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Flexible Models for Galaxy Star Formation Histories Both Shift and Scramble the Optical Color-M/L Relationship

The remarkably tight relationship between galaxy optical color and stellar mass-to-light ratio ($M_*/L$) is widely used for efficient stellar mass estimates. However, it remains unclear whether this low scatter comes from a natural order in the galaxy population, or whether it is driven by simple relationships in the models used to describe them. In this work we investigate the origins of the relationship by contrasting the derived relationship from a simple 4-parameter SED model with a more sophisticated 14-dimensional Prospector-$α$ model including nonparametric star formation histories (SFHs). We apply these models to 63,430 galaxies at $0.5<z<3$ and fit a hierarchical Bayesian model (HBM) to the population distribution in the $(g-r)$--$\log(M/L_g)$ plane. We find that Prospector-$α$ infers systematically higher $M_*/L$ by 0.12 dex, a result of nonparametric SFHs producing older ages, and also systematically redder rest-frame $(g-r)$ by 0.06 mag owing to the contribution from nebular emission. Surprisingly, the combined effects of the $M_*/L$ and $(g-r)$ offsets produce a similar average relationship for the two models, though Prospector-$α$ produces a higher scatter of 0.28 dex compared to the simple model of 0.12 dex. Also, unlike the simple model, the Prospector-$α$ relationship shows substantial redshift evolution due to stellar aging. These expected and testable effects produce overall older and redder galaxies, though the color--$M_*/L$ relationship is measured only at $0.5<z<3$. Finally, we demonstrate that the HBM produces substantial shrinkage in the individual posteriors of faint galaxies, an important first step toward using the observed galaxy population directly to inform the SED fitting priors.