8. STATUS AND OUTLOOK

Empirical studies of the galaxy–halo connection have exploded since their birth roughly 15 years ago. They are now an essential tool in the interpretation of galaxy surveys for both galaxy formation and cosmology. These models have provided key insights into the problems of galaxy formation and evolution. They also play an increasing role in cosmological modeling and in understanding the physics of dark matter. Accurate methodologies have been developed for modeling the galaxy–halo connection, and there is increasing interplay between modeling approaches (from physical to empirical models, and from simple few parameter models to more flexible models with tens of parameters) that leverages the strengths of each of them.

Some of the key aspects of the galaxy–halo connection that have been learned from this body of research are as follows:

• Galaxy formation is surprisingly inefficient: the efficiency of turning gas into stars peaks at ∼ 20–30% of the baryon fraction in halos of 10¹² M_⊙ and is significantly lower for higher and lower mass halos.
• The stellar masses of central galaxies are a strong function of dark matter halo mass below 10¹² M_⊙, scaling like M_* ∝ M_h²⁻³, and a weaker function above this pivot point, M_* ∝ M_h^1/3.
• Galaxy masses are tightly connected to the masses of their dark matter halos. If halo properties are considered before substantive stripping by more massive systems, the scatter in galaxy stellar mass or luminosity at fixed halo mass has a scatter of less than 0.2 dex for objects above 10¹² M_⊙ where it is well measured; this likely increases by no more than a factor of two at lower mass.
• For most of the Universe's history from z∼ 8–0, the bulk of all star formation occurs in galaxies that live in a narrow range of halo mass around 10¹² M_⊙.
• Most galaxies at any stellar mass are the central galaxies in their own dark matter halo; the fraction of satellite galaxies at a given galaxy stellar mass declines from ∼ 30% at low mass to ∼ 5% at high mass.
• Most trends of galaxy properties with large-scale environment can be reasonably well explained by the fact that the halo mass function and average halo properties vary with environment, combined with a galaxy–halo connection that is independent of environment.
• Although halo mass is the dominant determinant of the state of the galaxy occupying it, there is statistically significant evidence that some galaxy properties are influenced by other halo properties, and that this manifests in galaxy clustering properties (assembly bias).

The next generation of surveys is likely to transform the study of the galaxy–halo connection into a precision science, including enabling the community to pin down the dependence of the wide range of multi-modal galaxy properties on the key properties of dark matter halos and their environments within the cosmic web. These surveys include massive imaging and spectroscopic surveys from the ground and space whose combination will jointly constrain the abundance and clustering of galaxies and the mass distribution around them, as well as surveys of 21-cm, UV absorption, X-rays, and the CMB at high resolution that will map the gas and its connection to galaxies and their halos.

In the next decade, we expect that our understanding of the detailed connection between galaxies and halos over mass, redshift, and environment will provide major strides forward in galaxy formation, cosmological parameters, and the nature of dark energy and neutrino mass, and in understanding the nature of dark matter. At the same time, it is clear that for this promise to be realized, the precision of models for the galaxy–halo connection will need to keep up with the pace of the data. In closing, we highlight some of the most interesting near-term future issues.

FUTURE ISSUES

1. The detailed manifestations of assembly bias and their connection to the observable properties of galaxies are still relatively unconstrained. Characterizing them will likely provide interesting insights into galaxy formation physics; in addition, effectively modeling assembly bias will be important to mitigate systematic uncertainties in some cosmological constraints.
2. The mass dependence of the normalization and scatter in the galaxy–halo connection is still poorly constrained at halo masses below ∼ 10¹² M_⊙. This has important consequences for interpreting measurements of dwarf galaxies in the context of dark matter models.
3. Characterizing the halo occupation of galaxies identified with complex selection criteria, including for example colors, star formation rates, sizes, morphologies, and line widths, will be increasingly important for cosmological studies.
4. The relationship between galaxy color, galaxy size, and galaxy morphologies and halo properties at fixed stellar mass is still uncertain; there is a need for models and observational tests of models that connect galaxy sizes and morphologies to dark matter halos across cosmic time.
5. Statistically mapping the relationship between halos and the gas surrounding and fueling galaxies is still in the early stages, and constraints on these relationships should provide new physical insight into galaxy formation.
6. Baryonic processes, especially various forms of feedback, may modify the abundance and clustering properties of dark matter halos, with important implications for inferences about the galaxy–halo connection.
7. A primary challenge for future surveys is optimizing joint constraints on the galaxy–halo connection and cosmological parameters, which will require judicious choices in parameterizing the former to retain maximal constraining power.

DISCLOSURE STATEMENT

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

ACKNOWLEDGMENTS

We are grateful to our many collaborators on these topics over the years. RHW in particular thanks all of the participants of the 2017 KITP program “The Galaxy–Halo Connection” for extensive discussions that helped frame the perspective of this review, and we thank the KITP for support via the National Science Foundation under Grant No. NSF PHY-1125915 while this review was being written. We thank Yao-Yuan Mao, Andrew Hearin, and our scientific editor Sandy Faber for extensive helpful comments on the manuscript. Susmita Adhikari, Peter Behroozi, Andreas Berlind, Jonathan Blazek, Joe DeRose, Ashley King, Andrey Kravtsov, Sean McLaughlin, Ethan Nadler, Rachel Somerville, Chun-Hao To, and Frank van den Bosch also provided helpful feedback. We thank Ralf Kaehler for assistance with Figures 1 and 6, Sasha Safonova for assistance with data compilation for Figure 8, and Chang Hahn for assistance with Figure 11. We thank Peter Behroozi for providing data for Figures 2, 8, 9, and 10. Figures 1 and 6 made use of the Chinchilla simulation run at the NERSC supercomputing center. Figures 3 and 5 made use of the Bolshoi simulations; these were performed within the Bolshoi project of the University of California High-Performance AstroComputing Center (UC-HiPACC) and were run at the NASA Ames Research Center. We have made extensive use of NASA's Astrophysics Data System and the arXiv.