The ALMaQUEST Survey IX: The nature of the resolved star forming main sequence

We investigate the nature of the scaling relations between the surface density of star formation rate ($\Sigma _{\rm SFR}$), stellar mass ($\Sigma _*$), and molecular gas mass ($\Sigma _{\rm H_2}$), aiming at distinguishing between the relations that are primary, i.e. more fundamental, and those which are instead an indirect by-product of the other relations. We use the ALMaQUEST survey and analyse the data by using both partial correlations and Random Forest regression techniques. We unambiguously find that the strongest intrinsic correlation is between $\Sigma _{\rm SFR}$ and $\Sigma_{\rm H_2}$ (i.e. the resolved Schmidt-Kennicutt relation), followed by the correlation between $\Sigma _{\rm H_2}$ and $\Sigma _*$ (resolved Molecular Gas Main Sequence, rMGMS). Once these two correlations are taken into account, we find that there is no evidence for any intrinsic correlation between $\Sigma _{\rm SFR}$ and $\Sigma _*$, implying that SFR is entirely driven by the amount of molecular gas, while its dependence on stellar mass (i.e. the resolved Star Forming Main Sequence, rSFMS) simply emerges as a consequence of the relationship between molecular gas and stellar mass.