Aims. We investigate the star formation process across M33, which is characterized by a low molecular content and can be sampled with high spatial resolution out to regions where star formation activity drops. Methods. We used a multiwavelength dataset and disk dynamics to extract the local physical parameters across the M33 disk, such as the atomic, molecular, stellar and dust mass surface densities, dark matter densities, and hydrostatic pressure. We computed numerically equilibrium values of gas densities and scale heights across the disk, testing several analytic approximations that are often used to estimate these variables. Orthogonal regressions and hierarchical Bayesian models, as well as random forest (RF) analyses, were used to establish the fundamental relations at physical scales from 160 pc to 1 kpc. Results. The gas hydrostatic pressure, Phy, which balances the local weight, is the main driver of the star formation rate surface density, ΣSFR, throughout the whole star-forming disk of M33. High-pressure regions enhance the atomic-to-molecular gas conversion, with the molecular hydrogen mass surface density, ΣH2, being tightly correlated to Phy and a uniform scaling law throughout the M33 disk. The Phy–ΣSFR relation differs, showing a change in slope from the inner to the outer disk. Our use of an accurate analytic expression and database to compute Phy for a multicomponent disk minimizes observational scatter. This points to scaling laws that do not depend on the physical scale and brings out an intrinsic scatter linked to variations in the efficiency and relative age of the molecular gas-to-stars conversion. In the inner disk, where spiral arms are present and the stellar surface density dominates gravity, Phy and ΣSFR establish an almost linear correlation with a smaller dispersion than in the ΣH2–ΣSFR relation. In the atomic gas-dominated outer disk, ΣSFR has a steeper dependence on Phy, which we propose could be the result of an increasing fraction of diffuse molecular gas that does not form stars.
Corbelli et al. (Tue,) studied this question.