The volumetric star formation law in the Milky Way

Several open questions on galaxy formation and evolution have their roots in the lack of a universal star formation law that could univocally link the gas properties, such as its density, to the star formation rate (SFR) density. In a recent paper we used a sample of nearby disc galaxies to infer the volumetric star formation (VSF) law, a tight correlation between the gas and the SFR volume densities derived under the assumption of hydrostatic equilibrium for the gas disc. However, due to the dearth of information about the vertical distribution of the SFR in these galaxies, we could not find a unique slope for the VSF law, but two alternative values. In this paper, we use the scale height of the SFR density distribution in our Galaxy adopting classical Cepheids (age less than or similar to 200 Myr) as tracers of star formation. We show that this latter is fully compatible with the flaring scale height expected from gas in hydrostatic equilibrium. These scale heights allowed us to convert the observed surface densities of gas and SFR into the corresponding volume densities. Our results indicate that the VSF law rho(SFR) proportional to rho(alpha)(gas)rho SFR proportional to rho gas alphaSFR is valid in the Milky Way as well as in nearby disc galaxies.