2025MNRAS.543.2507F

We present a steady-state analytical model for pressure-regulated formation of molecular clouds (MC) and stars in gaseous galactic discs and apply it to the Milky Way (MW). MC formation depends on mid-plane interstellar pressure $P_{\mathrm{ISM}}$ and metallicity Z, and for galactocentric distances $R\gtrsim 5$ kpc, $P_{\mathrm{ISM}}(R)$ scales approximately linearly with molecular gas surface density $\Sigma _{\rm mol}(R)$. The molecularization of the cold neutral medium (CNM) is due to the opacity of small dust grains that protect the centre of the cloud from dissociating radiation when the column density is $\Sigma _{\rm d}\ge 5 ({\rm Z}_\odot/Z) \, {\rm M}_\odot \, \text{pc}^{-2}$. The H$_2$ formation rate per hydrogen atom is $F\sim 10^{-15} (P_{\mathrm{ISM}}/{\rm P}_\odot)T_{100}^{-1/2} \, \text{s}^{-1}$, and the corresponding formation rate per unit area is $\dot{\Sigma }^{+}_{\rm mol}\sim 5 \times 10^{-2}\left(P_{\mathrm{ISM}}/{{\rm P}_\odot }\right)T_{100}^{-1/2} \, {\rm M}_\odot \, \text{kpc}^{-2} \, \text{yr}^{-1}$, where ${\rm P}_\odot$ is the pressure at the solar circle and $T_{100}=T/100 \, \text{K}$ is the temperature of the cloud. In equilibrium, this equals the molecular gas destruction rate $\dot{\Sigma }^{-}_{\rm mol}$ due to star formation. Self-gravity sets in when the column density of a cloud reaches $\Sigma _{\rm sg}=\Sigma _{\rm sg,\odot }(P_{\mathrm{ISM}}/{\rm P}_\odot)^{1/2}$, with $\Sigma _{\rm sg,\odot }\sim 30\, {\rm M}_\odot \, \text{pc}^{-2}$. Given the distribution of $P_{\mathrm{ISM}}(R)$ and $Z(R)$ in the MW, the star formation process at $5\lesssim R\lesssim 11$ kpc follows a two-step track: first, MCs form from CNM gas and then they form stars when self-gravity sets in. The resulting star formation rate surface density is $\Sigma _\text{SFR}(R)\approx (1.6\!-\!4)\times 10^{-3}\left(P_{\mathrm{ISM}}/{\rm P}_\odot \right)\, \text{M}_\odot \, \text{kpc}^{-2} \, \text{yr}^{-1}$ with an average final star formation efficiency of $\epsilon _{\rm sf}\sim (3\!-\!8)\times 10^{-2}$.