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.
