwarf galaxies with low SFRs and in
low SFR density regions is observed (Sullivan et al. 2000;
Bell & Kennicutt 2001; Lee et al. 2009a; Meurer et al.
2009). Recent work suggests however that the systematic dependence of the Hα/UV ratio may be produced
instead by temporal variations in SFRs, without having
to resort to modifying the IMF itself (Fumagalli et al.
2011; Weisz et al. 2012).
3.4. Infrared Emission: The Impact of Spitzer and
Interstellar dust absorbs approximately half the
starlight in the universe and re-emits it in the infrared, so
measurements in the IR are essential for deriving a complete inventory of star formation. This section focusses
on the transformational results which have come from
the Spitzer Space Telescope (Werner et al. 2004) and the
Herschel Space Observatory (Pilbratt et al. 2010). A re-
Kennicutt and Evans
view in this journal of extragalactic science from Spitzer
can be found in Soifer et al. (2008).
Three other space missions are beginning to influence
this subject: the AKARI mission (Murakami et al. 2007),
the Wide-field Infrared Survey Explorer (WISE) mission
(Wright et al. 2010), and the Planck mission (Planck Collaboration et al. 2011a). These observatories conducted
all-sky surveys, with AKARI imaging in the 2.4−160 µm
region, WISE in the range of 3.4 − 22 µm, and Planck
at 350 − 850 µm (with several bands extending to longer
wavelengths). Much of the science from these missions
is just beginning to emerge, but they will provide very
important results in this subject in the coming decade.
While early applications of dust-based SFR measurements effectively (and necessarily) assumed a onecomponent dust model, subsequent observations show
that the dust emission is comprised of distinct components, each with different spatial distributions and couplings to the young stars. At wavelengths of ∼5–20 µm,
the emission is dominated by molecular bands arising
from polycyclic aromatic hydrocarbons (PAHs). Longward of λ ∼ 20 µm, the emission is dominated by thermal
continuum emission from the main dust grain population.
Emission from small grains transiently heated by intense
radiation fields (usually in or near star-forming regions)
is important out to about 60 µm, whereas at longer wavelengths, emission from larger grains with steady state
temperatures dominates (Draine 2003).
The distribution of these different emission components is illustrated in Figure 2, which shows Spitzer
and Herschel images of the nearby star-forming galaxy,
NGC 6946, at wavelengths ranging from 3.6–500 µm. At
24 µm, the emission peaks around the youngest starforming regions and H II regions, with a more diffuse
component extending between these regions. As one progresses to longer wavelengths, the prominence of the diffuse component increases. Recent measurements with
Herschel show that this is mainly a physical change, and
not an artifact of lower spatial resolution at longer wavelengths (Boquien et al. 2011). This diffuse emission is
analogous to the “infrared cirrus” emission observed in
our own Galaxy. Interestingly PAH emission appears to
correlate the most strongly with the longer-wavelength
component of the thermal dust emission (e.g., Bendo
et al. 2008), though it often also appears as resolved
shells around the young star-forming regions (Helou et al.
These variations in the morphologies in the different
dust emission components translate into considerable
variations in the dust SEDs within and between galaxies (e.g., Dale & Helou 2002; Dale et al. 2005; Smith
et al. 2007), and as a consequence the conversion of infrared luminosities into SFRs must change for different
IR wavelengths. Most early applications of the dust emission as a SFR tracer were based on the integrated totalinfrared (TIR) emission. This parameter has the physical advantage of effectively representing the bolometric
luminosity of a completely dust-enshrouded stellar population. The TIR-based SFR calibration derived in K98,
applicable in the limits of complete dust obscuration and
dust heating fully dominated by young stars, is still in
widespread use today. For most galaxies however this
complete wavelength coverage will not be available, so
many workers have calibrated monochromatic SFR in-
dices, usually tuned to one of the Spitzer or Herschel
bands, including 24 µm (e.g., Wu et al. 2005a; AlonsoHerrero et al. 2006; Calzetti et al. 2007; Relaño et al.
2007; Rieke et al. 2009, and references therein), and 70
and 160 µm (Calzetti et al. 2010a). The latter paper
contains an excellent discussion comparing the various
calibrations in the literature at the time.
As with all of the SFR indicators, the dust emission is
subject to important systematic effects. Just as the UV
and visible tracers miss radiation that has been attenuated by dust, the infrared emission misses the starlight
that is not absorbed by dust (e.g., Hirashita et al. 2001).
As discussed earlier, dust attenuates only about half of
the integrated starlight of galaxies on average, so the
infrared emission will systematically underestimate the
SFR if the missing fraction of star formation is not incorporated into the calibrations. This “missing” unattenuated component varies from essentially zero in dusty
starburst galaxies to nearly 100% in dust-poor dwarf
galaxies and metal-poor regions of more massive galaxies. Another major systematic error works in the opposite direction; in most galaxies, evolved stars (e.g.,
ages above ∼100–200 Myr) contribute significantly to the
dust heating, which tends to cause the IR luminosity to
overestimate the SFR. The fraction of dust heating from
young stars varies by a large factor among galaxies; in
extreme circumnuclear starburst galaxies or individual
star-forming regions, nearly all of the dust heating arises
from young stars, whereas in evolved galaxies with low
specific SFRs, the fraction can be as low as ∼10% (e.g.,
Sauvage & Thuan 1992; Walterbos & Greenawalt 1996;
Cortese et al. 2008). In practical terms this means that
the conversion factor from dust luminosity to SFR— even
in the limit of complete dust obscuration— is not fixed,
but rather changes as a function of the stellar population mix in galaxies. The difference in conversion factor between starbursts and quiescient galaxies with constant SFR, for example, is about a factor of 1.3–2 (e.g.,
Sauvage & Thuan 1992; Kennicutt et al. 2009; Hao et al.
The calibration of the mid-IR PAH emission as a quantitative SFR tracer deserves special mention. This index
is of particular interest for studies of galaxies at high redshift, because the observed-frame 24 µm fluxes of galaxies
at z = 1 − 3 tend to be dominated by redshifted PAH
emission. A number of studies have shown that the PAH
luminosity scales relatively well with the SFR in metalrich luminous star-forming galaxies (e.g., Roussel et al.
2001; Peeters et al. 2004; Förster Schreiber et al. 2004;
Wu et al. 2005a; Farrah et al. 2007; Calzetti et al. 2007),
but the PAH bands weaken dramatically below metal
abundances of approximately 1/4 to 1/3 Z⊙ (e.g., Madden 2000; Engelbracht et al. 2005; Calzetti et al. 2007;
Smith et al. 2007), rendering them problematic as quantitative SFR tracers in this regime.
The best way to overcome these systematic biases is
to combine the IR measurements with UV or visiblewavelength SFR tracers, to measure the unattenuated
starlight directly and to constrain the dust-heating stellar population (§3.7). However, in cases where only IR
observations are available one can attempt to incorporate corrections for these effects into the SFR calibrations themselves, and this approach has been taken by
most authors (e.g., Calzetti et al. 2010b and references
Star Formation
therein). Fortunately, for most galaxies with moderate
to high specific SFRs, the effects of partial dust attenuation and cirrus dust heating by evolved stars appear to
roughly compensate for each other. For example, Kewley
et al. (2002) showed that for a sample of spiral galaxies
with integrated emission-line spectra, the TIR-based calibration of K98 for dusty starburst galaxies was in good
agreement with SFRs based on attenuation-corrected Hα
line fluxes. However, one must avoid applying these IRbased recipes in environments where they are bound to
fail, for example, in low-metallicity and other largely
dust-free galaxies or in galaxies with low specific SFRs
and a strong radiation field from more evolved stars.
3.5. Radio Continuum Emission
The centimeter-wavelength radio continuum emission
of galaxies consists of a relatively flat-spectrum, freefree component, which scales with the ionizing luminosity (subject to a weak electron temperature dependence) and a steeper spectrum synchrotron component,
which overwhelmingly dominates the integrated radio
emission at ν ≤ 5 GHz. The free-free component can be
separated with multi-frequency radio measurements or
high-frequency data (e.g., Israel & van der Hulst 1983;
Niklas et al. 1997; Murphy et al. 2011), to provide a
photoionization-based measure of the SFR, without the
complications of dust attenuation which are encountered
with the Balmer lines.
At lower frequencies the integrated emission is dominated by the synchrotron emission from charged particles produced by supernovae. A SFR calibration has
not been derived from first principles, but observations
have repeatedly confirmed a tight correlation between
this non-thermal emission and the far-infrared emission
of galaxies, which favors its application as a SFR tracer
(e.g., Helou et al. 1985; Condon 1992). Moreover, improvements to receiver technology with the Expanded
Very Large Array (EVLA) and other instruments have
made the radio continuum a primary means of identifying star-forming galaxies at high redshift and estimating
their SFRs. As a result it is appropriate to include it in
this discussion of SFR tracers.
Current calibrations of the radio continuum versus
SFR relation are bootstrapped from the far-infrared calibrations, using the tight radio–IR correlation. The steep
synchrotron spectrum makes this calibration strongly
wavelength dependent, and most are referenced to
1.4 GHz (e.g., Yun et al. 2001; Condon 1992; Bell 2003).
The calibration adopted here in §3.8 is derived in similar
fashion, but adapted to the Kroupa IMFs.
As described above, the IR–based SFR calibrations
break down severely in faint galaxies with low dust contents, yet the radio–IR correlation remains tight and
nearly linear over the entire luminosity range. How can
this arise? The likely explanation can be found in Bell
(2003) and references therein, where it is shown that the
decrease in dust opacity in low-mass galaxies is accompanied by a decline in synchrotron emission relative to
other tracers of the SFR. This is seen most directly as a
decline in the ratio of non-thermal radio emission (still
dominant in the 1–5 GHz region) to the free-free thermal radio emission. Since the thermal radio emission is
directly coupled to the stellar ionization rate and SFR,
the relative decline in synchrotron luminosity must re-
flect a physical decline per unit SFR. If correct then the
continuity of the radio–IR relation to low luminosities is
the result of a “cosmic conspiracy” (Bell 2003), and one
should beware of applying the method in galaxies fainter
than ∼0.1 L∗ .
3.6. X-ray Emission
Over the past decade, the integrated hard X-ray emission of galaxies has been increasingly applied as a SFR
tracer. The component of X-ray emission that does not
arise from AGN accretion disks is dominated by massive
X-ray binaries, supernovae and supernova remnants, and
massive stars, all associated with young stellar populations and recent star formation. Furthermore the observed 2–10 keV fluxes of galaxies are observed to be
strongly correlated with their infrared and non-thermal
radio continuum fluxes (e.g., Bauer et al. 2002; Ranalli
et al. 2003; Symeonidis et al. 2011), strengthening the
link to the SFR.
Since there is no way to calibrate the relation between
X-ray luminosity and SFR from first principles, the calibration is usually bootstrapped from the infrared or radio. Ranalli et al. (2003) derived such a calibration for
integrated 2–10 keV X-ray luminosities, referenced to the
K98 calibrations and IMF, and this relation is still widely
applied today. Persic et al. (2004) derived an alternate
calibration in terms of the hard X-ray binary luminosity
alone, which is useful for nearby resolved galaxies. Calibrations of the SFR in terms of X-ray luminosity and
stellar mass have been published by Colbert et al. (2004)
and Lehmer et al. (2010). For simplicity, we have listed
in Table 1 the widely-applied relation of Ranalli et al.
(2003), but adjusted to the Kroupa IMF used for the
other calibrations.
3.7. Composite Multi-Wavelength Tracers
Large multi-wavelength surveys of galaxies allow tests
and calibrations of SFR indices that combine information from more than one tracer and exploit the complementary strengths of different wavelengths. Currently
this capability is mainly limited to nearby galaxies, but
with the expansion of far-infrared to millimeter surveys
of high-redshift galaxies, opportunities to apply multiwavelength diagnostics to distant galaxies should expand
in the coming decade (e.g., Overzier et al. 2011; Reddy
et al. 2012).
The most widely explored of these methods have combined UV (usually FUV) observations with infrared measurements to construct dust-corrected SFRs, using an
approximate energy-balancing approach. In its simplest
form one can use a linear combination of UV and IR luminosities to correct the UV fluxes for dust attenuation:
LUV (corr) = LUV (observed) + η LIR
where the luminosities are usually calculated from flux
densities using the definition L = ν Lν , and the coefficient η is dependent on the bandpasses chosen for the
UV and IR measurements. The most common form of
this correction uses GALEX FUV (155 nm) and totalinfrared luminosities, hence:
LFUV (corr) = LFUV (observed) + η LTIR
Kennicutt and Evans
Other prescriptions sometimes adopt a higher order polynomial dependence on LIR (e.g., Buat et al. 2005), but
for brevity we only discuss the linear combinations here.
In most cases, η < 1, because only part of the dustheating radiation is contained in the FUV band, and in
many galaxies there is significant dust heating and TIR
emission arising from stars other than the UV-emitting
population (IR cirrus). The coefficient η can be calibrated theoretically using evolutionary synthesis models,
or empirically, using independent measurements of dustcorrected SFRs (e.g., Treyer et al. 2010; Hao et al. 2011).
Early applications of this method were largely restricted to luminous starburst galaxies and star-forming
regions, for which UV and IR data could be obtained
prior to the advent of GALEX, Spitzer, and Herschel
(e.g., Buat et al. 1999; Meurer et al. 1999; Gordon et al.
2000), yielding values of η ∼ 0.6. Subsequent analyses extending to normal star-forming galaxies (e.g., Hirashita et al. 2003; Kong et al. 2004; Burgarella et al.
2005; Buat et al. 2005; Treyer et al. 2010; Hao et al.
2011) typically produce values of η which are somewhat lower (e.g., 0.46 for Hao et al. 2011), which almost certainly reflects the larger contribution to dust
heating from starlight longward of the FUV. Considering
the wide differences in dust heating populations between
starburst and normal galaxies, however, this difference
of ∼30% is hardly crippling, especially when it reduces
dramatically the much larger systematic errors from UV
or IR-based SFRs alone.
A similar energy-balancing approach has been applied to derive dust-corrected emission-line luminosities
of galaxies (Calzetti et al. 2007; Zhu et al. 2008; Kennicutt et al. 2009; Treyer et al. 2010). Here the equivalent
parameter to η above is calibrated using independent estimates of the Hα attenuation, usually the recombination
line decrement as measured from the Paα/Hα or Hα/Hβ
ratio. Kennicutt et al. (2009) have shown that this approach can be more broadly applied to estimate attenuation corrections for other emission lines (e.g., [O II]),
and it can be calibrated using TIR fluxes, single-band
IR fluxes, or even 1.4 GHz radio continuum fluxes. An
illustration of the effectiveness of the method is shown
in Figure 3, taken from Kennicutt et al. (2009). The top
panel shows the consistency between an IR-based tracer
(24 µm luminosity) used alone and the dust-corrected Hα
luminosity (via the integrated Balmer decrement). There
is a general correlation but considerable scatter and a
pronounced non-linearity, which reflects a general correlation of average dust attenuation with the SFR itself.
The lower panel plots the best fitting linear combination
of Hα and IR (in this case 24 µm) luminosities against the
Balmer-decrement-corrected Hα luminosities. The scatter between the tracers now is reduced severalfold, and
the non-linearity in the comparison with IR luminosities
alone is essentially removed.
These composite SFR indicators are not without systematic uncertainties of their own. Questions remain
about the systematic reliability of the independent attenuation calibrations (in particular with the effects of
dust geometry on the Balmer decrements), and most of
the recipes still retain a dependence on stellar population
age, via the infrared term; for example the best fitting
values of η for H II regions and young starbursts differ
from those of normal star forming galaxies by a factor
of ∼1.5, consistent with expectations from evolutionary
synthesis models, as discussed in §3.8 (Kennicutt et al.
2009). Nevertheless they represent a major improvement
over single-wavelength tracers, and provide a valuable
testing ground for calibrating and exploring the uncertainties in the monochromatic indicators (e.g., Calzetti
et al. 2010b).
Table 2 lists examples of dust attenuation corrections
using combinations of FUV and Hα fluxes with various
infrared and radio tracers, taken from Hao et al. (2011)
and Kennicutt et al. (2009), respectively. These can
be applied in combination with the monochromatic SFR
zeropoint calibrations listed in Table 1 (§3.8) to derive
dust-corrected SFR measurements.
3.8. An Updated Compendium of Integrated SFR
K98 presented calibrations for SFRs derived from UV
continuum, TIR, Hα emission-line, and [O II] emissionline luminosities, which have come into common usage in
the field. The considerable expansion of the subject to
other wavelengths and SFR diagnostics since that time
motivates a revisit of these calibrations.
Nearly all of these calibrations are based on evolutionary synthesis models, in which the emergent SEDs
are derived for synthetic stellar populations with a prescribed age mix, chemical composition, and IMF. The
K98 calibrations employed a mix of models from the literature, and assumed a single power-law IMF (Salpeter
1955), with mass limits of 0.1 and 100 M⊙ . This IMF
gave satisfactory SFR calibrations relative to that of
more realistic IMFs for Hα, but for other wavelengths,
the relative calibrations using different tracers are sensitive to the precise form of the IMF. Today most workers calibrate SFR tracers using a modern IMF with a
turnover below ∼1 M⊙ , for example the IMF of Kroupa
& Weidner (2003), with a Salpeter slope (α∗ = −2.35)
from 1–100 M⊙ and α∗ = −1.3 for 0.1–1 M⊙ . The calibrations presented here use this IMF, but the IMF fit
from Chabrier (2003) yields nearly identical results (e.g.,
Chomiuk & Povich 2011). The past decade has also seen
major improvements in the stellar evolution and atmospheric models which are used to generate the synthetic
SEDs. The results cited here use the Starburst99 models
of Leitherer et al. (1999), which are regularly updated in
the on-line version of the package.
Table 1 presents in compact form calibrations for a
suite of SFR tracers in the form:
log Ṁ∗ (M⊙ yr−1 ) = log Lx − log Cx
The table lists for each tracer the units of luminosity
(Lx ), the logarithmic SFR calibration constant Cx , and
the primary reference(s) for the calibration. For methods presented in K98, we also list the scaling constant
between the new (Kroupa IMF, SB99 model) SFRs and
those from K98. As in K98, the recipes for infrared dust
emission are in the limit of complete dust attenuation
and continuous star formation over a period of 0–100
Myr, which is appropriate for a typical dust-obscured
starburst galaxy. Virtually all of the SFR calibrations
presented in Table 1 are taken from the literature, and
we strongly encourage users of these calibrations to cite
the primary sources, whether or not they choose to cite
Star Formation
this paper as well.
The second column of Table 1 lists the approximate
age sensitivity of the different star formation tracers.
These were estimated using the Starburst99 models in
the approximation of constant star formation. The second number lists the mean stellar age producing the relevant emission, while the third column lists the age below
which 90% of the relevant emission is produced. For
the dust emission in the infrared these ages can only be
estimated, because they depend on the detailed star formation history over periods of up to 100 Myr and longer,
and they are also convolved with the level of dust attenuation as a function of stellar age. The numbers are given
for the assumed starburst timescales above; for normal
galaxies the 90th percentile age can be 500 Myr or longer.
