It has long been regarded as difficult if not impossible for a cosmological model to account simultaneously for the galaxy luminosity, mass, and velocity distributions. We revisit this issue using a modern compilation of observational data along with the best available large-scale cosmological simulation of dark matter (DM). We find that the standard cosmological model, used in conjunction with halo abundance matching (HAM) and simple dynamical corrections, fits—at least on average—all basic statistics of galaxies with circular velocities V circ > 80 km s–1 calculated at a radius of ~10 kpc. Our primary observational constraint is the luminosity-velocity (LV) relation—which generalizes the Tully-Fisher and Faber-Jackson relations in allowing all types of galaxies to be included, and provides a fundamental benchmark to be reproduced by any theory of galaxy formation. We have compiled data for a variety of galaxies ranging from dwarf irregulars to giant ellipticals. The data present a clear monotonic LV relation from ~50 km s–1 to ~500 km s–1, with a bend below ~80 km s–1 and a systematic offset between late- and early-type galaxies. For comparison to theory, we employ our new ΛCDM "Bolshoi" simulation of DM, which has unprecedented mass and force resolution over a large cosmological volume, while using an up-to-date set of cosmological parameters. We use HAM to assign rank-ordered galaxy luminosities to the DM halos, a procedure that automatically fits the empirical luminosity function and provides a predicted LV relation that can be checked against observations. The adiabatic contraction of DM halos in response to the infall of the baryons is included as an optional model ingredient. The resulting predictions for the LV relation are in excellent agreement with the available data on both early-type and late-type galaxies for the luminosity range from Mr = –14 to Mr = –22. We also compare our predictions for the "cold" baryon mass (i.e., stars and cold gas) of galaxies as a function of circular velocity with the available observations, again finding a very good agreement. The predicted circular velocity function (VF) is also in agreement with the galaxy VF from 80 to 400 km s–1, using the HIPASS survey for late-type galaxies and Sloan Digital Sky Survey (SDSS) for early-type galaxies. However, in accord with other recent results, we find that the DM halos with V circ < 80 km s–1 are much more abundant than observed galaxies with the same V circ. Finally, we find that the two-point correlation function of bright galaxies in our model matches very well the results from the final data release of the SDSS, especially when a small amount of scatter is included in the HAM prescription.
S. Trujillo-Gomez, A. Klypin, J. Primack, and Aaron J. Romanowsky. "Galaxies in CDM with Halo Abundance Matching: luminosity-velocity relation, baryonic mass-velocity relation, velocity function, and clustering" Astrophysical Journal (2011): 1-23. doi:10.1088/0004-637X/742/1/16