Variations in the Sigma(SFR)-Sigma(mol)-Sigma(star) plane across galactic environments in PHANGS galaxies

Aims. There exists some consensus that the stellar mass surface density (Sigma(star)) and molecular gas mass surface density (Sigma(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(SFR)), which have been extensively studied in a wide variety of works. 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. Methods. We performed a hierarchical Bayesian linear regression to find the best set of parameters C-star, C-mol, and C-norm that describe the star-forming plane conformed by Sigma(star), Sigma(mol), and Sigma(SFR), such that log Sigma(SFR) = C-star log Sigma(star) + C-mol log Sigma(mol) + C-norm. We also explored variations in the determined parameters across galactic environments, focusing our analysis on the C-star and C-mol slopes. Results. We find signs of variations in the posterior distributions of C-star and C-mol across different galactic environments. The dependence of Sigma(SFR) on Sigma(star) spans a wide range of slopes, with negative and positive values, while the dependence of Sigma(SFR) on Sigma(mol) is always positive. Bars show the most negative value of C-star (-0.41), which is a sign of longer depletion times, while spiral arms show the highest C-star among all environments (0.45). Variations in C-mol also exist, although they are more subtle than those found for C-star. Conclusions. We conclude that systematic variations in the interplay of Sigma(star), Sigma(mol), and Sigma(SFR) across different galactic environments exist at a spatial resolution of 150 pc, and we interpret these variations to be produced by an additional mechanism regulating the formation of stars that is not captured by either Sigma(star) or Sigma(mol). Studying environmental variations in single galaxies, 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.