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The cosmic history of star formation is one of the most fundamental observables in astrophysical cosmology. We have reviewed the range of complementary techniques and theoretical tools that are allowing astronomers to map the transformation of gas into stars, the production of heavy elements, and the reionization of the Universe from the cosmic dark ages to the present epoch. Under the simple assumption of a universal IMF, there is reasonable agreement between the global SMD inferred at any particular time and the time integral of all the preceding instantaneous star-formation activity, although modest offsets may still point toward systematic uncertainties. A consistent picture is emerging, whereby the SFRD peaked ~ 3.5 Gyr after the Big Bang, and dropped exponentially at z < 1 with an e-folding timescale of 3.9 Gyr. The Universe was a much more active place in the past: Stars formed at a peak rate approximately nine times higher than is seen today. Approximately 25% of the present-day SMD formed at z > 2, before the peak of the SFRD, and another 25% formed since z = 0.7, i.e., roughly over the last half of the Universe's age. From the peak of the SFRD at z ≈ 2 to the present day, and perhaps earlier as well, most stars formed in galaxies that obey a relatively tight SFR-M correlation, and only a small fraction formed in starbursts with significantly elevated specific SFRs. The smooth evolution of this dominant main-sequence galaxy population suggests that the evolution of the cosmic SFH is primarily determined by a balance between gas accretion and feedback processes, both closely related to galaxy mass, and that stochastic events such as merger-driven starbursts play a relatively minor role. The growth histories of the stellar component of galaxies and their central black holes are similar in shape, suggesting broad co-evolution of black holes and their host galaxies. The rise of the mean metallicity of the Universe to 0.001 solar by redshift six, 1 Gyr after the Big Bang, appears to have been accompanied by the production of fewer than 10 hydrogen LyC photons per baryon, indicating a rather tight budget for cosmological reionization. The SFRD at z ≈ 7 was approximately the same as that of today, at z ≈ 0, but only 1% of today's SMD was formed during the epoch of reionization.

As far as the observations and data are concerned, there is still room for improvement in both SFRD and SMD measurements at virtually every redshift, from the local Universe to the epoch of reionization (Section 4.6). That said, it would be somewhat surprising if new measurements changed the picture dramatically at z < 1; it is more likely that stellar population modeling, e.g., for deriving stellar masses or SFRs, could still change the details of the picture during the decline and fall of the cosmic SFH. Indeed, at all redshifts, limitations of our methods for interpreting light as mass may play a significant, even dominant, role in the error budget for the analyses described in this review. The peak era of cosmic star formation has been extensively mapped, and yet even with the current data (Figure 9), it is still hard to accurately pinpoint the redshift of maximum SFRD within a range Δz = 1. Our fitting function (Equation 15) places this peak at z ≈ 1.85, which is plausible but still uncertain. Uncertainties in the faint-end slope of the IRLF and in extinction corrections for the UVLF still dominate at this peak era of cosmic star formation. Although evidence seems to point clearly to a steady increase in the SFRD from z = 8 to z ≈ 2, our direct knowledge of dust-obscured star formation at these redshifts is, for the most part, limited to the rarest and most ultraluminous galaxies, leaving considerable uncertainty about how much SFRD we may be missing in the UV census of that early phase of galaxy evolution. At z > 4, our galaxy surveys have been strongly biased toward UV-bright galaxies, and may underestimate both SFRDs and SMDs. Even for UV-selected galaxies, the measurements at z ≥ 8 are very new and likely uncertain, unsupported by spectroscopic confirmation to date. In addition to measuring redshifts, spectroscopy from the JWST will help clarify basic issues about nebular line emission and the degree to which it has affected the photometric analyses that have been carried out to date.

Painstaking though all this vast effort has been, it does miss a crucial point. It says little about the inner workings of galaxies, i.e., their "metabolism" and the basic process of ingestion (gas infall and cooling), digestion (star formation), and excretion (outflows). Ultimately, it also says little about the mapping from dark matter halos to their baryonic components. Its roots are in optical-IR astronomy, statistics, stellar populations, and phenomenology, rather than in the physics of the ISM, self-regulated accretion and star formation, stellar feedback, and SN-driven galactic winds. It provides a benchmark against which to compare semi-analytic modeling and hydrodynamical simulations of galaxy formation, but it offers little guidance in identifying the smaller-scale basic mechanisms that determine the rate of conversion of gas into stars and lead to the grandiose events in the history of the Universe described in this review.

