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 for red central galaxies from the Sloan Digital Sky Survey. In the M _H = 10^11.5-10^13.5 h ⁻¹ M _⊙ range, central galaxy stellar mass (M _*) is correlated with the number density of galaxies within 10 h ⁻¹ Mpc (δ ₁₀), a common proxy for halo formation time. This galaxy assembly bias signal is also present when M _H, M _*, and δ ₁₀ are substituted with group luminosity, galaxy luminosity, and metrics of the large-scale density field. To associate differences in δ ₁₀ with variations in halo formation time, we fitted a model that accounts for (1) errors in the M _H measured by the J. L. Tinker 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 galaxy formation time (from stellar population fitting). These results are indicative that halo properties other than M _H can impact central galaxy assembly.