[Paper Review] A Bayesian Population Model for the Observed Dust Attenuation in Galaxies

Gautam Nagaraj, John C. Forbes+3 more|arXiv (Cornell University)|Feb 10, 2022

Galaxies: Formation, Evolution, Phenomena97 references31 citations

TL;DR

This paper introduces a hierarchical Bayesian population model to jointly infer dust attenuation properties—such as the attenuation slope (n) and optical depth (τ)—across 30,000 galaxies from the 3D-HST survey, using stellar mass, SFR, metallicity, redshift, and inclination as predictors. The model uses flexible 5D linear interpolation with marginalized uncertainties and projection-based averaging to resolve degeneracies, revealing that τ increases with SFR, flattens with optical depth, and varies strongly with redshift and geometry, especially in massive, high-SFR galaxies.

ABSTRACT

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 ($ au$), though less so than in previous studies. $ au$ increases strongly with SFR, though when $\log~{ m SFR}\lesssim 0$, $ au$ remains roughly constant over a wide range of stellar masses. Edge-on galaxies tend to have larger $ au$ 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.

Motivation & Objective

• To address the dust-metallicity-age degeneracy in SED fitting by modeling dust attenuation as a function of multiple galaxy properties.
• To improve inference on dust attenuation by accounting for correlated parameters and non-Gaussian error distributions in ensemble galaxy data.
• To develop a flexible, publicly available 5D interpolation model for attenuation curves that depends on stellar mass, SFR, metallicity, redshift, and inclination.
• To demonstrate that population-level modeling outperforms simple Bayesian fitting by incorporating data density and marginalized uncertainties.

Proposed method

• Employs a hierarchical Bayesian model with hyperparameters θ representing interpolated values of dust parameters (n, τ) at control points in a 5D space of galaxy properties.
• Uses 5D linear interpolation to model how dust attenuation varies with M∗, SFR, Z∗, z, and b/a (inclination), enabling smooth, flexible predictions.
• Applies Monte Carlo sampling over posterior distributions of model hyperparameters and Prospector posterior samples to compute marginalized expectations.
• Uses a weighted projection method to average over suppressed dimensions (e.g., redshift, metallicity) using data density as a weight function to avoid bias from sparse regions.
• Incorporates inverse prior weights (1/p(tq, uq|α)) to correct for Prospector’s interim priors when aggregating over galaxy samples.
• Approximates integrals over parameter space via sums over M posterior samples of the population model and Q galaxy-Prospector sample pairs, enabling scalable inference.

Experimental results

Research questions

• RQ1 How does dust attenuation (n and τ) vary with stellar mass, SFR, metallicity, redshift, and inclination in a statistically rigorous way?
• RQ2 To what extent do degeneracies between age, metallicity, and dust affect SED fitting, and how can they be mitigated at the population level?
• RQ3 How do the relationships between dust attenuation and galaxy properties evolve with redshift, especially in low-mass, low-SFR systems?
• RQ4 Can a flexible 5D interpolation model accurately recover known trends in synthetic data while handling non-Gaussian uncertainties?

Key findings

• The attenuation slope (n) flattens with increasing optical depth (τ), though less strongly than in previous studies, indicating a nonlinear dust geometry response.
• Optical depth (τ) increases strongly with SFR, but for log SFR ≤ 0, τ remains nearly constant across a wide range of stellar masses.
• Edge-on galaxies have higher τ than face-on galaxies only for log M∗ ≥ 10, reflecting the lack of triaxial structure in low-mass galaxies.
• Redshift evolution of dust attenuation is most pronounced in low-mass, low-SFR galaxies, which show higher τ and flatter curves at high redshift.
• The relationship between n and stellar mass is complex, revealing non-monotonic behavior that underscores the importance of star-dust geometry.
• The model successfully recovers synthetic trends in test simulations, with minimal systematic bias and accurate intrinsic scatter estimation (log σ recovered as −4.95 and −5.09 vs. simulated −5.30).