Constraining the Low-mass End of the Stellar-to-halo Mass Relation with Surveys of Satellite Galaxies

The abundance of satellite galaxies is set by the hierarchical assembly of their host halo. We leverage this to investigate the low-mass end (MH < 1011M⊙) of the stellar-to-halo mass relation (SHMR), which is key to constraining theories of galaxy formation and cosmology. We argue that recent analyses of satellite galaxies in the Local Group environment have not adequately modeled the dominant source of scatter in satellite stellar mass functions: the variance in accretion histories for a fixed host halo mass. We present a novel inference framework that not only properly accounts for this halo-to-halo variance but also naturally identifies the amount of host halo mass mixing, which is generally unknown. Specifically, we use the semianalytical SatGen model to construct mock satellite galaxy populations consistent with the third data release of the Satellites Around Galactic Analogs survey. We demonstrate that even under the most idealized circumstances, the halo-to-halo variance makes it virtually impossible to put any meaningful constraints on the scatter in the SHMR. Even a satellite galaxy survey made up 100 hosts can at best only place an upper limit of ∼0.5 dex on the scatter (at the 95% confidence level). This is because the large variance in halo assembly histories dominates over the scatter in the SHMR. This problem can be overcome by increasing the sample size of the survey by an order of magnitude (∼1000 host galaxies), something that should be fairly straightforward with forthcoming spectroscopic surveys.