Galaxy formation models set within the hierarchical CDM paradigm have made remarkable progress over the past decade. In this review, we have focused on the methods and phenomenology of models that attempt to track astrophysical processes and predict galaxy properties within a cosmological framework. We identified a set of key observations that current models strive to reproduce, and which describe the assembly of galaxies from Cosmic Noon (z ∼ 2–3) to the present. These observations include distribution functions of global properties such as stellar mass functions and global scaling relations such as those between stellar mass and SFR, gas fraction, and ISM metallicity. In addition, observations are now starting to provide measurements of galaxy demographics, how the break-down of the galaxy population in terms of star-forming and quiescent, and disk and spheroid dominated objects, has evolved over this time period. The observed relationships between global and structural properties (such as light profile shape, size or internal density, and kinematics) and their evolution provide even stronger constraints on models. We described how well current state-of-the-art galaxy formation models are able to reproduce these observations, and what we have learned from their successes and failures about the physics of galaxy formation.
Although many discrepancies with observations remain, overall we would give today’s suite of galaxy formation models a passing grade. Summarizing the scorecard we have discussed in detail in this article:
Although there remain a wide range of models, and a healthy diversity of computational methods, virtually all models implement a qualitatively similar set of core physical processes. While it is possible that all models are being led down the garden path due to their reliance on phenomenology, the concordance among models using different methods is encouraging, and strongly suggests that we are making fundamental progress in at least identifying the main physical players involved. Some of the core processes identified include the prevalance of cold smooth accretion in building disks and fueling star-forming galaxies, the ubiquity and efficiency of star formation-driven outflows, the importance of black hole-related feedback in quenching star formation in massive galaxies, merger-driven morphological evolution that depends on the gas content of progenitors, and various physical processes that uniquely impact satellite galaxies once they fall into a larger halo containing hot gas. In addition, the convergence towards a similar qualitative view of the types of processes that are needed in different circumstances, based on more empirical considerations (e.g., preventative vs. ejective feedback, internal vs. environmental quenching, etc.) is also encouraging.
Many of these processes connect stellar scales to cosmological scales, making ab initio modeling nearly impossible, and forcing models to rely on phenomenological prescriptions to describe sub-grid physics, which must be calibrated in some way by observations. It is clear that many model results are sensitive to the details of these sub-grid recipes and their implementation, leading to a valid concern that these models may have little genuine predictive power (Haas et al. 2013a, b). There are perhaps two ways to combat this concern. First, although the sub-grid recipes and their parameters are tuned to match a subset of observations, the current suite of available observations is diverse and rich enough that by confronting models with as wide as possible a set of complementary constraints, and by exploring different sub-grid recipes and implementations, one can isolate the approach that satisfies the broadest set of constraints. Second, by studying “small scale” simulations (for example, of the ISM and the formation of individual stars, or regions near SMBH), one may hope to place the sub-grid recipes used in our cosmological simulations on a physically grounded foundation. Zoom techniques are now enabling simulations that are starting to bridge the gap between the scales of individual stars and SMBH and galactic scales. Although it will not be feasible to simulate cosmological volumes with these techniques in the near future, they will allow us to learn much about the interface between the “micro”-scales of stars and BH and the “macro” scales of galaxies.
In addition, there are physical processes that may be important in regulating galaxy formation, but which are not commonly included in current “mainstream” models. These include turbulence, magnetic fields, cosmic rays, and self-consistent radiative transfer. It is important to carry out experiments to determine the importance of these processes in shaping the observable properties of galaxies, and there has been significant recent progress on this front as well (e.g. Scannapieco & Brüggen 2010, Kotarba et al. 2011, Wise & Abel 2011, Mendygral et al. 2012, Hanasz et al. 2013, Pfrommer 2013).
Ideally, we would obtain direct observational confirmation (or refutation) of the set of core processes that models currently invoke. However, in many cases this is challenging. Smooth gas accretion (i.e. in small enough lumps that adiabatically add to the fuel supply without disrupting galactic structure) is expected to be very diffuse and in a phase that is difficult (T ∼ 104 K) to nearly impossible (T ∼ 105 K) to detect. The key parameter characterizing outflow efficiency in models is the mass loss rate, but since outflows are highly multi-phase it is difficult to account for all the mass (Veilleux et al. 2005). We observe the signatures of black hole activity in the form of AGN and jets associated with massive galaxies, but it is difficult to observationally constrain how efficiently this energy couples to surrounding gas to enact quenching. We can observe signposts and signatures of mergers in the form of close pairs and morphologically disturbed galaxies, but their rate is difficult to quantify precisely and their effect is difficult to directly constrain observationally. We can measure the statistics of galaxies in different environments, but it has been difficult with existing samples to disentangle the correlations between environment and internal properties, and to locate the environments at high redshift that are the progenitors of typical groups and clusters in the local Universe.
