The EDGE-CALIFA survey: Using optical extinction to probe the spatially resolved distribution of gas in nearby galaxies

We present an empirical relation between the cold gas surface density (Σ_gas) and the optical extinction (A_V) in a sample of 103 galaxies from the Extragalactic Database for Galaxy Evolution (EDGE) survey. This survey provides CARMA interferometric CO observations for 126 galaxies included in the Calar Alto Legacy Integral Field Area (CALIFA) survey. The matched, spatially resolved nature of these data sets allows us to derive the Σ_gas-A_V relation on global, radial, and kpc (spaxel) scales. We determine A_V from the Balmer decrement (H α/H β). We find that the best fit for this relation is Σ_gas (M☉ pc⁻²) ∼ 26 × A_V (mag), and that it does not depend on the spatial scale used for the fit. However, the scatter in the fits increases as we probe smaller spatial scales, reflecting the complex relative spatial distributions of stars, gas, and dust. We investigate the Σ_gas/A_V ratio on radial and spaxel scales as a function of EW(H α). We find that at larger values of EW(H α ) (i.e. actively star-forming regions) this ratio tends to converge to twice the value expected for a foreground dust screen geometry (∼30 M☉ pc⁻² mag⁻¹). On radial scales, we do not find a significant relation between the Σ_gas/A_V ratio and the ionized gas metallicity. We contrast our estimates of Σ_gas using A_V with compilations in the literature of the gas fraction on global and radial scales as well as with well-known scaling relations such as the radial star formation law and the Σ_gas-Σ_∗ relation. These tests show that optical extinction is a reliable proxy for estimating Σ_gas in the absence of direct sub/millimeter observations of the cold gas.