A Bayesian Population Model for the Observed Dust Attenuation in Galaxies

Dust plays a pivotal role in determining the observed spectral energy distribution (SED) of galaxies. Yet our understanding of dust attenuation is limited and our observations suffer from the dust-metallicity-age degeneracy in SED fitting (single galaxies), large individual variances (ensemble measurements), and the difficulty in properly dealing with uncertainties (statistical considerations). In this study, we create a population Bayesian model to rigorously account for correlated variables and non-Gaussian error distributions and demonstrate the improvement over a simple Bayesian model. We employ a flexible 5-D linear interpolation model for the parameters that control dust attenuation curves as a function of stellar mass, star formation rate (SFR), metallicity, redshift, and inclination. Our setup allows us to determine the complex relationships between dust attenuation and these galaxy properties simultaneously. Using Prospector fits of nearly 30,000 3D-HST galaxies, we find that the attenuation slope ($n$) flattens with increasing optical depth ($\tau$), though less so than in previous studies. $\tau$ increases strongly with SFR, though when $\log~{\rm SFR}\lesssim 0$, $\tau$ remains roughly constant over a wide range of stellar masses. Edge-on galaxies tend to have larger $\tau$ than face-on galaxies, but only for $\log~M_*\gtrsim 10$, reflecting the lack of triaxiality for low-mass galaxies. Redshift evolution of dust attenuation is strongest for low-mass, low-SFR galaxies, with higher optical depths but flatter curves at high redshift. Finally, $n$ has a complex relationship with stellar mass, highlighting the intricacies of the star-dust geometry. We have publicly released software (https://github.com/Astropianist/DustE) for users to access our population model.