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 .