All of the results were calculated for solar metal abundances, and readers should beware that all of the calibrations are sensitive to metallicity. These have been
estimated by several authors using evolutionary synthesis models (e.g., Smith et al. 2002; Raiter et al. 2010), but
the precise dependences are sensitive to the details of the
input stellar models, in particular how effects of stellar
rotation are modelled. The models cited above (which do
not adopt a dependence of rotation on metallicity) show
that a decrease in metal abundance by a factor of ten increases the FUV luminosity of a fixed mass and IMF population by ∼ 0.07±0.03 dex (for the IMFs assumed here),
while the ionizing luminosity is more sensitive, increasing
by ∼ 0.4 ± 0.1 dex for a tenfold decrease in Z/Z⊙ . The
change in infrared luminosities for completely obscured
regions should roughly track that for the FUV luminosity, but in most low-metallicity environments, the dust
opacity will be severely reduced, producing a sharp fall
in infrared emission for a given SFR.
3.9. The Challenge of Spatially-Resolved Star
Formation Rates in Galaxies
Nearly all of the diagnostic methods described up to
now have been designed for measuring integrated SFRs
of galaxies or for regions such as starbursts, containing
thousands (or more) of massive stars. The resulting SFR
prescriptions implicitly assume that local variations in
stellar age mix, IMF population, and gas/dust geometry
largely average out when the integrated emission of a
galaxy is measured.
With the advent of high-resolution maps of galaxies in
the UV, IR, emission lines, and radio (and integral-field
spectroscopic maps in the visible and near-infrared), one
would like of course to extend these diagnostic methods
to create fully-sampled spatially-resolved “SFR maps”
of galaxies. This extrapolation to much smaller regions
within galaxies (or to galaxies with extremely low SFRs),
however, is not at all straightforward. At smaller linear
scales, nearly all of the statistical approximations cited
above begin to break down.
First, when the SFR in the region studied drops below ∼0.001-0.01 M⊙ yr−1 (depending on the SFR tracer
used), incomplete sampling of the stellar IMF will lead
to large fluctuations in the tracer luminosity for a fixed
SFR. These begin to become problematic for luminosities of order 1038 − 1039 ergs s−1 for emission-line, UV, or
IR tracers, and they are especially severe for the ionized
gas tracers, which are most sensitive to the uppermost
parts of the stellar IMF. For actively star forming normal
disk galaxies, this onset of stochasticity typically occurs
on spatial scales of order 0.1–1 kpc, but the region can
be considerably larger in galaxies, or parts of galaxies,
with lower SFRs. Note that this breakdown on local
scales occurs regardless of whether the IMF itself varies
As a prime example of this stochasticity, consider what
astronomers in M51 would observe if they examined the
solar neighborhood in the Milky Way from a distance
of 10 Mpc. In a pixel of 100 pc radius centered on the
Sun they would observe no molecular gas and no star
formation. If they degraded their resolution to a radius
of 300 pc, they would pick up all the Gould Belt clouds,
but no localized Hα emission. Within a slightly larger
radius of 500 pc, their beam would include Orion, with
its O stars and H II region. (For this example, we consider only the stars and emission from the Orion Nebula
Cluster (ONC) stars and emission, for which we have
good numbers, not the full Orion clouds and OB associations.) This roughly doubles the number of YSOs. Our
M51 observers would measure Σmol = 0.11 M⊙ pc−2 ,
but if they applied the relation between SFR and Hα luminosity from K98, they would derive Σ(SFR) a factor
of 10 lower than the actual SFR in Orion, based on the
actual stellar content of the ONC and a relatively long
timescale of 3 Myr (Chomiuk & Povich 2011), and they
would miss the total SFR within 500 pc by a factor of 20
because the other clouds produce no O stars. This severe
underestimate for Orion itself from Hα emission results
because the Orion cluster is too small to fully populate
the IMF; its earliest spectral type is O7 V, and so the star
cluster produces relatively little ionizing luminosity relative to its total mass and SFR. If the distant observers
used the total infrared emission of Orion instead, they
would still underestimate its SFR by a factor of 8 (Lada
et al. 2012) (a factor of 10 with the newer conversions in
Table 1).
Secondly, when the spatial resolution of the SFR
measurements encompass single young clusters, such
as Orion, the assumption of continuous star formation
which is embedded in the global SFR recipes breaks down
severely. In such regions that emission at all wavelengths
will be dominated by a very young population with ages
of typically a few Myr, which will be shorter than the averaging times assumed for all but the emission-line tracers. These changes affect both the relative luminosities of
star formation tracers in different bands and of course the
interpretation of the “star formation rate” itself. Technically speaking the luminosities of young star-forming
clusters only provide information on the masses of the
regions studied, and converting these to SFRs requires
independent information on the ages and/or age spreads
of the stars in the region.
A third measuring bias will set in if the resolution of
the measurements becomes smaller than the Strömgren
diameters of H II regions or the corresponding dust emission nebulae, which tend to match or exceed those of
the H II regions (e.g., Watson et al. 2008; Prescott et al.
2007). This scale varies from <100 pc in the Milky Way
to 200–500 pc in actively star-forming galaxies such as
NGC 6946 (Figure 2). On these small scales indirect tracers of the SFR (e.g., Hα, IR) tend to trace the surfaces
and bubbles of clouds rather than the young stars. By
Kennicutt and Evans
the same token, much of the Hα and dust emission in
galaxies, typically 30–60%, is emitted by diffuse ionized
gas and dust located hundreds of parsecs or more from
any young stars (e.g., Oey et al. 2007; Dale et al. 2007).
Such emission produces a false positive signal of star formation, and care is needed to account for its effects when
mapping the SFR within galaxies.
Taken together, these factors complicate, but do not
prevent, the construction of 2D maps of SFRs, so long as
the methodology is adapted to the astrophysical application. For example, radial profiles of SFR distributions in
galaxies may still be reliably derived using the integrated
SFR calibrations, providing that large enough annuli are
used to assure that the IMF is fully populated in aggregate, and the SFR is regarded to be averaged over
time scales of order 100 Myr. Likewise a 2D distribution of star formation over the last 5 Myr or so can be
derived from a short-lived tracer such as Hα emission, if
the spatial coverage is limited to very young regions, and
structure on scales smaller than individual H II regions is
ignored. Maps of integrated Hα and IR emission can be
used to study the population of star-forming regions and
the star formation law, when restricted to young regions
where the physical association of gas and stars is secure
(§6.4). An alternative approach is to apply direct stellar
photospheric tracers, such as the ultraviolet continuum
emission on large scales (bearing in mind the variable
10–300 Myr time scales traced by the UV), or resolved
stellar tracers such as YSOs or deep visible-wavelength
color-magnitude diagrams, to map the distributions of
young stars directly (§3.1). Likewise it should be possible to use pixel-resolved SEDs of galaxies in the UV–
visible to derive dust-corrected UV maps, and possibly
apply local corrections for age in the maps. With such a
multiplicity of approaches, we anticipate major progress
in this area, which will be invaluable for understanding
in detail the patterns of star formation in galaxies and
connecting to detailed studies within the MW.
4.1. Outline of low-mass star formation
The formation of low-mass stars can be studied in
greatest detail because it occurs in relatively nearby
clouds and sometimes in isolation from other forming
stars. The established paradigm provides a point of comparison for more massive, distant, and clustered star formation.
Physically, an individual star forming event, which
may produce a single star or a small number multiple
system, proceeds from a prestellar core, which is a gravitationally bound starless core (see §2.2, di Francesco
et al. 2007 for definitions), a dense region, usually within
a larger molecular cloud. Prestellar cores are centrally
condensed, and can be modeled as Bonnor-Ebert spheres
(Ward-Thompson et al. 1999; Evans et al. 2001; Kirk
et al. 2005), which have nearly power-law (n(r) ∝ r−2 )
envelopes around a core with nearly constant density.
Collapse leads to the formation of a first hydrostatic
core in a small region where the dust continuum emission becomes optically thick; this short-lived core is still
molecular and grows in mass by continued infall from the
outer layers (Larson 1969; Boss & Yorke 1995; Omukai
2007; Stahler & Palla 2005). When the temperature
reaches 2000 K, the molecules in the first hydrostatic
core collisionally dissociate, leading to a further collapse
to the true protostar, still surrounded by the bulk of the
core, often referred to as the envelope. Rotation leads
to flattening and a centrifugally supported disk (Terebey
et al. 1984). Magnetic fields plus rotation lead to winds
and jets (Shang et al. 2007; Pudritz et al. 2007), which
drive molecular outflows from young stars of essentially
all masses (Arce et al. 2007; Wu et al. 2004).
Stage 0 sources have protostars, disks, jets, and envelopes with more mass in the envelope than in the star
plus disk (Andre et al. 1993). Stage I sources are similar
to Stage 0, but with less mass in the envelope than in star
plus disk. Stage II sources lack an envelope, but have a
disk, while Stage III sources have little or no disk left.
There are several alternative quantitative definitions of
the qualitative terms used here (Robitaille et al. 2006;
Crapsi et al. 2008).
Stages I through III are usually associated with SED
Classes I through III defined by SED slopes rising, falling
slowly, and falling more rapidly from 2 to 25 µm (Lada
& Wilking 1984). A class intermediate between I and II,
with a slope near zero (Flat SED) was added by Greene
et al. (1994). In fact, orientation effects in the earlier stages can confuse the connection between class and
stage; without detailed studies of each source, one cannot
observationally determine the stage without ambiguity.
For this reason, most of the subsequent discussion will
use classes despite their questionable correspondence to
physical configurations. Evans et al. (2009) give a historical account of the development of the class and stage
For our present purposes, the main point is to establish time scales for the changing observational signatures,
so the classes are useful. Using the boundaries between
classes from Greene et al. (1994), Evans et al. (2009)
found that the combined Class 0/I phases last ∼ 0.5 Myr,
with a similar duration for Flat SEDs, assuming a continuous flow through the classes for at least the Class II
duration of 2 ± 1 Myr (e.g., Mamajek 2009), which is
essentially the age when about half the stars in a dated
cluster lack infrared excesses; hence all durations can be
thought of as half-lives.
To summarize, we would expect a single star-forming
core to be dominated by emission at far-infrared and submillimeter wavelengths for about 0.5 Myr, near-infrared
and mid-infrared radiation for about 1.5 Myr and nearinfrared to visible light thereafter. However, the duration
of emission at longer wavelengths can be substantially
lengthened by material in surrounding clumps or clouds
not directly associated with the forming star.
The star formation rates and efficiencies can be calculated for a set of 20 nearby clouds (hdi = 275 pc) with
uniform data from Spitzer. The star formation rate was
calculated from equation 9 and the assumptions in §3.1
by Heiderman et al. (2010), who found a wide range of
values for Ṁ∗ , with a mean value for the 20 clouds of
Ṁ∗ = 39 ± 18 M⊙ Myr−1 . The star formation efficiency
(ǫ = M⋆ /(M⋆ + Mgas )) can only be calculated over the
last 2 Myr because surveys are incomplete at larger ages;
averaging over all 20 clouds, only 2.6% of the cloud mass
has turned into YSOs in that period and hΣ(SFR)i = 1.2
Star Formation
M⊙ yr−1 kpc−2 (Heiderman et al. 2010). For individual
clouds, ǫ ranges from 2% to 8% (Evans et al. 2009; Peterson et al. 2011). The final efficiency will depend on
how long the cloud continues to form stars before being
disrupted; cloud lifetimes are poorly constrained (McKee
& Ostriker 2007; Bergin & Tafalla 2007), and they may
differ for clouds where massive stars form.
For comparison to extragalactic usage, the mean tdep =
1/ǫ′ (§1.2) is about 82 Myr for seven local clouds, longer
than most estimates of cloud lifetime, and much longer
than either htf f i (1.4 Myr) or htcross i (5.5 Myr) (Evans
et al. 2009). The htdep i for local clouds is, on the other
hand, about 10% of the tdep for the MW molecular gas
as a whole (§5.1).
4.2. Formation of Clusters and High-mass Stars
The study of young clusters provides some distinct opportunities. By averaging over many stars, a characteristic age can be assigned, with perhaps more reliability
than can be achieved for a single star. As noted (§4.1),
the set point for ages of all SED classes is determined
by the fraction of mid-infrared excesses in clusters. This
approach does implicitly assume that the cluster forms
“coevally”, by which one really means that the spread in
times of formation is small compared to the age of the
cluster. Because objects ranging from prestellar cores to
Class III objects often coexist (Rebull et al. 2007), this
assumption is of dubious reliability for clusters with ages
less than about 5 Myr, exactly the ones used to set the
timescales for earlier classes. Note also that assuming
coeval formation in this sense directly contradicts the
assumption of continuous flow through the classes. We
live with these contradictions.
Most nearby clusters do not sample very far up the
IMF. The nearest young cluster that has formed O stars
is 415-430 pc away in Orion (Menten et al. 2007; Hirota
et al. 2007), and most lie at much larger distances, making study of the entire IMF difficult.
Theoretically, the birthplace of a cluster is a clump
(Williams et al. 2000). The clumps identified by 13 CO
maps in nearby clouds are dubious candidates for the
reasons given in §2.5. The structures identified by Kainulainen et al. (2009) in the power-law tail of the probability distribution function are better candidates, but most
are still unbound. Objects found in some surveys of dust
continuum emission (§2.3) appear to be still better candidates. For example, analysis (Schlingman et al. 2011;
Dunham et al. 2011b) of the sources found in millimeterwave continuum emission surveys of the MW (§2.3) indicates typical volume densities of a few × 103 cm−3 , compared to about 200 cm−3 for 13 CO structures. Mean
surface densities are about 180 M⊙ pc−2 , higher than
those of gas in the the power-law tail (Σgas ∼ 40 − 80
M⊙ pc−2 ). These structures have a wide range of sizes,
with a median of 0.75 to 1 pc.
Studies of regions with signposts of massive star formation, using tracers requiring higher densities (e.g.,
Plume et al. 1992; Beuther et al. 2002) or millimeter
continuum emission from dust (e.g., Beuther et al. 2002;
Mueller et al. 2002) have identified slightly smaller structures (r ∼ 0.5 pc) that are much denser, indeed denser
on average than cores in nearby clouds. In addition to
having a mass distribution consistent with that of clus-
ters (§2.5), many have far-infrared luminosities consistent with the formation of clusters of stars with masses
ranging up to those of O stars. The properties of the
Plume et al. (1992) sample have been studied in a series
of papers (Plume et al. 1997; Mueller et al. 2002; Shirley
et al. 2003), with the most recent summary in Wu et al.
(2010a). The properties of the clumps depend on the
tracer used. Since the HCN J = 1 → 0 line is used in
many extragalactic studies, we will give the properties
as measured in that line. The mean and median FWHM
are 1.13 and 0.71 pc; the mean and median infrared luminosities are 4.7 × 105 and 1.06 × 105 L⊙ ; the mean and
median virial mass are 5300 and 2700 M⊙ ; the mean and
median surface densities are 0.29 and 0.28 gm cm−2 ; and
the mean and median of the average volume densities (n)
are 3.2 × 104 and 1.6 × 104 cm−3 . As lines tracing higher
densities are used, the sizes and masses decrease, while
the surface densities and volume densities increase, as
expected for centrally condensed regions. Very similar
results were obtained from studies of millimeter continuum emission from dust (Faúndez et al. 2004) toward a
sample of southern hemisphere sources surveyed in CS
J = 2 → 1 (Bronfman et al. 1996).
Embedded clusters provide important testing grounds
for theories of star formation. Using criteria of 35 members with a stellar density of 1 M⊙ pc−3 for a cluster,
Lada & Lada (2003) argue that most stars form in clusters, and 90% of those are in rich clusters with more than
100 stars, but that almost all clusters (> 93%) dissipate
as the gas is removed, a process they call “infant mortality.” With more complete surveys enabled by Spitzer,
the distributions of numbers of stars in clusters and stellar densities are being clarified. Allen et al. (2007) found
that about 60% of young stars within 1 kpc of the Sun are
in clusters with more than 100 members, but this number is heavily dominated by the Orion Nebula cluster.
Drawing on the samples from Spitzer surveys of nearly
all clouds within 0.5 kpc, Bressert et al. (2010) found a
continuous distribution of surface densities and no evidence for a bimodal distribution, with distinct “clustered” and “distributed” modes. They found that the
fraction of stars that form in clusters ranged from 0.4
to 0.9, depending on which definition of “clustered” was
used. Even regions of low-mass star formation, often
described as distributed star formation, are quite clustered and the youngest objects (Class I and Flat SED
sources, see §4.1) are very strongly concentrated to regions of high extinction, especially after the samples have
been culled of interlopers (Fig. 4, §6.4). Similarly, studies of three clouds found that 75% of prestellar cores lay
above thresholds in AV of 8, 15, and 20 mag, while most
of the cloud mass was at much lower extinction levels
(Enoch et al. 2007).
A Spitzer study (Gutermuth et al. 2009) of 2548 YSOs
in 39 nearby (d < 1.7 kpc), previously known (primarily from the compilation by Porras et al. 2003) young
clusters, but excluding Orion and NGC2264, found the
following median properties: 26 members, core radius of
0.39 pc, stellar surface density of 60 pc−2 , and embedded in a clump with AK = 0.8 mag, which corresponds
to AV = 7.1 mag. Translating to mass surface density
using hM⋆ i = 0.5 M⊙ , the median stellar mass surface
density would be 30 M⊙ pc−2 and the gas surface den-
Kennicutt and Evans
sity would be 107 M⊙ pc−2 . The distributions are often
elongated, with a median aspect ratio of 1.82. The median spacing between YSOs, averaged over all 39 clusters,
is 0.072 ± 0.006 pc, comparable to the size of individual
cores, and a plausible scale for Jeans fragmentation. The
distributions are all skewed toward low values, with a tail
to higher values.
While various definitions of “clustered” have been
used, one physically meaningful measure is a surface density of ∼ 200 YSOs pc−2 (Gutermuth et al. 2005), below which individual cores are likely to evolve in relative isolation (i.e., the timescale for infall is less than the
timescale for core collisions). With their sample, Bressert
et al. (2010) found that only 26% were likely to interact
faster than they collapse. However, that statistic did not
include the Orion cluster, which exceeds that criterion.
The fact that the Orion cluster dominates the local
star formation warns us that our local sample may be
unrepresentative of the Galaxy as a whole. Leaving aside
globular clusters, there are young clusters that are much
more massive than Orion. Portegies Zwart et al. (2010)
have cataloged massive (M⋆ ≥ 104 M⊙ ), young (age ≤
100 Myr) clusters (12) and associations (13), but none of
these are more distant than the Galactic Center, so they
are clearly undercounted. The mean half-light radius of
the 12 clusters is 1.7 ± 1.3 pc compared to 11.2 ± 6.4
pc for the associations. For the clusters, hlogM⋆ (M⊙ )i =
4.2±0.3. Three of the massive dense clumps from the Wu
et al. (2010a) study have masses above 104 M⊙ and are
plausible precursors of this class of clusters. Still more
massive clusters can be found in other galaxies, and a
possible precursor (Mcloud > 1 × 105 M⊙ within a 2.8 pc
radius) has recently been identified near the center of the
MW (Longmore et al. 2012).
