Star Formation Law in the Milky Way

Abstract: The Schmidt law (SF law) in the Milky Way was investigated using 3D distribution maps of HII regions, HI and molecular (\Htwo) gases with spatial resolutions of $\sim 1$ kpc in the Galactic plane and a few tens of pc in the vertical direction. HII regions were shown to be distributed in a star-forming (SF) disk with nearly constant vertical full thickness 92 pc in spatial coincidence with the molecular gas disk. The vertically averaged volume star formation rate (SFR) $\rho_{\rm SFR}$ in the SF disk is related to the surface SFR $\Sigma_{\rm SFR}$ by $\rho_{\rm SFR} /[{\rm M_\odot y^{-1} kpc^{-3}}] =9.26\times \Sigma_{\rm SFR}/[{\rm M_\odot y^{-1} kpc^{-2}}]$. The SF law fitted by a single power law of gas density in the form of $\Sigma_{\rm SFR} \propto \rho_{\rm SFR} \propto \rho_{\rm gas}^\alpha$ and $\propto \Sigma_{\rm gas}^\beta$ showed indices of $\alpha=0.78 \pm 0.05$ for $\rho_{\rm H_2}$ and $2.15 \pm 0.08$ for $\rho_{\rm total}$, and $\beta=1.14\pm 0.23$ for $\Sigma_{\rm total}$, where $\rho$ and $\Sigma$ denote volume and surface densities, respectively. The star formation rate is shown to be directly related to the molecular gas, but indirectly to HI and total gas densities. The dependence of the SF law on the gaseous phase is explained by the phase transition theory between HI and H$_2$ gases.