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

## TL;DR

This study investigates the scatter in the stellar mass--halo mass relation for low-mass galaxies using SDSS data and dark matter simulations, finding current data insufficient for tight constraints but outlining a promising future method.

## Contribution

The paper introduces a method to constrain scatter in the stellar mass--halo mass relation at low masses using observable signatures and mock catalogues, with potential for improved future constraints.

## Key findings

- Current SDSS data cannot tightly constrain scatter (<0.6 dex).
- Observable signatures like stellar mass functions are sensitive to scatter.
- Future larger surveys could significantly improve constraints.

## Abstract

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 catalogues 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 $\textit{Bolshoi-Planck}$ 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 most values of scatter ($<$0.6 dex), and SDSS statistics are insufficient to provide firm constraints. However, 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. Constraining the value of scatter could have important implications for galaxy formation and evolution.