The topic of clusters is connected to the topic of massive stars because 70% of O stars reside in young clusters or associations (Gies 1987). Furthermore, most of
the field population can be identified as runaways (de
Wit et al. 2005), with no more than 4% with no evidence of having formed in a cluster. While there may be
exceptions (see Zinnecker & Yorke 2007 for discussion),
the vast majority of massive stars form in clusters. The
most massive star with a dynamical mass (NGC 3603A1) weighs in at 116 ± 31 M⊙ and is a 3.77 day binary
with a companion at 89 ± 16 M⊙ (Schnurr et al. 2008).
Still higher initial masses (105-170 M⊙ ) for the stars in
NGC3603 and even higher in R136 (165-320 M⊙ ) have
been suggested (Crowther et al. 2010). Many of the most
massive stars exist in tight (orbital periods of a few days)
binaries (Zinnecker & Yorke 2007). For a recent update
on massive binary properties, see Sana & Evans (2011).
There is some evidence, summarized by Zinnecker &
Yorke (2007), that massive stars form only in the most
massive molecular clouds, with max(M⋆ ) ∝ Mcloud 0.43
suggested by Larson (1982). Roughly speaking, it takes
Mcloud = 105 M⊙ to make a 50 M⊙ star. Recognizing
that clumps are the birthplaces of clusters and that efficiencies are not unity could make the formation of massive stars even less likely. The question (§2.5) is whether
the absence of massive stars in clumps or clusters of
modest total mass is purely a sampling effect (Fumagalli
et al. 2011; Calzetti et al. 2010a and references therein)
or a causal relation (Weidner & Kroupa 2006). If causal,
differences in the upper mass limit to clouds or clumps
(§2.5) in a galaxy could limit the formation of the most
massive stars. Larson (1982) concluded that his correlation could be due to sampling. As a concrete example,
is the formation of a 50 M⊙ star as likely in an ensemble
of 100 clouds, each with 103 M⊙ , as it is in a single 105
M⊙ cloud? Unbiased surveys of the MW for clumps and
massive stars (§5.1) could allow a fresh look at this question, with due regard for the difficulty of distinguishing
“very rarely” from “never.”
4.3. Theoretical Aspects
The fundamental problem presented to modern theorists of star formation has been to explain the low efficiency of star formation on the scale of molecular clouds.
Early studies of molecular clouds concluded that they
were gravitationally bound and should be collapsing at
free fall (e.g., Goldreich & Kwan 1974). Zuckerman &
Palmer (1974) pointed out that such a picture would produce stars at 30 times the accepted average recent rate
of star formation in the Milky Way (§5.1) if stars formed
with high efficiency. Furthermore, Zuckerman & Evans
(1974) found no observational evidence for large scale
collapse and suggested that turbulence, perhaps aided by
magnetic fields, prevented overall collapse. This suggestion led eventually to a picture of magnetically subcritical clouds that formed stars only via a redistribution of
magnetic flux, commonly referred to as ambipolar diffusion (Shu et al. 1987; Mouschovias 1991), which resulted
in cloud lifetimes about 10 times the free-fall time. If,
in addition, only 10% of the cloud became supercritical,
a factor of 100 decrease in star formation rate could be
Studies of the Zeeman effect in OH have now provided
enough measurements of the line-of-sight strength of the
magnetic field to test that picture. While there are still
controversies, the data indicate that most clouds (or,
more precisely, the parts of clouds with Zeeman measurements) are supercritical or close to critical, but not
strongly subcritical (Crutcher et al. 2010). Pictures of
static clouds supported by magnetic fields are currently
out of fashion (McKee & Ostriker 2007), but magnetic
fields are almost certain to play a role in some way (for
a current review, see Crutcher 2012, this volume). Simulations of turbulence indicate a fairly rapid decay, even
when magnetic fields are included (Stone et al. 1998).
As a result, there is growing support for a more dynamical picture in which clouds evolve on a crossing time
(Elmegreen 2000). However, this picture must still deal
with the Zuckerman-Palmer problem.
There are two main approaches to solving this problem at the level of clouds, and they are essentially extensions of the two original ideas, magnetic fields and turbulence, into larger scales. One approach, exemplified by
Vázquez-Semadeni et al. (2011) argues that clouds are
formed in colliding flows of the warm, neutral medium.
They simulate the outcome of these flows with magnetic
fields, but without feedback from star formation. Much
of the mass is magnetically subcritical and star formation happens only in the supercritical parts of the cloud.
A continued flow of material balances the mass lost to
star formation so that the star formation efficiency approaches a steady value, in rough agreement with the
Star Formation
A second picture, exemplified by Dobbs et al. (2011),
is that most clouds and most parts of clouds are not
gravitationally bound but are transient objects. Their
simulations include feedback from star formation, but
not magnetic fields. During cloud collisions, material is
redistributed, clouds may be shredded, and feedback removes gas. Except for a few very massive clouds, most
clouds lose their identity on the timescales of a few Myr.
In this picture, the low efficiency simply reflects the fraction of molecular gas that is in bound structures.
It is not straightforward to determine observationally if
clouds are bound, especially when they have complex and
filamentary boundaries. Heyer et al. (2001) argued that
most clouds in the outer galaxy with M > 104 M⊙ were
bound, but clumps and clouds with M < 103 M⊙ were
often not bound. Heyer et al. (2009) address the issues
associated with determining accurate masses for molecular clouds. In a study on the inner Galaxy, Roman-Duval
et al. (2010) concluded that 70% of molecular clouds
(both in mass and number) were bound.
If molecular clouds are bound and last longer than a
few crossing times, feedback or turbulence resulting from
feedback is invoked. For low-mass stars, outflows provide
the primary feedback (e.g., Li & Nakamura 2006) while
high-mass stars add radiation pressure and expanding
H II regions (e.g., Murray 2011). In addition, the efficiency is not much higher in most clumps, so the problem
persists to scales smaller than that of clouds.
Another longstanding problem of star formation theory has been to explain the IMF (§2.5). This topic has
been covered by many reviews, so we emphasize only two
aspects. The basic issue is that the typical conditions in
star forming regions suggest a characteristic mass, either
the Jeans mass or the Bonnor-Ebert mass, around 1 M⊙
(e.g., Bonnell et al. 2007). Recently, Krumholz (2011)
has derived a very general expression for a characteristic mass of 0.15 M⊙ , with only a very weak dependence on pressure. However, we see stars down to the
hydrogen-burning limit and a continuous distribution of
brown dwarfs below that, extending down even to masses
lower than those seen in extrasolar planets (Allers et al.
2006). An extraordinarily high density would be required
to make such a low mass region unstable.
On the other end, making a star with mass over 100
times the characteristic mass is challenging. Beuther
et al. (2007a) provide a nice review of both observations and theory of massive star formation. While dense
clumps with mass much greater than 100 M⊙ are seen,
they are likely to fragment into smaller cores. Fragmentation can solve the problem of forming low mass objects,
but it makes it hard to form massive objects. Simulations of unstable large clumps in fact tend to fragment so
strongly as the mean density increases that they overproduce brown dwarfs, but no massive stars (e.g., Klessen
et al. 1998; Martel et al. 2006). This effect is caused
by the assumed isothermality of the gas, because the
Jeans mass is proportional to (TK 3 /n)0.5 . Simulations
including radiative feedback, acting on a global scale,
have shown that fragmentation can be suppressed and
massive stars formed (e.g., Bate 2009; Urban et al. 2010;
Krumholz et al. 2010). Krumholz & McKee (2008) have
argued that a threshold clump surface density of 1 gm
cm−2 is needed to suppress fragmentation, allowing the
formation of massive stars.
The radiative feedback, acting locally, can in principle
also limit the mass of the massive stars through radiation
pressure. This can be a serious issue for the formation
of massive stars in spherical geometries, but more realistic, aspherical simulations show that the radiation is
channeled out along the rotation axis, allowing continued accretion through a disk (Yorke & Sonnhalter 2002;
Krumholz et al. 2009a; Kuiper et al. 2011).
The picture discussed so far is basically a scaled-up
version of the formation of low mass stars by accretion
of material from a single core (sometimes called Core
Accretion). An alternative picture, called Competitive
Accretion, developed by Klessen et al. (1998), Bate et al.
(2003), and Bonnell et al. (2003), builds massive stars
from the initial low-mass fragments. The pros and cons
of these two models are discussed in a joint paper by the
leading protagonists (Krumholz & Bonnell 2009). They
agree that the primary distinction between the two is
the original location of the matter that winds up in the
star: in Core Accretion models, the star gains the bulk
of its mass from the local dense core, continuing the connection of the core mass function to the initial stellar
mass function to massive stars; in Competitive Accretion models, the more massive stars collect most of their
mass from the larger clump by out-competing other, initially low mass, fragments. A hybrid picture, in which
a star forms initially from its parent core, but then continues to accrete from the surrounding clump, has been
advanced (Myers 2009, 2011), with some observational
support (e.g., Longmore et al. 2011).
Observational tests of these ideas are difficult. The
Core Accretion model requires that clumps contain a
core mass function extending to massive cores. Some
observations of massive dense clumps have found substructure on the scale of cores (Beuther et al. 2007b;
Brogan et al. 2009), but the most massive cores identified
in these works are 50-75 M⊙ . Discussions in those references illustrate the difficulties in doing this with current
capabilities. ALMA will make this kind of study much
more viable, but interpretation will always be tricky. The
Competitive Accretion model relies on a continuous flow
of material to the densest parts of the clump to feed the
growing oligarchs. Evidence for overall inward flow in
clumps is difficult; evidence for it is found in some surveys (Wu & Evans 2003; Fuller et al. 2005; Reiter et al.
2011a), but not in others (Purcell et al. 2006). Since special conditions are required to produce an inflow signature, the detection rates may underestimate the fraction
with inflow. The dense clumps are generally found to be
centrally condensed (Beuther et al. 2002; Mueller et al.
2002; van der Tak et al. 2000), which can also suppress
Other possible tests include the coherence of outflows
in clusters, as these should be distorted by sufficiently
rapid motions. The kinematics of stars in forming clusters, which should show more velocity dispersion in the
competitive accretion models, provide another test. Astrometric studies are beginning to be able to constrain
these motions (Rochau et al. 2010), along with cleaner
separation of cluster members from field objects. Relative motions of cores within clumps appear to be very
low (< 0.1 /kms), challenging the Competitive Accretion
model (Walsh et al. 2004).
Kennicutt and Evans
Theoretical studies include evolutionary tracks of premain-sequence stars (e.g., Chabrier & Baraffe 2000 for
low mass stars and substellar objects). These evolutionary calculations are critical for determining the ages
of stars and clusters. For more massive stars, it is essential to include accretion in the evolutionary calculations (Palla & Stahler 1992) and high accretion rates
strongly affect the star’s evolution (Zinnecker & Yorke
2007; Hosokawa & Omukai 2009). Assumptions about
accretion and initial conditions may also have substantial
consequences for the usual methods of determining ages
of young stars (Baraffe et al. 2009; Baraffe & Chabrier
2010; Hosokawa et al. 2011).
4.4. Summary Points from the Local Perspective
The main lessons to retain from local studies of star
formation as we move to the scale of galaxies are summarized here.
1. Star formation is not distributed smoothly over
molecular clouds but is instead highly concentrated
into regions of high extinction or mass surface density, plausibly associated with the theoretical idea
of a cluster-forming clump. This is particularly apparent when prestellar cores or the youngest protostars are considered (e.g., Figure 4). In contrast,
most of the mass in nearby molecular clouds is in
regions of lower extinction.
2. By counting YSOs in nearby clouds, one can obtain reasonably accurate measures of star formation rate and efficiency without the uncertainties of
extrapolation from the high-mass tail of the IMF.
The main source of uncertainty is the ages of YSOs.
3. There is no obvious bimodality between “distributed” and “clustered” star formation, but dense
clusters with massive stars tend to form in regions
of higher mean density and turbulence, which are
centrally condensed. Plausible precursors of quite
massive (up to 104 or perhaps 105 M⊙ ) clusters can
be found in the MW.
4. Despite much theoretical progress, the challenge of
explaining the low efficiency of star formation, even
in regions forming only low-mass stars, remains.
Similarly, an understanding of the full IMF, from
brown dwarfs to the most massive stars, remains
5.1. The Milky Way as a Star-forming Galaxy
As our nearest example, the Milky Way (hereafter denoted as MW) has obvious advantages in studies of star
formation in galaxies. However, living inside the MW
presents serious problems of distance determination and
selection effects, compared to studies of other galaxies.
We can “look in from the outside” only with the aid
of models. After reviewing surveys briefly, we consider
properties of gas and star formation within the MW,
bearing in mind the issues raised in §2.4 and §3, first
as a whole, and then the radial distribution, and finally
some notes on non-axisymmetric structure.
5.1.1. Surveys
Recent and ongoing surveys of the Galactic Plane at
multiple wavelengths are revitalizing the study of the
MW as a galaxy. Surveys of H I from both northern (Taylor et al. 2003) and southern (McClure-Griffiths et al.
2005) hemispheres, along with a finer resolution survey
of parts of the Galactic Plane (Stil et al. 2006) have given
a much clearer picture of the atomic gas in the MW (for a
review of H I surveys, see Kalberla & Kerp 2009). Based
on these surveys, properties of the cool atomic clouds
have been analyzed by Dickey et al. (2003).
Numerous surveys of the MW have been obtained in
CO J = 1 → 0 (e.g., Dame et al. 2001; Bronfman et al.
1988; Clemens et al. 1988). A survey of the inner part of
the MW in 13 CO (Jackson et al. 2006) has helped with
some of problems caused by optical depth in the main
Surveys for tracers of star formation have been made
in radio continuum (free-free) emission (Altenhoff et al.
1970) and recombination lines (Anderson et al. 2011;
Lockman 1989), in water masers (Cesaroni et al. 1988;
Walsh et al. 2011), and methanol masers (Pestalozzi et al.
2005; Green et al. 2009). In addition to being signposts
of (mostly massive) star formation, the masers provide
targets for astrometric studies using VLBI.
Complementary surveys of clouds have been done using
mid-infrared extinction (e.g., Perault et al. 1996; Egan
et al. 1998; Peretto & Fuller 2009), which can identify Infrared Dark Clouds (IRDCs) against the Galactic background emission. The MIPSGAL survey (Carey et al.
2009) should also provide a catalog of very opaque objects. At longer wavelengths, the dust is usually in emission, and millimeter continuum emission from dust (e.g.,
Aguirre et al. 2011; Rosolowsky et al. 2010; Schuller et al.
2009) provides a different sample of objects.
Each method has its own selection effects and efforts
are ongoing to bring these into a common framework. A
key ingredient is to determine the distances, using spectral lines and methods to break the distance ambiguity in
the inner galaxy; initial work is underway (Russeil et al.
2011; Schlingman et al. 2011; Dunham et al. 2011b; Foster et al. 2011). Ultimately, these studies should lead to a
better definition of the total amount and distribution of
dense gas (§1.2). The Herschel HIGAL survey (Molinari
et al. 2010) will add wavelengths into the far-infrared
and lead to a far more complete picture. Quantities like
LF IR /Mcloud and LF IR /Mdense , as used in extragalactic
studies, can be calculated for large samples.
5.1.2. The Milky Way as a Whole
The Milky Way is a barred spiral galaxy (Burton 1988;
Dame et al. 2001; Benjamin et al. 2005). The number and
position of spiral arms are still topics for debate, but the
best currently available data favor a grand-design, twoarmed, barred spiral with several secondary arms. A conception of what the MW would look like from the outside
(Churchwell et al. 2009) is shown in Figure 5. We can
expect continuing improvements in the model of the MW
as VLBI astrometry improves distance determinations of
star forming regions across the MW (Reid et al. 2009;
Brunthaler et al. 2011). As we will be comparing the
MW to NGC 6946, we also show images of that galaxy
at Hα, 24 µm, H I, and CO J = 2 → 1 in Fig. 6.
Star Formation
Based on a model including dark matter (Kalberla &
Kerp 2009; Kalberla et al. 2007; Kalberla & Dedes 2008),
the MW mass within 60 kpc of the center is M (tot) =
4.6 × 1011 M⊙ , with M (baryon) = 9.5 × 1010 M⊙ . The
total mass of atomic gas (H I plus He) is M (atomic) =
8 × 109 M⊙ , and the warm ionized medium contains
M (W IM ) = 2 × 109 M⊙ . The mass fraction of the HIM
(§2.1) is negligible. With a (perhaps high) estimate for
the molecular mass of M (mol) = 2.5 × 109 M⊙ , Kalberla
& Kerp (2009) derive a gas to baryon ratio of 0.13. As
explained in §5.1.3, for consistent comparison to the radial distribution in NGC 6946, we will use a constant
X(CO) = 2.0 × 1020 , correct for helium, and assume an
outer radius of the star forming disk of 13.5 kpc to define
masses, surface densities, etc. Within Rgal = 13.5 kpc,
M (mol) = 1.6 × 109 M⊙ and M (atomic) = 5.0 × 109
M⊙ with these conventions.
The volume filling factor of the CNM is about 1% (Cox
2005) and that of molecular clouds, as traced by the 13 CO
survey (Roman-Duval et al. 2010), has been estimated
at about 0.5% (M. Heyer, personal communication) in
the inner galaxy, but much lower overall. Denser (n ∼
few × 103 cm−3 ) structures found in millimeter continuum surveys, roughly corresponding to clumps, appear
to have a surface filling factor of 10−4 and a volume filling
factor of about 10−6 (M. K. Dunham, personal communication), but better estimates should be available soon.
The star formation rate of the MW has been estimated
from counting H II regions, which can be seen across
the MW and extrapolating to lower mass stars (Mezger
1987; McKee & Williams 1997; Murray & Rahman 2010).
These methods average over the effective lifetime of massive stars, about 3-10 Myr (Table 1). Estimates of Ṁ∗
from a model of the total far-infrared emission of the
MW (e.g., Misiriotis et al. 2006) are somewhat less sensitive to the high end of the IMF (§3) and average over
a longer time. An alternative approach, based on counting likely YSOs in the GLIMPSE survey of the Galactic
plane (Robitaille & Whitney 2010) is much less biased toward the most massive stars, but is limited by sensitivity,
issues of identification of YSOs, and models of extinction. Chomiuk & Povich (2011) have recently reviewed
all methods of computing Ṁ∗ for the MW and conclude
that they are consistent with Ṁ∗ = 1.9 ± 0.4 M⊙ yr−1 .
However they conclude that resolved star counts give
SFRs that are factors of 2-3 times higher (see §6.4 for
further discussion).
With a radius of active star formation of 13.5 kpc
(§5.1.3), Ṁ∗ = 1.9 M⊙ yr−1 yields hΣ(SFR)i =
3.3 × 10−3 M⊙ yr−1 kpc−2 .
Taking M (mol, Rgal <
13.5) = 1.6 × 109 M⊙ , tdep = 0.8 Gyr, 10 times longer
than htdep i in local clouds (§4.1). For all the gas in the
(60 kpc) MW, tdep = 6.6 Gyr, or 5.5 Gyr if the WIM is
excluded. If we attribute all non-gaseous baryons in the
Kalberla & Kerp (2009) model (8.25 × 1010 M⊙ ) to stars
and stellar remnants, ignore recycling, and take an age
of 1 × 1010 yr, we would derive an average star formation
rate of 8.25 M⊙ yr−1 , about 4 times the current rate.
5.1.3. Radial Distributions
The MW also offers a wide range of conditions, from
the far outer Galaxy to the vicinity of the Galactic Cen-
ter, for detailed study. The hurdle to overcome, especially in the inner MW, is to assign accurate distances.
