ARlogo Annu. Rev. Astron. Astrophys. 2012. 50:531-608
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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.

Table 3. Star Formation Regimes

Name Σgas Gas Properties Star Formation Examples
  (M pc-2)      

Low < 10 Mostly atomic low, sparse outer disks
Density       early type galaxies
        LSB galaxies
        dwarf galaxies
        solar nbd in MW
Intermediate 10- Σdense atomic → molecular moderate normal disks
Density       inner MW
        molecular clouds
High > Σdense molecular → dense high, concentrated some nuclear regions
Density       starbursts
        clumps and cores

The dividing line between Intermediate and High-density regimes (Σdense) ranges from 100 to 300 M pc-2.

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 low-density 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 HII regions only observed in regions of unusually high cold gas densities. The global "efficiency" of star formation, є (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 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 gas-rich, 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 (§ 5.1).

The transition from the low-density regime roughly corresponds to the transition between HI-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 є (§ 1.2), the star formation rate per unit total gas mass, nearly all studies suggest that є 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 є is constant, but others suggest є 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, García-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" (є). As discussed in § 6.3, the constancy of the molecular є at intermediate surface densities is uncertain. Observations of CO in high-redshift 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 є 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 є 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 HI 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 (García-Burillo et al. 2012), and physically based models, rather than simple conversion factors, are needed.

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 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 є and є) 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 20-40 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 sub-threshold 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 formation 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 free-fall 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 bottom-up 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 ∝ Σgas0.5.

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 self-gravitational 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, 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. 2010).

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), 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 tff ∝ ρ-0.5, a volumetric star formation law, ρSFR ∝ ρ / tff ∝ 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 tff 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 tff face two problems. First, no evidence has been found in well-studied molecular clouds for collapse at tff (§ 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 tff, 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 tff 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 tff from the mean density of the whole cloud (tff ∝ 1 / ⟨ρ⟩). A computation of ⟨tff⟩ from ⟨1 / ρ⟩ 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 tff 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 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 sub-cloud 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 star-forming 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 HII 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 "zoomed-in" observations of other galaxies. For such studies the weakest link currently is the knowledge of the molecular gas. We can trace HI 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 HI 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 free-free 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 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 spatially-resolved 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; Blanc et al. 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 HII 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 formation.

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. 2008).

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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