The volumetric star formation law for nearby galaxies. Extension to dwarf galaxies and low-density regions

In the last decades, much effort has been put into finding the star formation law which could unequivocally link the gas and the star formation rate (SFR) densities measured on sub-kiloparsec scale in star-forming galaxies. The conventional approach of using the observed surface densities to infer star formation laws has however revealed a major and well-known issue, as such relations are valid for the high-density regions of galaxies but break down in low-density and HI-dominated environments. Recently, an empirical correlation between the total gas (HI+H$_2$) and the star formation rate (SFR) volume densities was obtained for a sample of nearby disc galaxies and for the Milky Way. This volumetric star formation (VSF) law is a single power-law with no break and a smaller intrinsic scatter with respect to the star formation laws based on the surface density. In this work, we explore the VSF law in the regime of dwarf galaxies in order to test its validity in HI-dominated, low-density, and low-metallicity environments. In addition, we assess this relation in the outskirts of spiral galaxies, which are low-density and HI-dominated regions similar to dwarf galaxies. Remarkably, we find the VSF law, namely $\rho_\mathrm{SFR} \propto \rho_\mathrm{gas}^\alpha$ with $\alpha \approx 2$, is valid for both these regimes. This result indicates that the VSF law, which holds unbroken for a wide range of gas ($\approx 3$ dex) and SFR ($\approx 6$ dex) volume densities, is the empirical relation with the smallest intrinsic scatter and is likely more fundamental than surface-based star formation laws.