Variations in the $\Sigma_{\rm SFR} {-} \Sigma_{\rm mol} {-} \Sigma_{\rm
  \star}$ plane across galactic environments in PHANGS galaxies
  There exists some consensus that stellar mass surface density ($\Sigma_{*}$)
and molecular gas mass surface density ($\Sigma_{\rm mol}$) are the main
quantities responsible for locally setting the star formation rate. This
regulation is inferred from locally resolved scaling relations between these
two quantities and the star formation rate surface density ($\Sigma_{\rm
SFR}$). However, the universality of these relations is debated. Here, we probe
the interplay between these three quantities across different galactic
environments at a spatial resolution of 150 pc. We perform a hierarchical
Bayesian linear regression to find the best set of parameters $C_{*}$, $C_{\rm
mol}$, and $C_{\rm norm}$ that describe the star-forming plane conformed by
these quantities, such that $\log \Sigma_{\rm SFR} = C_{*} \log \Sigma_{*} +
C_{\rm mol} \log \Sigma_{\rm mol} + C_{\rm norm}$, and explore variations in
the determined parameters across galactic environments, focusing our analysis
on the $C_{*}$ and $C_{\rm mol}$ slopes. We find signs of variations in the
posterior distributions of $C_{*}$ and $C_{\rm mol}$ across different galactic
environments. Bars show the most negative value of $C_{*}$, a sign of longer
depletion times, while spiral arms show the highest $C_{*}$ among all
environments. We conclude that systematic variations in the interplay of
$\Sigma_{*}$, $\Sigma_{\rm mol}$ and $\Sigma_{\rm SFR}$ across galactic
environments exist at a spatial resolution of 150 pc, and we interpret these
variations as produced by an additional mechanism regulating the formation of
stars that is not captured by either $\Sigma_{*}$ or $\Sigma_{\rm mol}$. We
find that these variations correlate with changes in the star formation
efficiency across environments, which could be linked to the dynamical state of
the gas that prevents it from collapsing and forming stars, or to changes in
the molecular gas fraction.