The radial distributions of atomic and molecular gas,
along with the star formation rate surface density (here
in units of M⊙ Gyr−1 pc−2 ), are plotted in Figure 7,
along with a similar plot for NGC 6946 (Schruba et al.
2011). For consistency, we have used the same X(CO)
and correction for helium (for both molecular and atomic
gas) as did Schruba et al. (2011). These distributions for
the MW have considerable uncertainties, and should be
taken with appropriate cautions, especially in the innermost regions, as discussed below. Misiriotis et al. (2006)
presents a collection of estimates of Σ(SFR) and a model.
They all show a steady decline outward from a peak at
Rgal ∼ 5 kpc, but the situation in the innermost galaxy
is unclear. The data on H II regions that forms the basis
of most estimates are very old, and a fresh determination
of Σ(SFR)(Rgal ) is needed.
In comparison, NGC 6946 has a similar, rather flat, distribution of atomic gas, with Σ(atomic) ∼ 10 M⊙ pc−2 .
The molecular gas distribution is similar to that of the
MW, except for a clearer and stronger peak within
Rgal = 2 kpc. The distribution of Σ(SFR) follows the
molecular gas in both galaxies, more clearly so in NGC
We discuss the MW distributions from the outside,
moving inward. The average surface density of molecular gas drops precipitously beyond 13.5 kpc, after a local peak in the Perseus arm (Heyer et al. 1998), as does
the stellar density (Ruphy et al. 1996), thereby defining
the far outer Galaxy, and the radius used in our whole
Galaxy quantities (§5.1.2). The atomic surface density
also begins to drop around 13-17 kpc, following an exponential with scale length 3.74 kpc (Kalberla & Kerp
2009). Molecular clouds in the far outer galaxy are rare,
but can be found with large-scale surveys. Star formation
does continue in the rare molecular clouds (Wouterloot &
Brand 1989), and Figure 7 would suggest a higher ratio
of star formation to molecular gas, but there are issues of
incompleteness in the outer galaxy. A study of individual
regions (Snell et al. 2002) found a value of LF IR /M similar to that for the inner Galaxy. They conclude that the
star formation process within a cloud is not distinguishable from that in the inner Galaxy; the low global rate
of star formation is set by the inefficient conversion of
atomic to molecular gas in the far outer Galaxy. This result is consistent with the results of Schruba et al. (2011)
for other galaxies, as exemplified by NGC 6946.
Inside about 13 kpc, the atomic surface density is
roughly constant at 10-15 M⊙ pc−2 , while the average
molecular surface density increases sharply, passing 1
M⊙ pc−2 somewhere near the solar neighborhood (Dame
et al. 2001), to a local maximum around Rgal = 4-5 kpc
(Nakanishi & Sofue 2006). After a small decrease inside
4 kpc, the surface density rises sharply within Rgal = 1
kpc. Nakanishi & Sofue (2006) and thus Figure 7 use a
constant X(CO), which could overestimate the molecular
mass near the center (§2.4).
The innermost part of the MW, Rgal < 250 pc, known
as the Central Molecular Zone (CMZ), potentially provides an opportunity for a close look at conditions in
galactic nuclei without current AGN activity, provided
that the issues of non-circular motions, foreground and
Kennicutt and Evans
background confusion, and possible changes in X(CO)
(Oka et al. 1998) can be overcome. Despite their conclusion that X(CO) is lower, Oka et al. (1998) argue that the
CMZ has a molecular mass of 2-6 × 107 M⊙ . Analysis of
dust emission yields a mass of 5 × 107 M⊙ (Pierce-Price
et al. 2000), which leads to Σgas = 250 M⊙ pc−2 for the
CMZ. A TIR luminosity of 4 × 108 L⊙ (Sodroski et al.
1997) for the CMZ would imply Ṁ∗ ∼ 0.06 M⊙ yr−1 using the conversion in Table 1, roughly consistent with
other recent estimates (Immer et al. 2012), based on
analysis of point infrared sources, but new data from
the surveys mentioned above should allow refinement of
these numbers. Evidence for variations in star formation rate on short timescales is discussed by Yusef-Zadeh
et al. (2009). Using Ṁ∗ = 0.06 M⊙ yr−1 and Rgal = 0.25
kpc for the CMZ, Σ(SFR) = 300 M⊙ Gyr−1 pc−2 . These
values of Σmol and Σ(SFR) for the CMZ are plotted separately in Figure 7 and identified as “CMZ.” If correct,
the CMZ of the MW begins to look a bit more like the
inner few kpc of NGC 6946. The CMZ provides an excellent place to test scaling relations, including those for
dense gas, in detail, if the complicating issues can be
understood. Preliminary results suggest that Σ(SFR) is
similar to that expected from Σmol (see Fig. 7), but
lower than expected from dense gas relations (S. Longmore, personal communcation).
The properties of clouds and clumps also may vary
with Rgal . Heyer et al. (2009) reanalyzed cloud properties in the inner Galaxy based on CO and 13 CO surveys. For the area of the cloud defined roughly by
the 1 K CO detection threshold, he found a median
Σmol (cloud) = 42 M⊙ pc−2 for clouds, substantially less
than originally found by Solomon et al. (1987), and only
a few clouds have Σmol (cloud) > 100 M⊙ pc−2 . Analysis
based on detection thresholds for 13 CO yield a median
Σmol (13 CO clump) = 144 M⊙ pc−2 for “13 CO clumps”
(Roman-Duval et al. 2010, who refer to them, however as
clouds). The mean in 0.5 kpc bins of surface density per
CO clump is roughly constant at 180 M⊙ pc−2 from
Rgal = 3 to 6.6 kpc, beyond which it drops sharply toward the much lower values in the solar neighborhood.
Assuming the region sampled is representative, RomanDuval et al. (2010) have plotted the azimuthally averaged
surface density of 13 CO clumps versus Galactocentric radius; it peaks at 2.5 M⊙ pc−2 at 4.5 kpc, declining to
< 0.5 M⊙ pc−2 beyond 6.5 kpc. The clouds do appear
to be associated with spiral arms, so azimuthal averaging
should be taken with caution. The cloud mass function of
246 clouds in the far outer galaxy has a power-law slope
of αcloud = −1.88, similar to but slightly steeper than
that found inside the solar circle (§2.5) and a maximum
mass of about 104 M⊙ (Snell et al. 2002). The lower
value for the maximum mass of a cloud seems to result
in a concomitant limit on the number of stars formed
in a cluster, but no change is inferred for the intrinsic
IMF (Casassus et al. 2000). A piece of a spiral arm at
Rgal = 15 kpc has been recently identified in H I and
CO, containing a molecular cloud with M = 5 × 104 M⊙
(Dame & Thaddeus 2011).
5.1.4. Non-axisymmetric Structure
The molecular gas surface density shows a strong local
maximum around Rgal = 4.5 kpc in the northern surveys
(Galactic quadrants I and II), while southern surveys
(quadrants III and IV) show a relatively flat distribution
of Σmol from about 2 to 7 kpc (Bronfman et al. 2000).
This asymmetry is likely associated with spiral structure (Nakanishi & Sofue 2006) and a long (half-length
of 4.4 kpc) bar (Benjamin et al. 2005). The star formation rate, measured from LF IR , does not, however,
reflect this asymmetry; in fact, it is larger in quadrant
IV than in I, suggesting a star formation efficiency up
to twice as high, despite the lower peak Σmol (Bronfman et al. 2000). Interestingly, the distribution of denser
gas, traced by millimeter-wave dust continuum emission
(Beuther et al. 2012), is also symmetric on kpc scales,
but asymmetries appear within the CMZ region (Bally
et al. 2010). Major concentrations of molecular clouds
with very active star formation appear to be associated
with regions of low shear (Luna et al. 2006), and with
the junction of the bar and spiral arms (Nguyen Luong
et al. 2011).
5.2. Demographics of Star-Forming Galaxies Today
The recent influx of multi-wavelength data has expanded the richness of information available on global
star formation properties of galaxies, and transformed
the interpretive framework from one based on morphological types to a quantitative foundation based on
galaxy luminosities, masses, and other physical properties.
The role of galaxy mass as a fundamental determinant
of the star formation history of a galaxy has been long
recognized (e.g., Gavazzi & Scodeggio 1996), but data
from SDSS and subsequent surveys have reshaped our
picture of the population of star-forming galaxies (e.g.,
Kauffmann et al. 2003; Baldry et al. 2004, 2006; Brinchmann et al. 2004). The integrated colors of galaxies,
which are sensitive to their star formation histories, show
a strongly bimodal dependence on stellar mass, with
a relatively tight “red sequence” populated by galaxies
with little or no current star formation, and a somewhat
broader “blue sequence” or “blue cloud” of actively starforming galaxies. The dominant population shifts from
blue to red near a transition stellar mass of ∼ 3×1010 M⊙
(Kauffmann et al. 2003). The relative dearth of galaxies
in the “green valley” between the red and blue sequences
suggests a deeper underlying physical bimodality in the
galaxy population and a rapid evolution of galaxies from
blue to red sequences.
A similar bimodality characterizes the mass dependence of the SFR per unit galaxy mass (SSFR). The mass
dependence of the SSFR has been explored by numerous
investigators (e.g., Brinchmann et al. 2004; Salim et al.
2007; Schiminovich et al. 2007; Lee et al. 2007). Figure 8 shows an example from Schiminovich et al. (2007),
based in this case on dust-corrected FUV measurements
of SDSS galaxies.
A clear separation between the blue and red sequences
is evident, and the dispersion of SSFRs within the blue
sequence is surprisingly small, suggesting that some kind
of self-regulation mechanism may be at work among the
actively star-forming galaxies. The bimodality is not absolute; there is a clear tail of less active but significantly
star forming galaxies between the two sequences. These
Star Formation
represent a combination of relatively inactive (usually
early-type) disk galaxies and unusually active spheroiddominated systems (§5.4). The sharp increase in the fraction of inactive galaxies above stellar masses of order a
few times 1010 M⊙ is also seen.
The blue sequence in Figure 8 is not horizontal; the
SSFR clearly increases with decreasing galaxy mass. The
slope (−0.36 for the data in Figure 8) varies somewhat
between different studies, possibly reflecting the effects
of different sampling biases. The negative slope implies
that lower-mass galaxies are forming a relatively higher
fraction of their stellar mass today, and thus must have
formed relatively fewer of their stars (compared to more
massive galaxies) in the past. The most straightforward
explanation is that the dominant star-forming galaxy
population in the Universe has gradually migrated from
more massive to less massive galaxies over cosmic time.
Direct evidence for this “downsizing” is seen in observations of the SSFR vs mass relation in high-redshift
galaxies (e.g., Noeske et al. 2007).
Another instructive way to examine the statistical
properties of star-forming galaxies is to compare absolute SFRs and SFRs normalized by mass or area. Several interesting trends can be seen in Figure 9, which
plots integrated measurements of the SFR per unit area
as a function of the absolute SFRs. The first is the extraordinary range in SFRs, more than seven orders of
magnitude, whether measured in absolute terms or normalized per unit area or (not shown) galaxy mass. Much
of this range is contributed by non-equilibrium systems
(starbursts). Normal galaxies occupy a relatively tight
range of SFRs per unit area, reminiscent of the tightness
of the blue sequence when expressed in terms of SSFRs.
The total SFRs of the quiescent star-forming galaxies
are also tightly bounded below a value of ∼20 M⊙ yr−1 .
Starburst galaxies, and infrared-luminous and ultraluminous systems in particular, comprise most of the galaxies
in the upper 2–3 decades of absolute SFRs and Σ(SFR).
The distribution of SFRs along the X-axis of Figure 9
(after correcting for volume completeness biases) is simply the SFR distribution function (e.g., Gallego et al.
1995; Martin et al. 2005b). Figure 10 shows a recent
determination of this distribution from Bothwell et al.
(2011), based on flux-limited UV and TIR samples of
galaxies and SFRs derived using the methods of Hao
et al. (2011), and corrections for AGN contamination
following Wu et al. (2010b, 2011). The SFR function is
well fitted by a Schechter (1976) exponentially truncated
power-law, with a faint-end slope α = −1.5 and characteristic SFR, SFR∗ = 9 M⊙ . Although SFRs as high
as ∼1000 M⊙ yr−1 are found in present-day ULIRGs, the
contribution of LIRGs and ULIRGs to the aggregate star
formation today is small (< 10% also see Goto et al.
2011). Steady-state star formation in galaxies dominates
today. The value of SFR∗ increases rapidly with z, and
galaxies with Lbol > 1011 L⊙ (i.e., LIRGs) become dominant by redshifts z > 1 (e.g., Le Floc’h et al. 2005). This
change partly reflects an increase in merger-driven star
formation at higher redshift, but at early epochs even
the steady-state star formation in massive galaxies attained levels of order tens to hundreds of solar masses per
year, thus placing those galaxies in the LIRG and ULIRG
regime. This suggests that most of the decrease in the
cosmic SFR in recent epochs has been driven by downsiz-
ing in the level of steady-state star formation (e.g., Bell
et al. 2005; Jogee et al. 2009).
5.3. The High-Density Regime: Starbursts
As highlighted in §1.2, the starburst phenomenon encompasses a wide range of physical scales and host galaxy
properties, and no precise physical definition of a starburst has been placed into wide use. Part of the explanation can be seen in Fig. 9; although the most extreme
starburst galaxies have properties that are well separated
from those of normal star-forming galaxies, there is no
clear physical break in properties; starbursts instead define the upper tails of the overall distributions in SFRs
within the general galaxy population.
Much of the attention in this area continues to focus
on the infrared-luminous and ultraluminous systems, because they probe star formation in the most extreme
high-density circumnuclear environments seen in the local Universe. A major breakthrough in recent years
has been the use of mid-infrared spectroscopy to distinguish dust heated by massive stars from that heated by a
buried AGN (e.g., Genzel et al. 1998; Laurent et al. 2000;
Dale et al. 2006; Armus et al. 2007). Regions heated by
AGNs are distinguished by the appearance of highly ionized atomic species, as well as suppressed mid-infrared
PAH emission relative to stellar-heated dust. Application of these diagnostics has made it possible to construct
clean samples of LIRGs and ULIRGs that are dominated
by star formation.
With the Spitzer and Herschel observatories, it has
been possible to extend imaging and spectroscopy of
the most luminous infrared-emitting galaxies to intermediate redshifts (e.g., Elbaz et al. 2005; Yan et al.
2007). As mentioned earlier the fraction of star formation in LIRGs and ULIRGs increases sharply with
redshift, but imaging and spectroscopy of these objects
reveals a marked shift in the physical characteristics of
the population. Whereas at low redshift, ULIRGs (and
many LIRGs) are dominated by very compact circumnuclear starbursts triggered by mergers, at higher redshifts the LIRG/ULIRG population becomes increasingly
dominated by large disk galaxies with extended star formation. As a consequence of cosmic downsizing (i.e.,
“upsizing” with increasing redshift), by redshifts z ∼ 1
the populations of LIRGs and ULIRGs become increasingly dominated by the progenitors of present-day normal galaxies, rather than by the transient merger-driven
starbursts which dominate the present-day populations
of ULIRGs, though examples of the latter are still found,
especially in the population of submillimeter-luminous
galaxies (SMGs) (e.g., Chapman et al. 2005).
Visible-wavelength observations of these high-redshift
galaxies with IFU instruments, both with and without
adaptive optics correction, have revealed many insights
into the physical nature of this population of starburst
galaxies (e.g., Genzel et al. 2008, 2011; Förster Schreiber
et al. 2009 and references therein). The Hα kinematics show a wide range of properties, from normal, differentially rotating disks to disturbed disks, and a subset with signatures of ongoing or recent mergers. The
disks tend to be characterized by unusually high velocity
dispersions, which have been interpreted as reflecting a
combination of dynamical instability and possibly energy
injection into the ISM from young stars. Further discus-
Kennicutt and Evans
sion of high-redshift galaxies is beyond the scope of this
article, but we shall return to the cold ISM properties
and SFRs of these galaxies in §6.
5.4. The Low SFR and Low Density Regimes
One of the most important discoveries from the
GALEX mission was the detection of low levels of star
formation in environments which were often thought
to have been devoid of star formation. These include
early-type galaxies, dwarf galaxies, low surface brightness galaxies, and the extreme outer disks of many normal galaxies.
Although star formation had been detected occasionally in nearby elliptical and S0 galaxies (e.g., Pogge &
Eskridge 1993), most of these galaxies have historically
been regarded as being “red and dead” in terms of recent
star formation. Deep GALEX imaging of E/S0 galaxies
(e.g., Kaviraj et al. 2007), however, has revealed that
approximately 30% of these early-type galaxies exhibit
near-ultraviolet emission in excess of what could reasonably arise from an evolved stellar population (e.g., Kaviraj et al. 2007). Confirmation of the star formation has
come from visible-wavelength IFU spectroscopy, as exploited for example by the SAURON survey (Shapiro
et al. 2010). The SFRs in these galaxies tend to be very
low, with at most 1–3% of the stellar mass formed over
the past Gyr. High-resolution UV imaging with HST often reveals extended star-forming rings or spiral arms in
these galaxies (Salim & Rich 2010). Follow-up CO observations of these galaxies reveals significant detections
of molecular gas in a large fraction of the galaxies with
detected star formation, with molecular gas masses of
107 − 1010 M⊙ (Combes et al. 2007; Crocker et al. 2011),
and with SFRs roughly consistent with the Schmidt law
seen in normal galaxies.
The GALEX images also reveal that star formation
in more gas-rich disk galaxies often extends much farther in radius than had previously been appreciated. In
exceptional cases (e.g., NGC 5236=M83, NGC 4625) the
star formation extends to 3–4 times the normal R25 optical radius, to the edge of the HI disk (Thilker et al.
2005; Gil de Paz et al. 2005). A systematic study by
Thilker et al. (2007) reveals that extended “XUV disks”
are found in ∼20% of spiral galaxies, with less distinct
outer UV structures seen in another ∼10% of disk galaxies. Follow-up deep Hα imaging and/or spectroscopy reveals extended disks of HII regions that trace the UV
emission in most cases (e.g., Zaritsky & Christlein 2007;
Christlein et al. 2010; Goddard et al. 2010), confirming
the earlier detection of HII regions at large radii (e.g.,
Ferguson et al. 1998; Ryan-Weber et al. 2004). Individual examples of extended UV features without Hα counterparts are sometimes found, however (Goddard et al.
2010). The GALEX images also have led to a breakthrough in measurements of star formation in low surface brightness spiral galaxies (LSBs). These provide a
homogeneous body of deep measurements of the star formation and the nature of the star formation law at low
surface densities (§6; Wyder et al. 2009). Comparison
to the outer MW (§5.1) suggests that deep searches for
molecular gas will find few clouds, which will nonetheless,
be the sites of star formation.
The other low-density star formation regime can be
found in dwarf irregular galaxies. Drawing general in-
ferences about the star formation properties of these
galaxies requires large samples with well-defined (ideally volume-limited) selection criteria, and studies of this
kind (based on UV, visible, and/or Hα observations)
have been carried out by several groups (e.g., Karachentsev et al. 2004; Blanton et al. 2005; Meurer et al. 2006;
Kennicutt et al. 2008; Dalcanton et al. 2009; Hunter et al.
