Constraining Scatter in the Stellar Mass--Halo Mass Relation for Haloes Less Massive than the Milky Way

Magdelena Allen, Peter Behroozi, Chung-Pei Ma

Published 2018-12-13Version 1

Most galaxies are hosted by massive, invisible dark matter haloes, yet little is known about the scatter in the stellar mass--halo mass relation for galaxies with host halo masses $M_{h}\le 10^{11} M_{\odot}$. Using mock catalogs based on dark matter simulations, we find that two observable signatures are sensitive to scatter in the stellar mass--halo mass relation even at these mass scales; i.e., conditional stellar mass functions and velocity distribution functions for neighbouring galaxies. We compute these observables for 179,373 galaxies in the Sloan Digital Sky Survey (SDSS) with stellar masses $M_{\ast} > 10^9 M_{\odot}$ and redshifts 0.01 $< z <$ 0.307. We then compare to mock observations generated from the Bolshoi-Planck dark matter simulation for stellar mass--halo mass scatters ranging from 0 to 0.6 dex. The observed results are consistent with simulated results for low values of scatter ($\sim$0.2 dex), but SDSS statistics are insufficient to provide firm constraints. This method could provide much tighter constraints on stellar mass--halo mass scatter in the future if applied to larger data sets, especially the anticipated Dark Energy Spectroscopic Instrument Bright Galaxy Survey, and constraining the scatter could have important implications for galaxy formation and evolution.