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 (M$_H$) - in the stellar-to-halo mass relation (SHMR) for red central galaxies from the Sloan Digital Sky Survey. In the M$_H = 10^{11.5}-10^{13.5} h^{-1}$ M$_{\odot}$ range, central galaxy stellar mass (M$_*$) is correlated with the number density of galaxies within $10 h^{-1}$ Mpc ($\delta_{10}$), a common proxy for halo formation time. This galaxy assembly bias signal is also present when M$_H$, M$_*$, and $\delta_{10}$ are substituted with group luminosity, galaxy luminosity, and metrics of the large-scale density field. To associate differences in $\delta_{10}$ with variations in halo formation time, we fitted a model that accounts for (1) errors in the M$_H$ measured by the Tinker 2021, 2022 group catalog and (2) the level of correlation between halo formation time and M$_*$ at fixed M$_H$. Fitting of this model yields that (1) errors in M$_H$ are 0.15 dex and (2) halo formation time and M$_*$ are strongly correlated (Spearman's rank correlation coefficient ~0.85). At fixed M$_H$, 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 M$_H$ can impact central galaxy assembly.