2010). One perhaps surprising result is the near ubiquity of star formation in the dwarf galaxies. Kennicutt
et al. (2008) observed or compiled Hα luminosities for
galaxies within the local 11 Mpc, which included ∼300
dwarf galaxies (MB > −17). Excluding a handful of
dwarf spheroidal galaxies which have no cold gas, only
10 of these (∼3%) were not detected in Hα, meaning that
star formation has taken place over the last 3–5 Myr in
the other 97% of the systems. Moreover many of the
handful of Hα non-detections show knots of UV emission, demonstrating that even fewer of the galaxies have
failed to form stars over the last ∼100 Myr (Lee et al.
2011). Recent star formation is seen in all of the galaxies
with MB < −13 and M (HI) > 5 × 107 M⊙ . For less
massive galaxies it is possible for star formation to cease
for timescales that are longer than the ionization lifetime
of an HII region (up to 5 Myr), but examples of galaxies
with extended periods of no star formation are extremely
These data also provide a fresh look at the temporal
properties of the star formation in dwarf galaxies generally. The distribution of SSFRs shows a marked increase
in dispersion for galaxies with MB > −14.5 or circular velocity of 50 km s−1 (Lee et al. 2007; Bothwell et al. 2009).
The corresponding neutral gas fraction does not show a
similar increase in dispersion (Bothwell et al. 2009), so
this suggests an increased short-term fluctuation of integrated SFRs in low-mass galaxies. Lee et al. (2009b)
analyzed the statistics of the SFRs in more depth and
confirmed a larger fraction of stars formed in bursts in
low-mass galaxies (∼25%), but these still represent only
a small fraction of the total stars formed– even in the
dwarfs the majority of stars appear to form in extended
events of duration longer than ∼10 Myr. Recent modelling of the statistics of Hα and UV emission by Weisz
et al. (2012) and Fumagalli et al. (2011) as well as analysis of resolved stellar populations (e.g., Weisz et al. 2008)
confirm the importance of fluctuations in the SFR.
The immense dispersion in SFR properties seen in Figure 9 collapses to a remarkably tight scaling law when
the SFR surface densities (Σ(SFR)) are plotted against
mean gas surface densities (Σgas ) (Kennicutt 1998b).
This emergent order reflects the fact that gas is the input driver for star formation. The concept of a powerlaw relation between SFR density and gas density dates
to Schmidt (1959, 1963), and relations of this kind are
commonly referred to as “Schmidt laws.” On physical
grounds we might expect the most fundamental relation
between the volume densities of star formation and gas,
but since most observations of external galaxies can only
measure surface densities integrated along the line of
sight, the most commonly used relation, often called a
Kennicutt-Schmidt (KS) law, is in terms of surface densities.
Star Formation
ΣSF R = A ΣN gas
The precise form of this relation depends on assumptions
about how Σgas is derived from the observations (§2.4),
but a strong correlation is clearly present.
6.1. The Disk-Averaged Star Formation Law
K98 presented a review of observations of the Schmidt
law up to the time, and nearly all of that work characterised the relation between the disk-averaged SFR and
gas surface densities in galaxies. The upper panel of Figure 11 presents an updated version of the global Schmidt
law in galaxies. Each point is an individual galaxy (color
coded as explained in the caption), with the surface density defined as the total gas mass (molecular plus atomic)
or SFR normalized to the radius of the main star-forming
disk, as measured from Hα, Paα, or IR maps. For simplicity, a constant X(CO) factor [2.3 × 1020 cm−2 (K km
s−1 )−1 with no correction for helium, see §2.4] has been
applied to all of the galaxies; the consequences of a possible breakdown in this assumption are discussed later.
The sample of galaxies has been enlarged from that studied in Kennicutt (1998b), and all of the Hα-based SFR
measurements have been improved by incorporating individual (IR-based) corrections for dust attenuation and
[N II] contamination.
The form of this integrated Schmidt law appears to be
surprisingly insensitive to SFR environment and parameters such as the atomic versus molecular fraction, but
some metal-poor galaxies (defined as Z < 0.3Z⊙ ) deviate systematically from the main relation, as shown by
the blue open circles in Figure 11 (upper panel). These
deviations could arise from a physical change in the star
formation law itself, but are more likely to reflect a breakdown in the application of a constant X(CO) factor (§2.4;
Leroy et al. 2011, and references therein). Adopting
higher values of X(CO) for metal-poor galaxies brings
the galaxies much more into accord with the main relation in Figure 11.
Recent observations of LSBs by Wyder et al. (2009) extend the measurements of the integrated star formation
law to even lower mean surface densities, as shown by the
purple crosses in the upper panel of Figure 11. A clear
turnover is present, which is consistent with breaks seen
in spatially-resolved observations of the star formation
law (§6.2).
The slope of the integrated Schmidt law is non-linear,
with N ≃ 1.4–1.5 (Kennicutt 1998b), when a constant
X(CO) factor is applied. This uncertainty range does
not include all possible systematic errors, arising for example from changes in X(CO) or the IMF with increasing surface density or SFR. Major systematic changes in
either of these could easily change the derived value of
N by as much as 0.2–0.3. For example, if X(CO) were
five times lower in the dense starburst galaxies (§2.4),
the slope of the overall Schmidt law would increase from
1.4–1.5 to 1.7–1.9 (Narayanan et al. 2012).
Usually the Schmidt law is parametrized in terms of
the total (atomic plus molecular) gas surface density,
but one can also explore the dependences of the diskaveraged SFR densities on the mean atomic and molecular surface densities individually. Among normal galaxies
with relatively low mean surface densities, the SFR den-
sity is not particularly well correlated with either component, though variations in X(CO) could partly explain
the poor correlation between SFR and derived H2 densities (e.g., Kennicutt 1998b). In starburst galaxies with
high gas surface densities, however, the gas is overwhelmingly molecular, and a strong non-linear Schmidt law is
observed (upper panel of Figure 11).
A similar non-linear dependence is observed for total
SFR (as opposed to SFR surface density) versus total
molecular gas mass (e.g., Solomon & Sage 1988; Gao &
Solomon 2004), and presumably is another manifestation of the same underlying physical correlation. The
dependence of the SFR on dense molecular gas mass is
markedly different, however. The lower panel of Figure
11, taken from Gao & Solomon (2004), shows the relation
between the integrated SFRs and the dense molecular
gas masses, as derived from HCN J = 1 → 0 measurements (§2.4) for a sample of normal and starburst galaxies. In contrast to the correlation with total molecular
mass from CO J = 1 → 0, this relation is linear, implying
a strong coupling between the masses of dense molecular
clumps and stars formed, which is largely independent of
the galactic star-forming environment. Wu et al. (2005b)
have subsequently shown that this linear relation extends
down to the scales of individual star-forming molecular
clouds and dense clumps in the Galaxy. Combined with
the MW studies (§4), these dense gas relations for galaxies suggest that dense clumps are plausible fundamental
star-forming units. If so, the mass fraction of the ISM
(and fraction of the total molecular gas) residing in dense
clumps must itself increase systematically with the SFR.
Because LHCN in the J = 1 → 0 line is only an approximate tracer for dense gas (§2.4.3) and because the
definition of a dense clump is by no means precise (§2.5),
one should be careful not to overinterpret these trends.
Similar comparisons of the SFR with the emission from
other molecular tracers suggest that the slope of the SFR
versus gas mass relation changes continuously as one proceeds from lower-density tracers such as CO J = 1 → 0
to higher-excitation (and higher-density) CO transitions,
and further to high-density tracers such as HCN and
HCO+ and to higher transitions of those molecules (e.g.,
Juneau et al. 2009). Multi-transition studies, along with
realistic modeling will help to refine the interpretation of
line luminosities of dense gas tracers (e.g., Graciá-Carpio
et al. 2008; Juneau et al. 2009).
The data shown in Figure 11 all come from observations of nearby galaxies (z < 0.03), but recently a number of studies have addressed the form of the molecular
gas Schmidt law for starburst galaxies extending to redshifts z ≥ 2 (e.g., Bouché et al. 2007; Daddi et al. 2010;
Genzel et al. 2010). The interpretation of these results
is strongly dependent on the assumptions made about
X(CO) in these systems. When a Galactic X(CO) conversion is applied, the high-redshift galaxies tend to fall
roughly on the upper parts of the Schmidt law seen locally (e.g., Figure 11). However if a lower X(CO) factor
is applied to the most compact starburst and submillimeter galaxies (SMGs), as suggested by many independent
analyses of X(CO) (§2.4), the Schmidt relations shift
leftwards by the same factor, forming a parallel relation
(Daddi et al. 2010; Genzel et al. 2010).
Taken at face value, these results suggest the presence of two distinct modes of star formation with differ-
Kennicutt and Evans
ent global efficiencies, which separate the extended starforming disks of normal galaxies from those in the densest
circumnuclear starbursts; this distinction is likely to be
present both in the present-day Universe and at early cosmic epochs. This inferred bimodality, however, is a direct
consequence of the assumption of two discrete values for
X(CO) in the two modes. A change in the interpretation
of CO emission is certainly plausible when the derived
molecular surface density is similar to that of an individual cloud (Σmol > 100 M⊙ pc−2 ), but the behavior of
X(CO) may be complex (§2.4). Variation of X(CO) over
a continuous range would indicate a steeper Schmidt law,
rather than a bimodal law (Narayanan et al. 2012).
Daddi et al. (2010) also note that the higher concentration of gas in the ULIRGs/SMGs is consistent with an enhanced fraction of dense gas and the dense gas relations
of Gao & Solomon (2004). However, the star formation
rate also appears to be larger for a given mass of dense
gas in extreme starbursts (Garcı́a-Burillo et al. 2012 and
references therein), especially when a lower value of αHCN
is used. As with CO, one can interpret these as bimodal
relations or as steeper than linear dependences on the
gas tracer lines. These results, together with evidence
for lower SFR per mass of dense gas in the CMZ of the
MW (§5.1) warn against an overly simplistic picture of
dense clumps as the linear building blocks for massive
star formation, with no other variables in the picture.
The correlations between SFR and gas surface densities (and masses) are not the only scaling laws that are
observed. Kennicutt (1998b) pointed out that the SFR
surface densities also correlate tightly with the ratio of
the gas surface density to the local dynamical time, defined in that case to be the average orbit time. This prescription is especially useful for numerical simulations
and semi-analytical models of galaxy evolution. Interestingly, Daddi et al. (2010) and Genzel et al. (2010)
found that the bifurcation of Schmidt laws between normal galaxies and ULIRGs/SMGs described above does
not arise in the dynamical form of this relation.
Blitz & Rosolowsky (2006) have discovered another
strong scaling relation between the ratio of molecular to
atomic hydrogen in disks and the local hydrostatic pressure. The relation extends over nearly three orders of
magnitude in pressure and H2 /H I ratio and is nearly linear (slope = 0.92). Technically speaking this scaling relation only applies to the phase balance of cold gas rather
than the SFR, but it can be recast into a predicted star
formation law if assumptions are made about the scaling between the SFR and the molecular gas components
(e.g., Blitz & Rosolowsky 2006; Leroy et al. 2008). Recent work by Ostriker et al. (2010) and Ostriker & Shetty
(2011) provides a theoretical explanation for these relations.
Finally, a number of workers have explored the scaling between SFR surface density and a combination of
gas and stellar surface densities. For example Dopita
(1985) and Dopita & Ryder (1994) proposed a scaling
between the SFR density and the product of gaseous
and stellar surface densities; the latter scales with the
disk hydrostatic pressure and hence bears some relation
to the picture of Blitz & Rosolowsky (2006). More recently Shi et al. (2011) show that the scatter in the star
formation law is minimized with a relation of the form
ΣSF R ∝ Σgas Σ0.5
∗ .
Determining which of these different formulations of
the star formation law is physical and which are mere
consequences of a more fundamental relation is difficult
to determine from observations alone. Some of the degeneracies between these various relations can be understood
if most gas disks lie near the limit of gravitational stability (Q ∼ 1; Kennicutt 1989), and the critical column
densities for the formation of cold gas phase, molecule
formation, and gravitational instability lie close to each
other (e.g., Elmegreen & Parravano 1994; Schaye 2004).
In such conditions it can be especially difficult to identify
which physical process is most important from observations. We return to this topic later.
We conclude this section by mentioning that there are
other SFR scaling laws that can be understood as arising from an underlying Schmidt law. The best known of
these is a strong correlation between characteristic dust
attenuation in a star-forming galaxy and the SFR itself,
with the consequence that galaxies with the highest absolute SFRs are nearly all dusty infrared-luminous and ultraluminous galaxies (e.g., Wang & Heckman 1996; Martin et al. 2005b; Bothwell et al. 2011). This opacity versus SFR relation is partly a manifestation of the Schmidt
law, because we now know that the most intense star
formation in galaxies takes place in regions with abnormally high gas surface densities, and thus also in regions
with abnormally high dust surface densities. The other
factor underlying the SFR versus opacity correlation is
the prevalence of highly concentrated circumnuclear star
formation in the most intense starbursts observed in the
present-day universe (§5.3); this may not necessarily be
the case for starburst galaxies at early cosmic epochs.
6.2. Radial Distributions of Star Formation and Gas
Over the past few years major progress has been
made in characterizing the spatially-resolved star formation law within individual galaxies. This work has
been enabled by large multi-wavelength surveys of nearby
galaxies such as the Spitzer Infrared Nearby Galaxies
Survey (SINGS) (Kennicutt et al. 2003), the GALEX
Nearby Galaxies Survey (Gil de Paz et al. 2007), the
Spitzer/GALEX Local Volume Legacy survey (LVL;
Dale et al. 2009; Lee et al. 2011), and the Herschel
KINGFISH Survey (Kennicutt et al. 2011). The resulting datasets provide the means to measure spatiallyresolved and dust-corrected SFRs across a wide range
of galaxy properties (§3). These surveys in turn have
led to large spinoff surveys in H I (e.g., THINGS, Walter et al. 2008; FIGGS, Begum et al. 2008; Local Volume H I Survey; Koribalski 2010; LITTLE THINGS,
Hunter et al. 2007) and in CO (e.g., BIMA-SONG, Helfer
et al. 2003; IRAM HERACLES, Leroy et al. 2009; JCMT
NGLS, Wilson et al. 2009; CARMA/NRO Survey, Koda
& Nearby Galaxies CO Survey Group 2009; CARMA
STING, Rahman et al. 2011, 2012).
The capabilities of these new datasets are illustrated in
Figure 6, which shows Spitzer 24 µm, Hα, VLA H I, and
CO (in this case from HERACLES) maps of NGC 6946
(see Figure 7 for the corresponding radial distributions
of gas and star formation).
The first step in exploiting the spatial resolution of the
new observations is to analyze the azimuthally-averaged
radial profiles of the SFR and gas components (as illustrated for example in Figure 7) and the resulting SFR
Star Formation
versus gas surface density correlations. This approach
has the advantage of spatially averaging over large physical areas, which helps to avoid the systematic effects
that are introduced on smaller spatial scales (§3.9). Radial profiles also have limitations arising from the fact
that a single radial point represents an average over subregions with often wildly varying local gas and SFR densities, and changes in other radially varying physical parameters may be embedded in the derived SFR versus
gas density relations.
Large-scale analyses of the star formation law derived
in this way have been carried out by numerous authors
(e.g., Kennicutt 1989; Martin & Kennicutt 2001; Wong
& Blitz 2002; Boissier et al. 2003; Heyer et al. 2004; Komugi et al. 2005; Schuster et al. 2007; Leroy et al. 2008;
Schruba et al. 2011; Gratier et al. 2010). A strong correlation between SFR and gas surface density is seen in
nearly all cases, with a non-linear slope when plotted in
terms of total (atomic+molecular) density. The best fitting indices N vary widely, however, ranging from 1.4–3.1
for the dependence on total gas density and 1.0–1.4 for
the dependence on molecular gas surface density alone
(for constant X(CO)). The measurements of the MW
range from N = 1.2 ± 0.2, when only molecular gas is
used (Luna et al. 2006), to 2.18±0.20 when total (atomic
and molecular) gas is used (Misiriotis et al. 2006).
Some of the differences between these results can be
attributed to different schemes for treating dust attenuation, different CO line tracers, different metallicities
(which may influence the choice of X(CO)), and different
fitting methods. The influence of a metallicity-dependent
X(CO) factor is investigated explicitly by Boissier et al.
(2003). Since any variation in X(CO) is likely to flatten the radial molecular density profiles, a variable conversion factor tends to steepen the slope of the derived
Schmidt law; for the prescription they use, the best fitting slope can increase to as high as N = 2.1 − 3.6,
underscoring once again the critical role that assumptions about X(CO) play in the empirical determination
of the star formation law. Despite these differences in
methodology, real physical variation in the SFR versus
gas density relation on these scales cannot be ruled out.
This body of work also confirms the presence of a
turnover or threshold in the star formation relation at
low surface densities in many galaxies. Early work on
this problem (e.g., Kennicutt 1989; Martin & Kennicutt
2001; Boissier et al. 2003) was based on radial profiles in
Hα, and some questions have been raised about whether
these thresholds resulted from breakdowns in the SFR
versus Hα calibration in low surface brightness regimes,
as opposed to real thresholds in the SFR. Subsequent
comparisons of UV and Hα profiles appear to confirm
the presence of radial turnovers in the SFR in most disks,
however, even in cases where lower levels of star formation persist to much larger radii (e.g., Thilker et al. 2007;
Christlein et al. 2010; Goddard et al. 2010). This extended star formation can be seen in Figure 7 (R > 7 − 8
kpc). Recent studies of nearby galaxies with unusually
extended XUV disks also show that the UV-based SFR
falls off much more rapidly than the cold gas surface density, with global star formation efficiencies (ǫ′ ) an order
of magnitude or more lower than those in the inner disks
(Bigiel et al. 2010). Taken together, these recent results
and studies of the outer MW (§5.1) confirm the presence
of a pronounced turnover in the Schmidt law for total
gas at surface densities of order a few M⊙ pc−2 (Figure
6.3. The Star Formation Law on Sub-Kiloparsec Scales
The same multi-wavelength data can be used in principle to extend this approach to point-by-point studies
of the star formation law. The angular resolution of the
currently available datasets (optical/UV, mid-far IR, H I,
CO) allows for extending this analysis down to angular
scales of ∼10′′ , which corresponds to linear scales of 30–
50 pc in the Local group and 200–1000 pc for the galaxies
in the local supercluster targeted by SINGS, THINGS,
KINGFISH, and similar surveys. Recent analyses have
become available (Kennicutt et al. 2007; Bigiel et al.
2008, 2010, 2011; Leroy et al. 2008; Blanc et al. 2009;
Eales et al. 2010; Verley et al. 2010; Liu et al. 2011; Rahman et al. 2011, 2012; Schruba et al. 2011), and several
other major studies are ongoing.
The most comprehensive attack on this problem to
date is based on a combination of SINGS, THINGS, and
HERACLES observations (papers above by Bigiel, Leroy,
and Schruba), and Figure 12, taken from Bigiel et al.
