SDSS-IV MANGA: A Star Formation -- Baryonic Mass Relation at Kpc Scales

Star formation rate density, $Σ_{\rm SFR}$, has shown a remarkable correlation with both components of the baryonic mass at kpc scales (i.e., the stellar mass density, and the molecular gas mass density; $Σ_{\ast}$, and $Σ_{\rm mol}$, respectively) for galaxies in the nearby Universe. In this study we propose an empirical relation between $Σ_{\rm SFR}$ and the baryonic mass surface density ($Σ_{\rm b}$ =$Σ_{\rm mol,Av}$ + $Σ_{\ast}$; where $Σ_{\rm mol,Av}$ is the molecular gas density derived from the optical extinction, Av) at kpc scales using the spatially-resolved properties of the MaNGA survey - the largest sample of galaxies observed via Integral Field Spectroscopy (IFS, $\sim$ 8400 objects). We find that $Σ_{\rm SFR}$ tightly correlates with $Σ_{\rm b}$. Furthermore, we derive an empirical relation between the $Σ_{\rm SFR}$ and a second degree polynomial of $Σ_{\rm b}$ yielding a one-to-one relation between these two observables. Both, $Σ_{\rm b}$ and its polynomial form show a stronger correlation and smaller scatter with respect to $Σ_{\rm SFR}$ than the relations derived using the individual components of $Σ_{\rm b}$. Our results suggest that indeed these three parameters are physically correlated, suggesting a scenario in which the two components of the baryonic mass regulate the star-formation activity at kpc scales.