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.