(2008), nicely encapsulates the main results from this
series of studies. The colored regions are the loci of individual sub-kiloparsec measurements of SFR surface densities (measured from a combination of FUV and 24 µm
infrared fluxes) and total gas densities (H I plus H2 from
CO(2–1) with a constant X(CO) factor), for 18 galaxies
in the SINGS/THINGS sample. Other data (including
Kennicutt 1998b) are overplotted as described in the figure legend and caption. The measurements show at least
two distinct regimes, a low-density sub-threshold regime
where the dependence of the SFR density on gas density
is very steep (or uncorrelated with gas density), and a
higher density regime where the SFR is strongly correlated with the gas density. The general character of this
relation, with a high-density power law and a low-density
threshold confirms most of the results presented earlier.
One can also examine separately the dependence of the
SFR density on the atomic and molecular surface densities and the two relations are entirely different. The local
SFR density is virtually uncorrelated with H I density, in
part because the range of H I column densities is truncated above ΣHI ∼ 10 M⊙ pc−2 or N (H I) ∼ 1021 cm−2 .
This upper limit to the local H I densities corresponds to
the column density where the H I efficiently converts to
molecular form. This phase transition also roughly coincides with the turnover in the SFRs in Figure 12, which
hints that the SFR threshold itself may be driven in part,
if not entirely, by an atomic–molecular phase transition
(see §7).
In contrast to the H I, the SFR surface density is
tightly correlated with the H2 surface density, as inferred
from CO. A recent stacking analysis of the HERACLES
CO maps made it possible to statistically extend this
comparison to low H2 column densities, and it shows
a tight correlation between SFR and CO surface brightness that extends into the H I-dominated (sub-threshold)
regime (Schruba et al. 2011), reminiscent of studies in the
outer MW (Fig. 7, §5.1).
The strong local correlation between Σ(SFR) and Σmol
is seen in all of the recent studies which probe linear
scales of ∼200 pc and larger. This is hardly surpris-
Kennicutt and Evans
ing, given the strong coupling of star formation to dense
molecular gas in local clouds (§4, §6.4). However, on
smaller linear scales the measurements show increased
scatter for reasons discussed in §3.9. On these scales we
expect the scaling laws to break down, as the stars and
gas may arise from separate regions; this effect has been
directly observed in high-resolution observations of M33
(Onodera et al. 2010).
The main results described above – the presence of
a power-law SFR relation with a low-density threshold,
the lack of correlation of the local SFR with H I column
density, the strong correlation with H2 column density,
and the rapidly increasing scatter in the Schmidt law
on linear scales below 100–200 pc – are seen consistently
across most, if not all, recent spatially-resolved studies.
Most of the recent studies also derive a mildly non-linear
slope to the SFR density versus total gas density Schmidt
law in the high-density regime, with indices N falling
in the range 1.2–1.6. Less clear from the recent work
is the linearity and slope of the Schmidt law on small
scales, especially the dependence of SFR surface density
on molecular gas surface density. The results from the
HERACLES/THINGS studies have consistently shown
a roughly linear ΣSF R versus Σmol relation (N = 1.0–
1.1), and similar results have been reported by Blanc
et al. (2009), Eales et al. (2010), and Rahman et al.
(2012). Other authors however have reported steeper
dependences (N = 1.2–1.7), closer to those seen in integrated measurements (e.g., Kennicutt et al. 2007; Verley
et al. 2010; Rahman et al. 2011; Liu et al. 2011; Momose
2012). The discrepancies between these results are much
larger than the estimated fitting errors, and probably
arise in part from systematic differences in the observations and in the way the data are analyzed (see discussion
in e.g., Blanc et al. 2009). One effect which appears to be
quite important is the way in which background diffuse
emission is treated in measuring the local SFRs (§3.9).
Liu et al. (2011) show that they can produce either a linear or non-linear local molecular SFR law depending on
whether or not the diffuse emission is removed. Another
CARMA-based study by Rahman et al. (2011), however,
suggests that the effects of diffuse emission may not be
sufficient to account for all of the differences between different analyses. Another important factor may be the excitation of the CO tracer used (e.g., Juneau et al. 2009).
It is important to bear in mind that nearly all of our
empirical knowledge of the form of the local star formation law is based on observations of massive gas-rich spiral galaxies with near-solar gas-phase metal abundances.
Most studies of the star formation relations in metal-poor
dwarf galaxies have been limited to H I data or marginal
detections in CO at best (e.g., Bigiel et al. 2008). A
recent study of the SMC (∼ 1/5 Z⊙) by Bolatto et al.
(2011) offers clues to how these results may change in
low-metallicity environments. They find that the atomicdominated threshold regime extends up to surface densities that are an order of magnitude higher than in spirals.
6.4. Local Measurements of Star Formation Relations
With the ongoing large-scale surveys of the Galaxy and
the Magellanic Clouds in recent years it is becoming possible to investigate star formation rate indicators, the
scaling laws, and other star formation relations for local
samples. These can provide valuable external checks on
the methods applied on larger scales to external galaxies and probe the star formation relations on physical
scales that are not yet accessible for other galaxies. Local
studies of the conversion of CO observations into column
density or mass were discussed in §2.4.
Comparison of various star formation rate indicators
for the MW (§5.1), as would be used by observers in
another galaxy, against more direct measures, such as
young star counts, suggests that star formation rates
based on the usual prescriptions (mid-infrared and radio continuum) may be underestimating absolute Ṁ∗
by factors of 2-3 (Chomiuk & Povich 2011). The authors suggest that changes to the intermediate mass IMF,
timescale issues, models for O stars, and stochastic sampling of the upper IMF can contribute to the discrepancy. As discussed earlier, measures of star formation
rate that use ionizing photons (Hα or radio continuum)
require regions with a fully populated IMF to be reliable, and they systematically underestimate the SFR in
small star-forming clouds (§3.9). For example, star formation in clouds near the Sun would be totally invisible
to these measures and the star formation rate would be
badly underestimated in the Orion cluster (§3.9). Tests
of other star formation rate tracers, such as 24 µm emission, within the Milky Way would be useful. Changes
in the IMF as large as those proposed by Chomiuk &
Povich (2011) should also be readily observable in more
evolved Galactic star clusters, if not in the field star IMF
Using a YSO-counting method for five GMCs in the
N159 and N44 regions in the LMC, Chen et al. (2010)
were able to reach stellar masses of about 8 M⊙ , below
which they needed to extrapolate. The resulting ratios
of Ṁ∗ (YSOs) to Ṁ∗ (Hα + 24µm) ranged from 0.37 to
11.6, with a mean of 3.5.
Recent studies have begun to probe the form of the
star formation relations on scales of clouds and clumps.
Using the YSO star counting method to get Ṁ∗ and extinction maps to get mean mass surface density of individual, nearby clouds, Evans et al. (2009) found that the
local clouds all lay well above the K98 relation. Taken
in aggregate, using the mean Σgas , they lay a factor of
20 above the Kennicutt et al. (1998b) relation and even
farther above the relation of Bigiel et al. (2008).
Subsequent studies show evidence for both a surface
density threshold for star-forming clumps and a Σ(SFR)Σmol relation in this high-density sub-cloud regime. Lada
et al. (2010) found a threshold surface density for efficient
star formation in nearby clouds; the star formation rate
per cloud mass scatters widely (Fig. 13), but is linearly
proportional to the cloud mass above a surface density
contour of 116 ± 28 M⊙ pc−2 (Fig. 14), and the coefficient agrees well with the dense gas relations of Gao
& Solomon (2004). Heiderman et al. (2010) studied the
behavior of Σ(SFR) on smaller scales using contours of
extinction. They limited the YSOs to Class I and Flat
SED objects to ensure that they were still closely related
to their surrounding gas and found a steep increase in
Σ(SFR) with increasing Σgas up to about 130 M⊙ pc−2 ,
above which a turnover was suggested. By adding the
dense clumps data from Wu et al. (2010a), they identified a turnover at 129 ± 14 M⊙ pc−2 , where the Σ(SFR)
began to match the dense gas relation, but was far above
Star Formation
the K98 relation for total gas (Figure 15). The agreement
between these two independent approaches is encouraging, suggesting that a contour of about 125 M⊙ pc−2
is a reasonable defining level for a star-forming clump
(§2.2). Other studies have found similar thresholds for
efficient star formation or the presence of dense cores
(Onishi et al. 1998; Enoch et al. 2007; Johnstone et al.
2004; André et al. 2010; Li et al. 1997; Lada 1992). Theoretical explanations for such thresholds can be found
by considering magnetic support (Mouschovias & Spitzer
1976) or regulation by photo-ionization (McKee 1989).
Alternatively, this threshold may simply correspond to
the part of the cloud that is gravitationally bound (cf.
The star formation rate density is even higher within
clumps. Gutermuth et al. (2011) find a continuation of
the steep increase in Σ(SFR) to higher Σgas in a study
including embedded clusters. They find that Σ(SFR) ∝
Σgas 2 up to several 100 M⊙ pc−2 , with no evidence of a
threshold. Near the centers of some centrally condensed
clumps, Σgas reaches 1 gm cm−2 , or about 4800 M⊙ pc−2
(Wu et al. 2010a), a threshold for the formation of massive stars suggested by theoretical analysis (Krumholz &
McKee 2008).
Other studies have identified possible scaling relations
in which SFR surface densities are not simply proportional to surface densities of dense gas. One analysis
found that clouds forming stars with masses over 10 M⊙
satisfied the following relation: m(r) ≥ 870M⊙(r/pc)1.33
(Kauffmann et al. 2010; Kauffmann & Pillai 2010), where
m(r) is the enclosed mass as a function of radius. This
is essentially a criterion they call “compactness”; it can
be thought of as requiring a central condensation, with
ρ(r) ∝ rp , with p ≥ 1.67.
Dunham et al. (2011b) have compared a subset of
clumps in the BGPS catalog (Aguirre et al. 2011;
Rosolowsky et al. 2010) with kinematic distances to the
Heiderman-Lada (HL) criterion for efficient star formation and to the Kauffman-Pillai (KP) criterion for massive star formation. About half the clumps satisfy both
criteria. Interestingly, Dunham et al. (2011a) found that
about half the BGPS sample contained at least one midinfrared source from the GLIMPSE survey. For the
clumps most securely identified with star formation, 70%
to 80% satisfy the HL or KP criteria.
All these studies consistently show that Σ(SFR), especially for massive stars, is strongly localized to dense gas,
and is much higher (for Σgas > 100 M⊙ pc−2 ) than in the
extragalactic Schmidt relations (Kennicutt 1998b; Bigiel
et al. 2008). This offset between the extragalactic and
dense clump “Schmidt laws” can be straightforwardly
understood as reflecting the mass fraction (or surface filling factor) of dense clumps in the star-forming ISM. If
most or all star formation takes place in dense clumps,
but the clumps contain only a small fraction of the total
molecular gas, we would expect the characteristic star
formation tdep measured for clumps to be proportionally shorter than tdep of the total cloud mass and the
efficiency (ǫ) to be higher. Using a threshold of C18 O
emission to define clumps, Higuchi et al. (2009) found
that the star formation efficiency (ǫ) in clumps varies
widely but averages 10%, about 4 times that in clouds
as a whole (§4.1). If this interpretation is correct, we
would also expect the relations between SFR and dense
gas mass for galaxies (Gao-Solomon relation) to be similar for galaxies and the clumps, and they indeed appear
to be roughly consistent (Wu et al. 2005b).
This conclusion is subject to some caveats, however. Various authors (Krumholz & Thompson 2007;
Narayanan et al. 2008; Juneau et al. 2009) have pointed
out that lines like those of HCN J = 1 → 0 are not thermalized at lower densities, so can result in a linear relation even if the underlying star formation relation is
a local version of a non-linear KS law that extends to
much lower densities. The SFR vs dense gas relation is
based on a correlation between total FIR and HCN luminosities, and LF IR is likely to underestimate the SFR
in young clusters (Urban et al. 2010; Gutermuth et al.
2011; Krumholz & Thompson 2007), perhaps by up to
factors of 3–30. However, Lada et al. (2012) find a similar continuity between the Gao-Solomon starbursts and
SFRs measured by counting YSOs in gas above a threshold surface density.
7.1. Summary: Clues from Observations
Before we embark on an interpretation of the observed
star formation law, it is useful to collect the main conclusions which can be drawn from the observations of star
formation both outside and inside the Galaxy.
Beginning on the galactic scale (> 1 kpc), we can identify at least two and probably three distinct star formation regimes (Table 3). Whole galaxies may lie in one
of these regimes, but a single galaxy may include two or
three regimes.
7.1.1. The Low-density Regime
The lowest-density regime (sometimes referred to as
the sub-threshold regime), is most readily observed in
the outer disks of spiral galaxies, but it also can be
found in the interarm regions of some spiral galaxies and
throughout the disks of some gas-poor galaxies. The solar neighborhood lies near the upper end of this lowdensity regime and the outer disk of the MW is clearly
in this regime (§5.1).
The cold gas in these regions is predominantly atomic,
though local concentrations of molecular gas are often
found. Star formation is highly dispersed, with young
clusters and H II regions only observed in regions of unusually high cold gas densities. The global “efficiency” of
star formation, ǫ′ (defined in §1.2), or Σ(SFR)/Σgas , is
very low, and it is uncorrelated with Σgas . The steep,
nearly vertical “Schmidt” relation seen in this regime
(e.g., Fig. 12) mainly reflects lack of correlation over a
region where the SFR has a much larger dynamic range
than the local gas density; any apparent correlation is not
physical. Recent stacking analysis of CO maps and studies of the outer MW suggest, however, that there may be
a strong correlation with molecular surface density (§6,
Schruba et al. 2011).
7.1.2. The Intermediate-density Regime
The next, intermediate-density regime is roughly characterized by average gas surface densities of Σgas > 10
M⊙ pc−2 , corresponding roughly to N (H) ∼ 1021 cm−2 ,
or AV ∼ 1 mag, for solar metallicity. The upper limit
Kennicutt and Evans
to this regime is about Σgas ∼ 100 − 300 M⊙ pc−2 , as
discussed in the next section. The intermediate regime
applies within the main optical radii (R25 ) of most gasrich, late-type spiral and irregular galaxies. The “Galactic Ring” region of the Milky Way lies at the low end of
this regime, while the CMZ may lie near the high end
The transition from the low-density regime roughly
corresponds to the transition between H I-dominated and
H2 -dominated ISMs. Above Σgas = 10 M⊙ pc−2 , both
the phase balance of the ISM and the form of the star
formation law begin to change. The intermediate range
features an increasing filling factor of molecular clouds,
and star formation becomes more pervasive. The SFR
surface density is strongly and tightly correlated with
the cold gas surface density, whether expressed in terms
of the total (atomic plus molecular) or only the molecular
surface density. In most massive spiral galaxies, the cold
gas in this regime is molecular-dominated. In low-mass
and irregular galaxies, atomic gas can dominate, though
this is somewhat dependent on the value of X(CO) that
is assumed. The characteristic depletion time (tdep §1.2)
for the interstellar gas is 1–2 Gyr (e.g., Bigiel et al. 2011).
When expressed in terms of ǫ′ (§1.2), the star formation rate per unit total gas mass, nearly all studies suggest that ǫ′ increases with gas surface density, with an
exponent of 0.2−0.5, (the Schmidt law exponent, N −1).
When measured against molecular mass (or surface density), some studies suggest ǫ′ is constant, but others suggest ǫ′ increasing systematically with surface density.
7.1.3. The High-density Regime
The two regimes discussed above were able to reproduce all of the early observations of the large-scale star
formation law by Kennicutt (1989, 1998b) and Martin
& Kennicutt (2001). However a number of recent observations suggest the presence of a third regime (and
second transition) around Σgas > 100 − 300 M⊙ pc−2 ,
into what one might call the high-density, or starburst,
regime. Around this value of Σgas , the interpretation of
I(CO) is likely to change (§2.4), and studies of local MW
clouds indicate that a similar Σgas value may correspond
to the theoretical notion of a cluster-forming clump, in
which the SFR is much higher than in the rest of the
cloud (§6.4). In the most extreme starburst galaxy environments, if standard values of X(CO) are used, the
average surface densities of gas (virtually all molecular)
reach 1000 to 104 M⊙ pc−2 , and the volume filling factor
of clumps could reach unity (Wu et al. 2009). While the
interpretation of molecular emission in these conditions
warrants skepticism (§2.4, Garcı́a-Burillo et al. 2012), the
highest inferred surface density also corresponds to the
densest parts of cluster forming clumps and the theoretical threshold of 1 gm cm−2 for efficient formation of
massive stars (§4.3).
Some recent observations strongly hint at the existence
of such a transition. As discussed in §6, luminous and ultraluminous starburst galaxies (and high-redshift SMGs)
have characteristic ratios of LIR /L(CO) that are as much
as 1–2 orders of magnitude higher than in normal galaxies, implying that at some point the SFR per molecular mass must increase dramatically. This could be explained by a break in the slope of the Schmidt law at
high densities, a continuous non-linear Schmidt law slope
extending from the intermediate to high-density regimes,
or a second mode of star formation in extreme starbursts
with much higher “efficiency” (ǫ′ ). As discussed in §6.3,
the constancy of the molecular ǫ′ at intermediate surface densities is uncertain. Observations of CO in highredshift galaxies have been interpreted in terms of just
such a bimodal Schmidt law (Daddi et al. 2010; Genzel
et al. 2010). This interpretation rests on the assumption
of a bimodality in X(CO) (§6.1), and a change in ǫ′ that
follows these changes in X(CO); this is not entirely implausible, because the same physical changes in the ISM
environment in the densest starbursts could affect both
the CO conversion factor and ǫ′ if an increasing fraction
of the gas is in dense clumps.
Both a Galactic value of X(CO) in the starbursts and
a much lower value have their discomforting aspects. Applying a Galactic conversion factor produces total molecular masses which often exceed dynamical mass limits for
the regions, whereas adopting values of X(CO) which are
factors of several lower produces gas consumption times
as short as 10 Myr (Daddi et al. 2010; Genzel et al. 2010),
with implications for the triggering and duty cycles of
these massive starbursts.
The relations between SFR and ISM properties summarized above strictly refer to the correlations with the
total cold gas surface density or in some cases the total
H I and total H2 densities; these are the relations of most
interest for applications to galaxy modelling and cosmology. However the observational picture is quite different when we correlate the SFR with the supply of dense
gas, as traced by HCN J = 1 → 0 and other dense clump
tracers. Here there seems to be a single linear relation
which extends across all of the SFR regimes described
above, and which even extends to star-forming clouds in
the Milky Way (Gao & Solomon 2004; Wu et al. 2005b;
Gao et al. 2007; Lada et al. 2012), However, there is
still some evidence of bimodality even if tracers of dense
gas are used (Garcı́a-Burillo et al. 2012), and physically
based models, rather than simple conversion factors, are
7.1.4. Clues from Studies of Molecular Clouds
The biggest hurdle one confronts when attempting to
interpret these observations of galaxies is the severe influences of spatial averaging, both across the sky and
along the line of sight. The star formation law relates
surface densities of young stars and interstellar gas– already smoothed along the line of sight– averaged over
linear dimensions ranging from order 100 pc to 50 kpc.
These are 2–4 orders of magnitude larger than the sizes of
the dense clump regions in which most stars form, and 4–
8 orders of magnitude larger in terms of the surface areas
being measured. This difference in scales means that the
“surface densities” measured in extragalactic studies are
really characterizing the filling factors of gas clumps and
star-forming regions, rather than any measure of physical
densities. Understanding how this “active component” of
the star-forming ISM works is essential to even an empirical understanding of large-scale star formation, much
less understanding its underlying physics. Detailed studies within the MW provide a way to “zoom in” further
than is possible for other galaxies.
