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, e.g. 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$\lesssim 200$ 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 $\rho_\mathrm{SFR} \propto
\rho_\mathrm{gas}^\alpha$ with $\alpha \approx 2$ is valid in the Milky Way as
well as in nearby disc galaxies.
