Connecting Galaxies, Halos, and Star Formation Rates Across Cosmic Time
  A simple, observationally-motivated model is presented for understanding how halo masses, galaxy stellar masses, and star formation rates are related, and how these relations evolve with time. The relation between halo mass and galaxy stellar mass is determined by matching the observed spatial abundance of galaxies to the expected spatial abundance of halos at multiple epochs -- i.e. more massive galaxies are assigned to more massive halos at each epoch. Halos at different epochs are connected by halo mass accretion histories estimated from N-body simulations. The halo--galaxy connection at fixed epochs in conjunction with the connection between halos across time provides a connection between observed galaxies across time. With approximations for the impact of merging and accretion on the growth of galaxies, one can then directly infer the star formation histories of galaxies as a function of stellar and halo mass. This model is tuned to match both the observed evolution of the stellar mass function and the normalization of the observed star formation rate -- stellar mass relation to z~1. The data demands, for example, that the star formation rate density is dominated by galaxies with Mstar~10^{10.0-10.5} Msun from 0<z<1, and that such galaxies over these epochs reside in halos with M~10^{11.5-12.5} Msun. The star formation rate -- halo mass relation is approximately Gaussian over the range 0<z<1 with a mildly evolving mean and normalization. This model is then used to shed light on a number of issues, including 1) a clarification of ``downsizing'', 2) the lack of a sharp characteristic halo mass at which star formation is truncated, and 3) the dominance of star formation over merging to the stellar build-up of galaxies with Mstar<10^11 Msun at z<1. 
Charlie Conroy, Risa H. Wechsler