A common observed feature across all of the density
Star Formation
regimes observed in galaxies is that star formation takes
place in molecular clouds. In the lowest-density regimes,
clouds are rare and widely separated, but within individual molecular clouds in the MW, which can be probed in
detail, the star formation seems to be indistinguishable
from that in regions of somewhat higher average surface
density (§5.1).
These observations also reveal that nearly all star formation within molecular clouds is highly localized, taking place in clumps, roughly defined by Σmol > 125
M⊙ pc−2 , or n > 104 cm−3 (§6.4). The clumps host
young stars, YSOs, and pre-stellar cores, the sites of individual star formation. This scale is as close to a deterministic environment for star formation as can be found.
Once a pre-stellar core reaches substantial central condensation, about one-third of its mass will subsequently
turn into young stars within a few Myr (Alves et al. 2007;
Enoch et al. 2008). The relatively low global efficiencies
(both ǫ and ǫ′ ) within GMCs are largely a reflection of
the low mass fraction in clumps and cores (§4.1). The
star formation rate surface density in the clumps is 2040 times that predicted for the mass surface density from
the extragalactic Schmidt relation (§6.4), and this likewise can be largely understood as reflecting the low mass
fraction of molecular gas in clumps and cores.
One might be tempted to identify the dense clumps
within molecular clouds as a possible fourth density
regime, in addition to the three regimes already discussed
from observations of galaxies. However this would be
very misleading, because so far as is currently known
the formation of most stars in dense clumps is a common feature of star formation across all of the ISM environments in galaxies, extending from low-density subthreshold disks to the most intense starbursts. The dense
clump may well be the fundamental unit of massive, clustered star formation (Wu et al. 2005b). If this picture is
correct, then the three regimes identified in galaxies and
the order-of-magnitude increases in gas-to-star formation
conversion rate across them must reflect changes in the
fraction of the ISM that is converted to dense clumps,
approaching 100% in the densest and most intense starbursts.
7.2. Some Speculations
The observations summarized in this review have stimulated a rich literature of theoretical ideas, models, and
simulations aimed at explaining the observed star formation relations and constructing a coherent picture of
galactic-scale star formation. Unfortunately we have neither the space nor the expertise to review that large body
of theoretical work here. A review of many of the theoretical ideas can be found in McKee & Ostriker (2007),
and an informative summary of the main models in the
literature up to 2008 can be found in Leroy et al. (2008).
Here we offer some speculations aimed toward explaining the observations and connecting the extragalactic and
MW studies, and identifying directions for future work.
Many of these speculations reflect ideas being discussed
in the literature, and we make no claims for originality
in the underlying concepts.
As mentioned in the introduction, the formation of
stars represents the endpoint of a chain of physical processes that begins with cooling and infall of gas from
the intergalactic medium onto disks, followed by the for-
mation of a cool atomic phase, contraction to gravitationally bound clouds, the formation of molecules and
molecular clouds, the formation of dense clumps within
those molecular clouds, and ultimately the formation of
pre-stellar cores, stars, and star clusters. Although the
beginning and end points of this process are relatively
clear, the sequence of intermediate steps, in particular
the respective roles of forming cool atomic gas, molecular
gas, and bound clouds is unclear, and it is possible that
different processes dominate in different galactic environments. By the same token, a variety of astrophysical
time scales may be relevant: e.g., the free-fall time of the
gas within clouds, the crossing time for a cloud, the freefall time of the gas layer, or the dynamical time scales for
the disc and spiral arm passages. Any of these timescales
may be invoked for setting the time scale for star formation and the form of the star formation law. However
one can construct two scenarios to explain the observations outlined in §7.1, which illustrate the boundaries
of fully locally-driven versus globally-driven approaches.
In some sense, these approaches are complementary, but
they need to be brought together.
The first approach, which might be called a bottomup picture, assumes that star formation is controlled locally within molecular clouds, (e.g., Krumholz & McKee
2005), building on what we observe in well-studied local regions of star formation. In this picture, one can
identify three distinct regimes (§7.1), and associate the
transitions between them to the crossing of two physically significant thresholds, the threshold for conversion
of atomic to molecular gas, and the threshold for efficient
star formation in a molecular cloud, identified with the
theoretical notion of a clump (§2.2). In the purest form of
this picture the SFR is driven completely by the amount
and structure of the molecular gas. Current evidence
from studies of nearby clouds indicates that the star formation rate scales linearly with the amount of dense gas
in clumps (Lada et al. 2010), and this relation extends to
starburst galaxies if the HCN emission is used as a proxy
for the dense gas (Wu et al. 2005b; Lada et al. 2012). In
this picture, the non-linear slope (N ∼ 1.5) of the global
Schmidt relation would arise from either a decrease in
the characteristic timescale (Krumholz et al. 2012) or
by an increase in the fraction of gas above the clump
threshold (fdense ), from its typical value in local clouds
[fdense ∼ 0.1 (Lada et al. 2012)] with fdense ∝ Σgas 0.5 .
The second approach, which we could call a top-down
picture, assumes that star formation is largely controlled
by global dynamical phenomena, such as disk instabilities (e.g., Silk 1997), and the dynamical timescales in
the parent galaxy. In this picture the transition between the low-density and higher-density SFR regimes
is mainly driven by gravitational instabilities in the disk
rather than by cooling or molecular formation thresholds, and the non-linear increase in the SFR relative
to gas density above this threshold reflects shorter selfgravitational timescales at higher density or the shorter
dynamical timescales. In this picture there is no particular physical distinction between the intermediate-density
and high-density regimes; in principle the same dynamical processes can regulate the SFR continuously across
this wide surface density regime. Likewise it is the total
surface density of gas, whether it be atomic or molecular,
Kennicutt and Evans
that drives the SFR. The asymptotic form of this picture
is a self-regulated star formation model: the disk adjusts
to an equilibrium in which feedback from massive star
formation acts to balance the hydrostatic pressure of the
disk or to produce an equilibrium porosity of the ISM
(e.g., Cox 1981; Dopita 1985; Silk 1997; Ostriker et al.
When comparing these pictures to the observations,
each has its particular set of attractions and challenges.
The bottom-up picture has the attraction of simplicity, associating nearly all of the relevant SFR physics
with the formation of molecular gas and molecular cloud
clumps. It naturally fits with a wide range of observations including the tight correlation of of the SFR and
molecular gas surface densities (e.g., Schruba et al. 2011
and references therein), the concentration of star formation within clouds in regions of dense gas (§4), and the
observation of a linear relation between the dense gas
traced by HCN emission and the total SFR in galaxies
(§6). If the resolved star formation relation at intermediate surface densities is linear (§6, Bigiel et al. 2008),
fdense would be constant in that regime, while increasing
monotonically with Σgas in the higher-density starburst
regime with the transition occuring where Σgas derived
from CO is similar to the threshold for dense gas. This
picture does not explain why a particular galaxy or part
of a galaxy lies in one of these regimes, a question perhaps best answered by the top-down picture.
Aspects of the top-down picture date back to early
dynamical models of the ISM and the first observations
of star formation thresholds in disks (e.g., Quirk & Tinsley 1973; Larson 1987; Zasov & Stmakov 1988; Kennicutt
1989; Elmegreen 1991; Silk 1997). There is some observational evidence for associating the observed low-density
thresholds in disks with gravitational instabilities in the
disk (e.g., Q instabilities), rather than with atomic or
molecular phase transitions (e.g., Kennicutt 1989; Martin
& Kennicutt 2001), but recent observations and theoretical analyses have raised questions about this interpretation (e.g., Schaye 2004; Leroy et al. 2008). At higher surface densities the global relation between Σ(SFR) and the
ratio of gas density to local dynamical time (Σgas /τdyn )
shows a correlation that is nearly as tight as the conventional Schmidt law (Kennicutt 1998b), and it also removes the double sequence of disks and starbursts that
results if X(CO) is systematically lower in the starbursts
(§6, Daddi et al. 2010; Genzel et al. 2010). In this picture, the higher star formation rate for a given gas surface
density in mergers is caused by the compaction of the gas
and the resulting shorter rotation period. However, the
efficiency per orbital period is not clearly explained in
this picture. Theories of feedback-regulated star formation show promise in explaining the low efficiency per
orbit in normal galaxies (Kim et al. 2011), and they may
also explain the less effective role of negative feedback in
merger-driven starbursts (e.g., Ostriker & Shetty 2011).
This model does not extend to cloud-level star formation.
If feedback from massive stars is fundamental, the similarity between the efficiency in local clouds forming only
low mass stars and regions with strong feedback from
massive stars (cf. Evans et al. 2009 and Murray 2011)
remains a mystery.
Both of these scenarios can claim some successes, but
neither provides a complete explanation that extends
over all scales and environments. As but one example,
the large changes in the present-day SFRs and past star
formation histories of galaxies as functions of galaxy mass
and type may well be dictated mainly by external influences such as the accretion history of cold gas from
the cosmic web and intergalactic medium. Neither the
bottom-up or top-down pictures as articulated above incorporate these important physical processes. On smaller
scales a complete model for star formation may combine
features of both scenarios. The dynamical picture is quite
attractive on the scales of galaxies, and it would be interesting to extend it to smaller scales. In doing so, the
question of what to use for τdyn arises. The galaxy rotation period cannot control star formation in individual
clouds, so a more local dynamical time is needed. One
option is the cloud or clump crossing time (essentially
the size over the velocity dispersion) (Elmegreen 2000),
which may be particularly relevant in regions of triggered
star formation. Since clumps are the star forming units,
their crossing times may be the more relevant quantities.
A popular option is the free-fall time (e.g., Krumholz
& McKee 2005). Since tf f ∝ ρ−0.5 , a volumetric star
formation law, ρSFR ∝ ρ/tf f ∝ ρ1.5 , where ρ is the gas
density, is a tempting rule. With this rule, the roughly
1.5 power of the KS relation appears to be explained if
we ignore the difference between volume and surface density. Indeed, Krumholz et al. (2012) argue that such a
volumetric law reproduces observations from the scale of
nearby clouds to starburst galaxies. However, the definition of tf f changes for compact starbursts (see eq. 9
in their paper), essentially at the boundary between the
intermediate-density and high-density regimes discussed
in §7.1. Including the atomic-molecular threshold, as
treated in Krumholz et al. (2009b), clarifies that this
“scale-free” picture implicitly recognizes the same three
regimes discussed in §7.1.
Theories that rely on tf f face two problems. First,
no evidence has been found in well-studied molecular
clouds for collapse at tf f (§4.3, e.g., Zuckerman & Evans
1974). To match observations, an “efficiency” of about
0.01 must be inserted. Why the star formation density
should remain proportional to tf f , while being slowed
by a factor of 100, is a challenging theoretical question.
Studies of the role of turbulence show some promise in
explaining this paradox (Krumholz & McKee 2005; Hennebelle & Chabrier 2011), and magnetic fields may yet
play a role.
The second problem is how to calculate a relevant tf f
in a cloud, much less a galaxy, with variations in ρ by
many orders of magnitude, and much of the gas unlikely
to be gravitationally bound. For example, Krumholz
et al. (2012) calculate tf f from the mean density of the
whole cloud (tf f ∝ 1/hρi). A computation of htf f i from
h1/ρi would emphasize the densest gas, where star formation is observed to occur. In a model that accounts for
this, Hennebelle & Chabrier (2011) reproduce at some
level the observations of surface density thresholds for
efficient star formation observed in nearby clouds (Lada
et al. 2010; Heiderman et al. 2010). An alternative view
to the models involving tf f and emphasizing instead the
critical role of the dense gas threshold can be found in
Lada et al. (2012). Because both models claim to apply
to cloud-level star formation, observations of MW clouds
Star Formation
should be able to test them.
7.3. Future Prospects
We hope that this review has conveyed the tremendous
progress over the last decade in understanding the systematic behavior of star formation, both in the MW and
in other galaxies. As often happens when major observational advances are made, observational pictures that
once seemed simple and certain have proven to be more
complex and uncertain. We have attempted to inject a
dose of skepticism about some well-accepted truisms and
to highlight important questions where even the observations do not present a completely consistent picture.
As we return to the key questions outstanding in this
subject (§1.3), a few clear themes emerge, many of which
lie at the cusp between MW and extragalactic observations, and between theory and simulation on the subcloud scale on the one hand, and the galactic and cosmological scales on the other. The recent observations
within the MW of a near-universal association of stars
with dense molecular clumps (§6.4) offers the potential
key of a fundamental sub-unit of high-efficiency star formation in all galactic environments, from the low-density
and quiescent environments of outer disks and dwarf
galaxies to the most intense starbursts. However this hypothesis needs to be validated observationally in a wider
range of environments. Restated from another perspective, we need much better information on the structure
(physical structure, substructure) and dynamics of starforming clouds across the full range of star-forming environments found in galaxies today.
Fortunately we are on the brink of major progress on
multiple fronts. One approach is to assemble more complete and “zoomed-out” views of the MW, while preserving the unparalleled spatial resolution and sensitivity of MW observations to fully characterise the statistical trends in cloud structure, kinematics, mass spectra, and associated star formation for complete, unbiased, and physically diverse samples. In the near-term,
Herschel surveys will deliver images of nearby clouds, the
plane of the MW, and many galaxies in bands from 60 to
500 µm. When the MW plane data are combined with
higher resolution surveys of the MW at 0.87 to 1.1 mm
from ground-based telescopes, spectroscopic follow-up,
and improved distances from ongoing VLBA studies, we
will have a much improved and nuanced picture of the gas
in the MW, which can then provide a more useful template for understanding similar galaxies. Recent surveys
have doubled the number of known H II regions in the
MW (Anderson et al. 2011), allowing study of a wider
range of star formation outcomes. Tests of the limitations on star formation rate tracers used in extragalactic
work will be possible, as will comparisons to KS relations
on a variety of spatial scales. The Magellanic Clouds also
offer great potential for extending this approach to two
sets of environments with different metallicities, ISM environments, and star formation properties (exploiting for
example the 30 Doradus region).
This expanded information from MW surveys will then
need to be combined with more sensitive and “zoomedin” observations of other galaxies. For such studies the
weakest link currently is the knowledge of the molecular
gas. We can trace H I and SFRs to much lower levels than we can detect CO, even with stacking of the
CO maps. When fully commissioned, ALMA will have a
best resolution of about 13 mas at 300 GHz (0.5 pc at
the distance of M51), and about 8 times the total collecting area of any existing millimeter facility, allowing
us to trace molecular emission to deeper levels and/or to
obtain resolution at least 10 times better than the best
current studies. It may be possible to study dense structures within molecular clouds in other galaxies for comparison to dense clumps in the MW clouds. To be most
effective, these programs will need to expand beyond the
typical surveys in one or two CO rotational transitions to
include the high-density molecular tracers and ideally a
ladder of tracers with increasing excitation and/or critical density. Continuum observations will gain even more
because of large bandwidths and atmospheric stability.
Maps of mm-wave dust emission may become the preferred method to trace the gas in other galaxies, as they
are becoming already in the MW, bypassing the issues of
X(CO). Observations of radio recombination lines may
also provide alternative tracers of star formation rate in
highly obscured regions. It is difficult to exaggerate the
potential transformational power of ALMA for this subject.
For molecular line observations of nearby galaxies,
large single dishes (the Nobeyama 45-m, the IRAM 30-m,
and the future CCAT), along with the smaller millimeter arrays, IRAM PdB and CARMA, will provide complementary characterization of the molecular and dense
gas on larger scales than can be efficiently surveyed with
ALMA. A substantial expansion of the IRAM interferometer (NOEMA) will provide complementary advances in
sensitivity in the northern hemisphere. This subject will
also advance with a substantial expansion of H I mapping (by e.g., the EVLA) to expand the range of environments probed and ideally to attain spatial resolutions
comparable to the rapidly improving molecular line observations. Although it is likely that star formation on
the local scale concentrates in molecular-dominated regions, the formation of this molecular gas from atomic
gas remains a critical (and possibly controlling) step in
the entire chain that leads from gas to stars.
Future opportunities also await for improving our measurements of SFRs in galaxies, though the truly transformational phase of that subject may already be passing
with the end of the ISO, Spitzer, GALEX, and Herschel
eras. HST continues to break new ground, especially
in direct mapping of young stars and their ages via resolved color-magnitude diagrams. Herschel surveys of
nearby galaxies will provide far-infrared data, complementary to the other wavelength regions that trace star
formation (§3), and multiband imaging with the EVLA
will allow better separation of non-thermal from the freefree continuum emission, which directly traces the ionization rate and massive SFR. SOFIA offers the opportunity for mapping the brightest regions of star formation
with higher spatial and spectral resolution than Spitzer.
Further into the future, major potential lies with JWST,
which will vastly improve our capabilities for tracing star
formation via infrared radiation, both on smaller scales
in nearby galaxies and in very distant galaxies. SPICA
may provide complementary capability at longer wavelengths. As highlighted in §1.3, key unknowns in this
subject include robust constraints on the ages and lifetimes of star-forming clouds; observations of resolved star
Kennicutt and Evans
clusters, both in the MW and nearby galaxies, offer potential for considerable inroads in this problem.
A number of the questions we have listed also can be
attacked with groundbased OIR observations. As discussed in §3.9, despite the availability now of spatiallyresolved multi-wavelength observations of nearby galaxies, we still do not have an absolutely reliable way to
measure dust-corrected SFRs, especially from short-lived
tracers that are critical for exploring the local Schmidt
law. For observations of normal galaxies where local attenuations are modest, integral-field mapping of galaxies
offers the means to produce high-quality Hα maps corrected for dust using the Balmer decrement (e.g., Blanc
et al. 2009, 2010; Sánchez et al. 2012). A “gold standard” for such measurements also is available in the hydrogen recombination lines of the Paschen and Brackett
series in the near-infrared. The emissivities of these lines
are directly related to ionizing luminosities in the same
way as are the more widely applied Balmer lines (albeit
with somewhat stronger density and temperature dependences), and these lines suffer much lower dust attenuation (readily calibrated by comparing to Hα or other
shorter wavelength lines). These lines are much fainter,
however, and are subject to strong interference from telluric OH emission (and thermal emission at longer wavelengths). Continuing advances in near-infrared detectors
have now brought many of these lines into the accessible
range, and soon we should begin to see large-scale surveys that will provide high-resolution emission maps and
robust “SFR maps”, at least on spatial scales larger than
individual H II regions. These maps in turn can be used
to test and hopefully recalibrate other dust-free tracers
such as combinations of infrared dust emission with UV
and optical emission-line maps. Looking further ahead,
spectral imaging in the near-infrared (and with Hα in
the visible) with massively parallel integral-field spectrometers will provide more precise and full views of star
The current, pioneering studies of star formation at
z ∼ 1 − 3 will become much easier with new instrumentation. Advances in submillimeter array technology
(e.g., SCUBA-2 on the JCMT) and larger dishes at very
high altitude, such as CCAT, will allow deep and wide
searches for dust continuum emission from distant galaxies. Many of the biases in current samples can be alleviated and a more complete picture of star formation
through cosmic time can be constructed. Huge surveys
of Lyα emitting galaxies will be undertaken to constrain
dark energy, providing as a by-product, nearly a million
star-forming galaxies at 1.9 < z < 3.5 and a large number of [OII] emitting galaxies for z < 0.5 (e.g., Hill et al.