However, there are several important observational developments taking place now, or on the horizon, that will challenge and help to refine our models of galaxy formation. First, a new generation of sub-mm and radio interferometers (including ALMA, NOEMA, JVLA, Apertif, ASKAP, MeerKAT, and the SKA) will literally revolutionize our ability to characterize the cold gas in the ISM of galaxies out to high redshifts (Carilli & Walter 2013). Second, high-resolution spectroscopy in the rest-frame UV is now able to probe the diffuse gas and metals in the circumgalactic medium of galaxies for galaxy-targetted sightlines spanning a diverse range of galaxy types, from nearby galaxies to z ∼ 2–3 (e.g. Rudie et al. 2012, Prochaska et al. 2013, Tumlinson et al. 2013, Peeples et al. 2014). This provides constraints on the gas and metals that have been ejected by the winds invoked by our models, which probably comprise a much larger fraction of the halo baryon budget than the stars and cold ISM within galaxies. Third, Integral Field Unit spectrographs on ground based telescopes and on JWST will allow us to better characterize stellar and AGN driven winds and to study spatially resolved stellar population parameters and kinematics for large samples of nearby and high-redshift galaxies. Finally, high-resolution, wide-field multi-wavelength imaging such as will be possible with WFIRST will enable us to study galaxy internal properties and demographics over a much larger range of environments, allowing us to better disentangle internal and environmental forces and accumulating better statistics for rare events such as mergers and luminous AGN.
We thus live in interesting times where modelers are now offering some specific and non-trivial challenges to observers to go out and confirm, or rule out, key physical processes. Just because a given mechanism is not observed does not mean it is not occuring; one must carefully assess whether that mechanism is expected to be observable. A general trend is that models make the most direct predictions about gas-related processes, particularly inflows and outflows in the baryon cycle, with the growth of stellar and black hole components being almost a side-effect. Hence, in principle, observations that trace gas processes directly offer the greatest potential for new advances and constraints. Modelers and observers must work together to identify key tests that can be conducted with present and upcoming facilities in order to constrain the core physical processes. The emerging interplay between galaxy formation models and state-of-the-art telescopes is the hallmark of a healthy and vibrant area of research.
The way forward for galaxy formation models is fairly clear, but immensely challenging. As a blueprint, consider the Lyman-α forest: several decades ago, studying the interplay of gas dynamics with cosmological structure formation led to a revolution in our understanding that eventually resulted in the Lyα forest becoming a pillar of precision cosmology. Our goal should be to equivalently turn galaxy formation into a precision field, where parameterized recipes are tied to the physics of small scale processes in such a way that the parameters no longer need to be empirically tuned, but are constrained by our physical understanding of those processes (e.g. stellar evolution models, or BH accretion disk models). Numerical simulations on different scales (zooms and cosmological volumes) and semi-analytic models have crucial and complementary roles to play in this process, helping to better understand the physics in detail as well as to synthesize and parameterize it within a ΛCDM context. It is almost surely the case that the physical processes included in models so far will not be sufficient to fully describe galaxy evolution, and there will be many twists and surprises forthcoming. Hence there is much work to be done, but it appears that cosmological models of galaxy formation are on a secure foundation for the exciting journey ahead.
Acknowledgements
It would take many more pages to thank all the colleagues who have provided valuable insights and participated in discussions that have shaped this work, and we apologize for the inevitable choices we had to make to review this vast topic while conforming to page limits. But we would particularly like to thank Andrew Benson, Richard Bower, Rob Crain, Darren Croton, Michelle Furlong, Violeta Gonzalez-Perez, Bruno Henriques, Yu Lu, Joop Schaye, Paul Torrey, Mark Vogelsberger, and their collaborators for providing the data from their models and simulations and for constructive comments on this article. We also thank Avishai Dekel, Thorsten Naab, and Gergö Popping for comments. We especially thank our Scientific Editor, John Kormendy, for his thorough reading of the paper, and for comments and suggestions that improved the article. rss gratefully acknowledges the generous support of the Downsbrough family. RD acknowledges support from the South African Research Chairs Initiative and the South African National Research Foundation. This work was supported in part by NASA grant NNX12AH86G.
Glossary of Acronyms
AGB: asymptotic giant branch
AGN: active galactic nucleus
ALMA: Atacama Large Millimeter/submillimeter Array
AMR: adaptive mesh refinement
ASKAP: Australian Square Kilometre Array Pathfinder
BH: black hole
BLR: broad line region
B/T: bulge to total ratio
CDM: cold dark Matter
ckpc: comoving kilaparsec
cMpc: comoving megaparsec
EC-SPH: entropy-conserving SPH
EoR: epoch of reionization
DI-SPH: density-independent SPH
FOF: friends of friends
GMC: giant molecular cloud
GR: General Relativity
H i: neutral hydrogen
HOD: halo occupation distribution
HST: Hubble Space Telescope
IGM: intergalactic medium
IMF: initial mass function
IR: infrared
ISM: interstellar medium
JVLA: Jansky Very Large Array
JWST: James Webb Space Telescope
LF: luminosity functions
MeerKAT:
http://www.ska.ac.za/meerkat/index.php
MZR: mass-metallicity relation
NFW: Navarro-Frenk-White
NOEMA: NOrthern Extended Millimeter Array;
http://iram-institute.org/EN/noema-project.php
PE-SPH: pressure-entropy SPH
PM: particle-mesh
PPM: Piecewise Parabolic Method
SAM: semi-analytic model
SDSS: Sloan Digital Sky Survey
SED: spectral energy eistribution
SF: star formation
SFE: star formation efficiency
SFMS: star forming main sequence
SFR: star formation rate
SKA: Square Kilometer Array
SMBH: supermassive black hole
SMF: stellar mass function
SN: supernova
sSFR: specific star formation rate
SHAM: sub-halo abundance matching
SO: spherical overdensity
SPH: smoothed particle hydrodynamics
ULIRG: ultra-luminous infrared galaxies
UV: ultraviolet
WFIRST: Wide-Field Infrared Survey Telescope
ΛCDM: cold dark matter with a cosmological constant (Λ)