Unravelling the Dust Attenuation Scaling Relations and their Evolution

We explore the dependence of dust attenuation, as traced by the $\rm H_{\alpha}/\rm H_{\beta}$ Balmer decrement, on galactic properties by using a large sample of SDSS spectra. We use both Partial Correlation Coefficients (PCC) and Random Forest (RF) analysis to distinguish those galactic parameters that directly and primarily drive dust attenuation in galaxies, from parameters that are only indirectly correlated through secondary dependencies. We find that, once galactic inclination is controlled for, dust attenuation depends primarily on stellar mass, followed by metallicity and velocity dispersion. Once the dependence on these quantities is taken into account, there is no dependence on star formation rate. While the dependence on stellar mass and metallicity was expected based on simple analytical equations for the interstellar medium, the dependence on velocity dispersion was not predicted and we discuss possible scenarios to explain it. We identify a projection of this multi-dimensional parameters space which minimises the dispersion in terms of the Balmer decrement and which encapsulates the primary and secondary dependences of the Balmer decrement into a single parameter defined as the reduced mass $\mu = \log {\rm M}_{\star} +3.67 [{\rm O/H}] + 2.96 \log (\sigma_v/100~km~s^{-1})$. We show that the dependence of the Balmer decrement on this single parameter also holds at high redshift, suggesting that the processes regulating dust production and distribution do not change significantly through cosmic epochs at least out to z$\sim$2.