Hierarchical Galaxy Growth and Scatter in the Stellar Mass - Halo Mass Relation

Abstract: The relation between galaxies and dark matter halos reflects the combined effects of many distinct physical processes. Observations indicate that the $z=0$ stellar mass-halo mass (SMHM) relation has remarkably small scatter in stellar mass at fixed halo mass ($\lesssim$ 0.2 dex) with little dependence on halo mass. We investigate the origins of this scatter by combining N-body simulations with observational constraints on the SMHM relation. We find that at the group and cluster scale ($M_{\rm vir}>10^{14}{M_\odot}$) the scatter due purely to hierarchical assembly is $\approx0.16$ dex, which is comparable to recent direct observational estimates. At lower masses, mass buildup since $z\approx2$ is driven largely by in-situ growth. We include a model for the in-situ buildup of stellar mass and find that an intrinsic scatter in this growth channel of $0.2$ dex produces a relation between scatter and halo mass that is consistent with observations from $10^{12}{M_\odot}<M_{\rm vir}<10^{14.75}{M_\odot}$. The approximately constant scatter across a wide range of halo masses at $z=0$ thus appears to be a coincidence as it is determined largely by in-situ growth at low masses and by hierarchical assembly at high masses. These results indicate that the scatter in the SMHM relation can provide unique insight into the regularity of the galaxy formation process.