Since the theoretical side of the subject lies outside
the scope of this review, we comment only briefly on
this area. Numerical simulations are poised to make
major contributions to the subject over the next several years. Simulations with higher resolution and more
sophisticated treatments of the heating, cooling, phase
balance, and feedback are providing deeper insights into
the physical nature of the star formation scaling laws
and thresholds and the life cycles of molecular clouds
(e.g., Robertson & Kravtsov 2008; Dobbs 2008; Dobbs &
Pringle 2010; Tasker & Tan 2009; Tasker 2011; Brooks
et al. 2011). Inclusion of realistic stellar feedback may
obviate the need for artificial constraints on efficiency
(e.g., Hopkins et al. 2011).
Analytical models which incorporate the wide range of
relevant physical processes on the scales of both molecular clouds and galactic disks are also leading to deeper
insights into the triggering and regulation of star formation on the galactic scale (e.g., Ostriker et al. 2010, and
papers cited in §7.2). Exploring different prescriptions
for cloud-scale star formation in galaxy evolution models will illuminate the effects of the cloud-scale prescription on galaxy-scale evolution. At the “micro-scale” of
molecular clouds, inclusion of radiative and mechanical
feedback from star formation is producing more realistic
models, and perhaps the relative importance of feeding
from the local core and from the greater clump may be
quantified (e.g., references in §4.3).
We conclude with a hope and a prediction. From the
start, this review was designed to exchange ideas between those studying star formation in the Milky Way
and those studying star formation in other galaxies. The
authors have benefited immensely from this exchange,
and we hope for more of this cross-talk between our two
communities: people studying star formation within the
Milky Way can put their results in a larger context;
those studying other galaxies can appreciate that our
home galaxy offers unique advantages for understanding galaxies. A common theme across both arenas has
been the rapid pace of advance, both in observations and
theory. When the next review of this subject is written,
we predict that it will focus on observational tests of detailed physical theories and simulations rather than on
empirical star formation laws. We conclude with heartfelt thanks to all of those who are working toward this
common goal.
We would like to acknowledge the many people who
have supplied information and preprints in advance of
publication. In addition, we thank Alberto Bolatto,
Leonardo Bronfman, Peter Kaberla, Jin Koda, Adam
Leroy, Yancy Shirley, and Linda Tacconi for useful
and stimulating discussions. Henrik Beuther, Guillermo
Blanc, Daniela Calzetti, Barbara Catinella, Reinhard
Genzel, Rob Gutermuth, Mark Krumholz, Charles Lada,
Fred Lo, Steve Longmore, Eve Ostriker, and Jim Pringle
provided valuable comments on an early draft. We both
would like to express special thanks to our current and
former students and postdocs, with whom we have shared
countless valuable discussions. NJE thanks the Institute
of Astronomy, Cambridge, and the European Southern
Observatory, Santiago, for hospitality during extended
visits, during which much of his work on the review was
done. NJE also acknowledges support from NSF Grant
AST-1109116 to the University of Texas at Austin.
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Kennicutt and Evans
Star Formation Rate Calibrations
24 µm
70 µm
1.4 GHz
2−10 keV
Age Range (Myr)a
0 − 10 − 100
0 − 10 − 200
0 − 3 − 10
0 − 5 − 100b
0 − 5 − 100b
0 − 5 − 100b
0 − 100 :
0 − 100 :
Lx Units
ergs s−1 (νLν )
ergs s−1 (νLν )
ergs s−1
ergs s−1 (3−1100 µm)
ergs s−1 (νLν )
ergs s−1 (νLν )
ergs s−1 Hz−1
ergs s−1
log Cx
Ṁ⋆ /Ṁ⋆ (K98)
1, 2
1, 2
1, 2
1, 2
Note. — References: (1) Murphy et al. (2011); (2) Hao et al. (2011); (3) Rieke et al. (2009); (4) Calzetti et al. (2010a);
(5) Ranalli et al. (2003)
a Second number gives mean age of stellar population contributing to emission, third number gives age below which 90% of emission is
b Numbers are sensitive to star formation history, those given are for continuous star formation over 0–100 Myr. For more quiescent regions
(e.g., disks of normal galaxies) the maximum age will be considerably longer.
Multi-Wavelength Dust-Corrections
Composite Tracer
L(F U V )corr = L(F U V )obs + 0.46L(T IR)
L(F U V )corr = L(F U V )obs + 3.89L(25µm)
L(F U V )corr = L(F U V )obs + 7.2 × 1014 L(1.4GHz)a
L(N U V )corr = L(N U V )obs + 0.27L(T IR)
L(N U V )corr = L(N U V )obs + 2.26L(25µm)
L(N U V )corr = L(N U V )obs + 4.2 × 1014 L(1.4GHz)a
L(Hα)corr = L(Hα)obs + 0.0024L(T IR)
L(Hα)corr = L(Hα)obs + 0.020L(25µm)
L(Hα)corr = L(Hα)obs + 0.011L(8µm)
L(Hα)corr = L(Hα)obs + 0.39 × 1013 L(1.4GHz)a
Note. — References: (1) Hao et al. (2011); (2) Kennicutt et al. (2009)
a Radio
luminosity in units of ergs s−1 Hz−1
Star Formation Regimes
(M⊙ pc−2 )
< 10
Gas Properties
Star Formation
Mostly atomic
low, sparse
10 − Σdense
atomic→ molecular
> Σdense
molecular→ dense
high, concentrated
outer disks
early type galaxies
LSB galaxies
dwarf galaxies
solar nbd in MW
normal disks
inner MW
molecular clouds
some nuclear regions
clumps and cores
Note. — The dividing line between Intermediate and High-density regimes (Σdense ) ranges from 100 to 300 M⊙ pc−2 .
Star Formation
IC10 Leroy 06
Milky Way
large scale
Arimoto, Boselli, Israel,Wilson 95-05
Davies 04
Bryant 99
N(H2)/ICO 1-0
/L (CO) (Msun/(K km s pc ) )
(cm /(K km/s))
ULIRGs global
Solomon 97
Downes 98
GC clouds
Oka 98
Shier 96
α= M
Wild 92
Weiss 01
log (Σgas (Msun pc ) )
Fig. 1.— Compilation of the conversion factor (X(CO)) from the CO J = 1 → 0 integrated intensity [ICO (K km s−1 )] or luminosity [L′CO
(K km s−1 pc2 )] to H2 column density (left vertical scale) and total (H2 and He) gas mass (right vertical scale), derived in various Galactic
and extragalactic targets. Blue circles denote measurements in the disk and center of the Milky Way, based on various virial, extinction, and
isotopomeric analyses. Crossed green squares denote measurements in starbursts and (U)LIRGs, mainly based on dynamical constraints.
Filled triangles denote conversion factors as a function of decreasing metallicity (vertical arrow) from (bottom) to 8.2 (top), derived mainly
from global (large scale) dust mass measurements in nearby galaxies and dwarfs by several groups. In contrast, red filled squares mark
X-factor measurements toward individual clouds, over the same range in metallicity. Taken from Tacconi et al. (2008); references to the
original work are given there. Reproduced by permission of the AAS.
Kennicutt and Evans
Fig. 2.— A montage of infrared images of NGC 6946 from Spitzer (SINGS) and Herschel (KINGFISH). Top panels: Spitzer IRAC images
at 3.6 µm and 8.0 µm, and MIPS image at 24 µm. The emission at these wavelengths is dominated by stars, small PAH dust grains, and
small dust grains heated by intense radiation fields, respectively. Middle panels: Herschel PACS images at 70 µm, 100 µm, and 160 µm,
processed with the Scanamorphos map making package. Note the excellent spatial resolution despite the longer wavelengths, and the
progressive increase in contributions from diffuse dust emission (“cirrus”) with increasing wavelength. Bottom panels: Herschel SPIRE
images at 250 µm, 350 µm, and 500 µm. These bands trace increasingly cooler components of the main thermal dust emission, with possible
additional contributions from “submillimeter excess” emission at the longest SPIRE wavelengths. FWHM beam sizes for the respective
Herschel bands are shown in the lower left corner of each panel. This figure originally appeared in the Publications of the Astronomical
Society of the Pacific (Kennicutt et al. 2011). Copyright 2011, Astronomical Society of the Pacific; reproduced with permission of the
Star Formation
Fig. 3.— Top: relation between observed 24 µm IR luminosity and dust-corrected Hα luminosity for nearby galaxies. The dust corrections
were derived from the absorption-corrected Hα/Hβ ratios in optical spectra. The dotted line shows a linear relation for comparison, while
the other lines show published fits to other samples of galaxies. Bottom: linear combination of (uncorrected) Hα and 24 µm luminosities
compared to the same Balmer-corrected Hα luminosities. Note the tightness and linearity of the relation over nearly the entire luminosity
range. Taken from Kennicutt et al. (2009); reproduced by permission of the AAS.
Kennicutt and Evans
Fig. 4.— Example of the strong concentration of star formation in regions of high extinction, or mass surface density in the Perseus
molecular cloud. The gray-scale with black contours is the extinction map ranging from 2 to 29 mag in intervals of 4.5 mag. The yellow
filled circles are Flat SED sources and the red filled circles are Class I sources. Sources with an open star were not detected in HCO+
J = 3 → 2 emission and are either older sources that may have moved from their birthplace or background galaxies. Essentially all truly
young objects lie within contours of AV ≥ 8 mag. Taken from Heiderman et al. (2010); reproduced by permission of the AAS.
Star Formation
Fig. 5.— Sketch of approximately how the Galaxy is likely to appear viewed face-on, with Galactic coordinates overlaid and the locations
of spiral arms and the Sun indicated. This sketch was originally made by Robert Hurt of the Spitzer Science Center in consultation with
Robert Benjamin at the University of Wisconsin-Whitewater. The image is based on data obtained from the literature at radio, infrared,
and visible wavelengths. As viewed from a great distance our Galaxy would appear to be a grand-design two-armed barred spiral with
several secondary arms: the main arms being the Scutum-Centaurus and Perseus arms and the secondary arms being Sagittarius, the outer
arm, and the 3 kpc expanding arm. Adapted from a figure in Churchwell et al. (2009) by R. Benjamin. The original figure appeared in the
Publications of the Astronomical Society of the Pacific, Copyright 2009, Astronomical Society of the Pacific; reproduced with permission
of the Editors.
Kennicutt and Evans
Fig. 6.— High-resolution maps of star formation tracers and cold gas components in NGC 6946. Top left: Spitzer 24 µm dust emission
from the SINGS/KINGFISH project (Kennicutt et al. 2011); Top right: Hα emission from Knapen et al. (2004); Bottom left: H I emission
from the VLA THINGS survey (Walter et al. 2008); Bottom right: CO J = 2 → 1 emission from the HERACLES survey (Leroy et al.
2009). Note that the H I map extends over a much wider area than the CO, Hα, and 24 µm observations.
Star Formation
Fig. 7.— Top: The radial distribution of surface densities of atomic gas, molecular gas, and star formation rate for the MW. The atomic
data were supplied by P. Kaberla, (Kalberla & Dedes 2008), but we corrected for helium. The discontinuity around 8.5 kpc reflects the
inability to model H I near the solar circle. The molecular data are taken from Table 1 in Nakanishi & Sofue (2006), but scaled up to be
consistent with the bottom panel, using X(CO) = 2.0 × 1020 and multiplying by 1.36 to include helium. The molecular surface density
in the innermost bin is highly uncertain and may be overestimated by using a constant value of X(CO) (§2.4). The Σ(SFR) is read from
Figure 8 in Misiriotis et al. (2006), but it traces back, through a complex history, to Guesten & Mezger (1982), based on radio continuum
emission from H II regions. That result was in turn scaled to the latest estimate of total star formation rate in the MW of 1.9 M⊙ yr−1
(Chomiuk & Povich 2011). Separate points for Σmol and Σ(SFR) are plotted for the CMZ (Rgal < 250 pc). An uncertainty of 0.3 was
assigned arbitrarily to the values of log Σ(SFR). Bottom: Same as the top panel, but for NGC 6946. It is based on a figure in Schruba
et al. (2011) but modified by A. Schruba to show radius in kpc for ready comparison to the plot for the MW. Reproduced by permission
of the AAS. All gas distributions for both galaxies include a correction for helium.
Kennicutt and Evans
Fig. 8.— Relation between specific star formation rate (Ṁ∗ /M∗ ) and galaxy mass for galaxies in the SDSS spectroscopic sample, and
with SFRs measured from GALEX ultraviolet luminosities. Gray contours indicate the (1/Vmax-weighted) number distribution of galaxies
in this bivariate plane. The blue solid line shows the fit to the star-forming sequence fit, and the red line shows approximate position of
non-star-forming red sequence on this diagram. The dotted line shows the locus of constant SF R = 1 M⊙ yr−1 . Figure adapted from
Schiminovich et al. (2007). Reproduced by permission of the AAS.
Star Formation
Fig. 9.— Distribution of integrated star formation properties of galaxies in the local Universe. Each point represents an individual galaxy
or starburst region, with the average SFR per unit area (SFR intensity) plotted as a function of the absolute SFR. The SFR intensities
are averaged over the area of the main star-forming region rather than the photometric area of the disk. Diagonal lines show loci of
constant star-formation radii, from 0.1 kpc (top) to 10 kpc (bottom). Several sub-populations of galaxies are shown: normal disk and
irregular galaxies measured in Hα and corrected for dust attenuation (solid black points) from the surveys of Gavazzi et al. (2003), James
et al. (2004), Hameed & Devereux (2005), and Kennicutt et al. (2008); luminous star-formation dominated infrared galaxies (LIRGs) and
ultraluminous infrared galaxies (ULIRGs), plotted as red points, from Dopita et al. (2002) and Scoville et al. (2000); blue compact starburst
galaxies measured in Hα (blue points) from Pérez-González et al. (2003) and Gil de Paz et al. (2005); and circumnuclear star-forming
rings in local barred galaxies measured in Paα (green points) as compiled by Kormendy & Kennicutt (2004). The MW (magenta square)
lies near the high end of normal spirals in total star formation rate, but it is near the average in Σ(SFR) (§5.1). The relative numbers of
galaxies plotted does not reflect their relative space densities. In particular the brightest starburst galaxies are extremely rare.
Kennicutt and Evans
log ϕ(ψ) [Mpc−3 dex−1]
log ψ [MO· /yr ]
Fig. 10.— Volume-corrected SFR distribution function for disk and irregular galaxies in the local Universe, as derived from a combination
of large flux-limited ultraviolet and infrared catalogs and a multi-wavelength survey of the local 11 Mpc volume. Vertical lines indicate
uncertainties due to finite sampling; these are especially important for low SFRs, where the statistics are dominated by dwarf galaxies,
which can only be observed over small volumes. Statistics on gas-poor (elliptical, dwarf spheroidal) galaxies are not included in this study.
The blue line shows a maximum-likelihood Schechter function fit, as described in the text. Figure is original, but similar to one in Bothwell
et al. (2011).
Star Formation
Fig. 11.— Upper: Relationship between the disk-averaged surface densities of star formation and gas (atomic and molecular) for different
classes of star-forming galaxies. Each point represents an individual galaxy, with the SFRs and gas masses normalized to the radius of the
main star-forming disk. The line shows the original N = 1.4 fit from Kennicutt (1998b) superimposed on the data. Most of the galaxies
form a tight relation (exceptions discussed below), and with the improved dataset, even the normal galaxies (shown with black points)
follow a well-defined Schmidt law on their own. The dispersion of the normal galaxies overall from the average relation (±0.30 dex rms)
is considerably higher than can be attributed to observational uncertainties, which suggests that much of the dispersion is physical. The
Milky Way (magenta square) fits well on the main trend seen for other nearby normal galaxies. The purple crosses show data for low surface
brightness galaxies. The sample of galaxies has been enlarged from that studied in Kennicutt (1998b), with many improved measurements
as described in the text. Lower: Corresponding relation between the total (absolute) SFR and the mass of dense molecular gas as traced
in HCN. The line is a linear fit, which contrasts with the non-linear fit in the upper panel. Figure adapted from Gao & Solomon (2004).
Reproduced by permission of the AAS.
Kennicutt and Evans
Fig. 12.— Relation between SFR surface densities and total (atomic and molecular) gas surface densities for various sets of measurements,
from Bigiel et al. (2008). Colored contours show the distribution of values from measurements of sub-regions of SINGS galaxies. Overplotted
as black dots are data from measurements in individual apertures in M51 (Kennicutt et al. 2007). Data from radial profiles from M51
(Schuster et al. 2007), NGC 4736, and NGC 5055 (Wong & Blitz 2002), and NGC 6946 (Crosthwaite & Turner 2007) are shown as black
filled circles. The disk-averaged measurements from 61 normal spiral galaxies (filled gray stars) and 36 starburst galaxies (triangles) from
Kennicutt (1998b) are also shown. The black filled diamonds show global measurements from 20 low surface brightness galaxies (Wyder
et al. 2009). In all cases, calibrations of IMF, X(CO), etc. were placed on a common scale. The three lines extending from lower left to
upper right show lines of constant global star formation efficiency. The two vertical lines denote regimes which correspond roughly to those
discussed in §6 of this review. Figure taken from Bigiel et al. (2008). Reproduced by permission of the AAS.
Star Formation
Orion A
Lupus 3
Lupus 1
Orion B
Lupus 4
7 8
10 3
7 8
10 4
7 8
10 5
Cloud Mass (solar masses)
Fig. 13.— Plot of the ratio of the total YSO content of a cloud to the total cloud mass vs. total cloud mass. This is equivalent to a
measure of the star formation efficiency as a function of cloud mass for the local sample. It is also equivalent to the measure of the SFR
per unit cloud mass as a function of the cloud mass. The plot shows large variations in the efficiency and thus the SFR per unit mass for
the local cloud sample. Taken from Lada et al. (2010). Reproduced by permission of the AAS.
Kennicutt and Evans
Ori A
Ori B
rho Oph
Lupus 1
Lupus 3
Lupus 4
Cloud mass (M⊙ )
Fig. 14.— Taken from Lada et al. (2010). Relation between N(YSOs), the number of YSOs in a cloud, and M0.8 , the integrated cloud
mass above the threshold extinction of AK0 = 0.8 mag. For these clouds, the SFR is directly proportional to N(YSOs), and thus this graph
also represents the relation between the SFR and the mass of highly extincted and dense cloud material. A line representing the best-fit
linear relation is also plotted for comparison. There appears to be a strong linear correlation between N(YSOs) (or SFR) and M0.8 , the
cloud mass at high extinction and density. Taken from Lada et al. (2010). Reproduced by permission of the AAS.
Star Formation
Fig. 15.— Comparison of Galactic total c2d and GB clouds, YSOs, and massive clumps to extragalactic relations. SFR and gas surfaces
densities for the total c2d and GB clouds (cyan squares), c2d Class I and Flat SED YSOs (green and magenta stars), and LIR > 104.5 L⊙
massive clumps (yellow diamonds) are shown. The range of gas surface densities for the spirals and circumnuclear starburst galaxies in the
Kennicutt (1998b) sample is denoted by the gray horizontal lines. The gray shaded region denotes the range for Σth = 129 ± 14 M⊙ pc−2 .
Taken from Heiderman et al. (2010). Reproduced by permission of the AAS.
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