A variety of physical processes are thought to shape the observed distribution of galaxy properties, ranging from those responsible for galaxy growth (e.g., star formation and galaxy merging) to those that regulate such growth (e.g., energetic feedback from SNe, AGN, and the UV radiation background). However, many of these processes likely depend primarily on the mass of a galaxy's dark matter halo. Relating the stellar masses and SFRs of galaxies to the masses and assembly histories of their parent halos is a crucial piece of the galaxy formation and evolution puzzle. With the accumulation of data from large surveys and from cosmological numerical simulations, several statistical methods have been developed over the past decade to link the properties of galaxies to the underlying dark matter structures (e.g. Berlind & Weinberg 2002, Yang et al. 2003, Vale & Ostriker 2004). One of them, the "abundance matching" technique, assumes in its simplest form a unique and monotonic relation between galaxy light and halo mass, and it reproduces galaxy clustering as a function of luminosity over a wide range in redshift (e.g. Conroy et al. 2006, Guo et al. 2010, Moster et al. 2010). Modern versions of this approach (Moster et al. 2013, Behroozi et al. 2013) have shown that a) halos of mass ~ 1012 M are the most efficient at forming stars at every epoch, with baryon conversion efficiencies of 20-40% that fall rapidly at both higher and lower masses; b) in halos similar to that of the Milky Way, approximately half of the central stellar mass is assembled after redshift 0.7; and c) in low-mass halos, the accretion of satellites contributes little to the assembly of their central galaxies, whereas in massive halos more than half of the central stellar mass is formed "ex-situ." These studies represent promising advances, albeit with serious potential shortcomings (e.g. Guo & White 2013, Zentner et al. 2013). The assumption of a monotonic relation between stellar mass and the mass of the host halo is likely incorrect in detail, and it predict only numerically converged properties on scales that are well resolved in simulations. The matching procedure requires minimal assumptions and avoids an explicit treatment of the physics of galaxy formation. As such it provides relatively little new insight into this physics. In the version of this technique by Behroozi et al. (2013), for example, the cosmic SFH is reproduced by construction.

As of this writing, a solid interpretation of the cosmic SFH from first principles is still missing (for a recent review, see Mac Low 2013). Generically, one expects that star formation may be limited at early times by the build-up of dark matter halos and quenched at low redshift as densities decline from Hubble expansion to the point where gas cooling is inhibited. These two regimes could then lead to a peak in the SFH at intermediate redshifts (Hernquist & Springel 2003). A decade ago, hydrodynamical simulations predicted that the peak in star-formation activity should occur at a much higher redshift, z gtapprox 5, than is actually observed (Springel & Hernquist 2003, Nagamine et al. 2004). Theoretical modeling has been unable to correctly forecast the evolution of the SFRD because of the large range of galaxy masses that contribute significantly to cosmic star formation and the difficulty in following the feedback of energy into the ISM and circumgalactic medium from stellar radiation, SN explosions, and accreting massive black holes. Gas cooling in an expanding Universe is an intrinsically unstable process because cooling acts to increase the density of the gas, which in turn increases the cooling rate. Systems collapsing at low redshift have low mean densities and long cooling times, whereas systems collapsing at higher redshifts have higher mean densities and cool catastrophically. Without feedback processes that transfer energy to the ISM and reheat it, one is faced with the classical overcooling problem - the unphysical cooling of hot gas in the poorly resolved inner regions of galaxies - and with the consequent overproduction of stars at early times. And yet, a completely satisfactory treatment of feedback in hydrodynamical simulations that capture large cosmological volumes remains elusive, as these mechanisms operate on scales too small to be resolved and must therefore be incorporated via ad-hoc recipes that are too simplistic to capture the complex subgrid physics involved (e.g., Schaye et al. 2010).

In-depth knowledge of the mechanisms responsible for suppressing star formation in small halos (e.g., Governato et al. 2010, Krumholz & Dekel 2012, Kuhlen et al. 2012), more powerful supercomputers, better algorithms as well as more robust numerical implementations of stellar feedback (e.g., Agertz et al. 2013) all now appear as crucial prerequisites for predicting more realistic SFHs. Newer and deeper observations from the ground and space should improve our measurements of the galaxy population and its integrated properties, especially at and beyond the current redshift frontier where data remains sparse. It seems likely, however, that the most important contribution of new surveys and better modeling will be toward a detailed understanding of the physics of galaxy evolution, not simply its demographics.


The authors are not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review.


This review has benefited from many discussions with and the help of J. Aird, R. Chary, C. Conroy, O. Cucciati, D. Elbaz, S. Faber, H. Ferguson, A. Gallazzi, V. González, A. Klypin, K.-S. Lee, D. Maoz, P. Oesch, M. Pettini, J. Pforr, L. Pozzetti, J. Primack, J. X. Prochaska, M. Rafelski, A. Renzini, B. Robertson, M. Schenker, and D. Stark. Support for this work was provided by the National Science Foundation (NSF) through grant OIA-1124453, by NASA through grant NNX12AF87G (P.M.), and by NOAO, which is operated by the Association of Universities for Research in Astronomy, under a cooperative agreement with the NSF (M.D.).

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