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.
