Galaxy Assembly Bias in the Stellar-to-halo Mass Relation for Red Central Galaxies from SDSS

We report evidence of galaxy assembly bias - the correlation between galaxy properties and biased secondary halo properties at fixed halo mass (MH) - in the stellar-to-halo mass relation (SHMR) for red central galaxies from the Sloan Digital Sky Survey. In the MH = 1011.5-1013.5 h⁻¹ M_ range, central galaxy stellar mass (M_*) is correlated with the number density of galaxies within 10 h⁻¹ Mpc (δ₁₀), a common proxy for halo formation time. This galaxy assembly bias signal is also present when MH, M_*, and δ₁₀ are substituted with group luminosity, galaxy luminosity, and metrics of the large-scale density field. To associate differences in δ₁₀ with variations in halo formation time, we fitted a model that accounts for (1) errors in the MH measured by the Tinker 2021, 2022 group catalog and (2) the level of correlation between halo formation time and M_* at fixed MH. Fitting of this model yields that (1) errors in MH are 0.15 dex and (2) halo formation time and M_* are strongly correlated (Spearman's rank correlation coefficient ~0.85). At fixed MH, variations of ~0.4 dex in M_* are associated with ~1-3 Gyr variations in halo formation time and in galaxy formation time (from stellar population fitting; Oyarz\'un et al. 2022). These results are indicative that halo properties other than MH can impact central galaxy assembly.