Constancy of SHMR scatter for centrals/satellites and at low halo masses

Determine whether the scatter in the stellar mass–halo mass relations for central and satellite galaxies, P_c(M_* | M_h) and P_s(M_* | M_s), remains approximately constant when the central and satellite relations are modeled separately and when the analysis is extended to lower halo masses.

Background

Prior PAC-based work inferred an approximately constant scatter in the central stellar mass–halo mass relation over halo masses 1010–1015 h{-1} M_⊙. In this paper, the authors model centrals and satellites with separate relations and push to much lower masses using DESI PAC measurements, raising the question of whether the constant-scatter approximation still holds.

Because the central and satellite relations may differ and the low-mass regime can introduce additional astrophysical effects (e.g., reionization and occupation fraction), establishing the mass dependence (or lack thereof) of the scatter is necessary to interpret dwarf-galaxy constraints robustly.

References

Although it is unclear whether this remains true when $P_{\rm c}$ and $P_{\rm s}$ are modelled separately or when extending to lower masses, we adopt a constant scatter as a first step and introduce two parameters, $\sigma_{\rm c}$ and $\sigma_{\rm s}$, to describe the scatter for haloes and subhaloes, respectively.

— PAC in DESI. II. Galaxy-halo connection into the $10^{6}{\rm M}_{\odot}$ frontier  (2603.29331 - Xu et al., 31 Mar 2026) in Section 4.2 (SHMR-based SHAM model)