The ALMaQUEST Survey. XVI. The Balmer decrement as a probe of molecular gas in nearby kiloparsec-resolved galaxies

Abstract

We investigate the relation between molecular gas and dust extinction on kiloparsec scales. We analysed 15,253 spaxels across 51 nearby galaxies with CO(1--0) measurements and optical spectroscopy from the ALMA-MaNGA QUEnching and STar formation (ALMaQUEST) survey. Dust extinction was traced by the Balmer decrement (Hα/Hβ), while molecular gas was traced by the CO(1--0) line intensity (I_ CO). Focusing on the 12,173 spaxels classified as star-forming, we found a significant and robust correlation between Hα/Hβ and I_̊m CO (Pearson r = 0.61, Spearman ̊ho = 0.59). This correlation becomes even stronger when considering deprojected quantities ( r = 0.65, ̊ho = 0.64), revealing a close connection between the effective V-band optical depth (τ_V) inferred from the Balmer decrement and the molecular gas surface density (Σ_̊m mol), derived assuming a constant CO-to-H_2 conversion factor. The observed Σ_̊m mol--τ_V relation is sub-linear, deviating from the expectation for a simple foreground-screen geometry and suggesting a more complex distribution of dust, molecular gas, and emitting regions, and/or variations in the CO-to-H_2 conversion factor. Existing literature prescriptions fail to reproduce the observed distribution over the full extinction range. We parametrized this relation and derived a new empirical calibration linking Σ_̊m mol and τ_V. The relation is largely independent of galaxy stellar mass, star formation rate, gas-phase metallicity, morphology, and specific star formation rate, but it shows a secondary dependence primarily on inclination, highlighting the role of geometry. The relation becomes less tight in both composite and active galactic nucleus (AGN)-dominated regions, which exhibit a substantially larger scatter than star-forming regions. Using the independent EDGE--CALIFA dataset, we show that the ALMaQUEST calibration predicts Σ_̊m mol with a scatter of ∼ 0.3 dex and no significant systematic offset (-0.01 dex), demonstrating its applicability to independent kiloparsec-scale datasets. Our calibration thus provides a practical empirical method for estimating molecular gas surface density from optical spectroscopy alone, without requiring direct CO observations.