Pressure Regulated Formation of Molecular Clouds and Stars: The case of the Milky Way

TL;DR

This paper presents a steady-state analytical framework in which molecular cloud formation is regulated by midplane interstellar pressure $P_{ ext{ISM}}$ and metallicity $Z$, while the onset of star formation is governed by self-gravity at a characteristic threshold. H$_2$ forms on dust grains with a rate that scales with $P_{ ext{ISM}}$ and $T_{100}$, and the HI-H$_2$ transition is set by the dust opacity proxy $ au_d\sim1$, tying the molecular fraction to local pressure and metallicity. A two-step evolution is predicted for $5\lesssim R\lesssim11$ kpc: CNM gas first forms MCs, then self-gravity drives the collapse and star formation, yielding a surface SFR $Σ_{\rm SFR} \approx (1.6{-}4)\times10^{-3}\,(P_{\text{ISM}}/P_{\odot})\,M_⊙\,\text{kpc}^{-2}\,\text{yr}^{-1}$ and a final star formation efficiency $ε_{\rm sf} \sim (3{-}8)\times10^{-2}$. The model reproduces MW radial trends and agrees with EDGE-CALIFA/ALMaQUEST results for $\log(P_{ ext{ISM}}/k) \lesssim 5.5$, highlighting the central role of interstellar pressure in regulating molecular cloud formation and star formation in disk galaxies.

Abstract

We present a steady-state analytical model for pressure-regulated formation of molecular clouds (MC) and stars (SF) in gaseous galactic disks and apply it to the Milky Way (MW). MC formation depends on midplane interstellar pressure $P_{\text{ISM}}$ and metallicity $Z$, and for galactocentric distances $R\gtrsim5$ kpc, $P_{\text{ISM}}(R)$ scales approximately linearly with molecular gas surface density $Σ_{\rm mol}(R)$. The molecularization of the cold neutral medium (CNM) is due to the opacity of small dust grains that protect the center of the cloud from dissociating radiation when the column density is $Σ_d\geq 5\ (Z_\odot/Z)M_\odot\text{ pc}^{-2}$. The H$_2$ formation rate per hydrogen atom is $F\sim10^{-15}(P_{\text{ISM}}/P_\odot)T_{100}^{-1/2}\text{s}^{-1}$, and the corresponding formation rate per unit area is $\dotΣ^{+}_{\rm mol}\sim 5\times10^{-2}\left(P_{\text{ISM}}/{P_\odot}\right)T_{100}^{-1/2}M_\odot~\text{kpc}^{-2}~\text{yr}^{-1}$, where $P_\odot$ 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 $\dotΣ^{-}_{\rm mol}$ due to SF. Self-gravity sets in when the column density of a cloud reaches $Σ_{\rm sg}=Σ_{\rm sg,\odot}(P_{\text{ISM}}/P_\odot)^{1/2}$, with $Σ_{\rm sg,\odot}\sim30\ M_\odot\ \text{pc}^{-2}$. Given the distribution of $P_{\text{ISM}}(R)$ and $Z(R)$ in the MW, the SF process at $5\lesssim R\lesssim11$ kpc follows a two-step track: first, MCs form from CNM gas and then they form stars when self-gravity sets in. The resulting SFR surface density is $Σ_\text{SFR}(R)\approx (1.6-4)\times10^{-3}\left(P_{\text{ISM}}/P_\odot\right)\ \text{M}_\odot~\text {kpc}^{-2}\text{yr}^{-1}$ with an average final SF efficiency of $ε_{\rm sf}\sim (3-8)\times 10^{-2}$.

Figures (5)

• Figure 1: Left Panel: The product of surface gas mass density and total mass surface density (solid line) and the approximate fit (dashed line), as a function of galactocentric radius. Right Panel: The product of the surface gas mass density and total mass surface density divided by the molecular surface gas mass density. This is proportional to the pressure-H$_2$ relation described in the text and shows that $P_\text{ISM}/\Sigma_{\text{H}_{2}}$ is almost constant between 5 and 12 kpc. In both panels, the dotted lines shows the location of our assumed solar circle, $R_\odot=8$ kpc.
• Figure 2: The threshold mass surface density across the whole cloud to become molecular, $2\Sigma_d$ (red line), and the threshold condition to become self-gravitating, $\Sigma_{sg}$ (blue line). Clouds with gas mass surface densities above the red line are molecular (shaded in pink), while those above the blue line are self-gravitating (shaded in blue).
• Figure 3: The median mass surface density between 6 and 10 kpc from the compilation of Miville-Deschenes+2017, as approximated in Ec. (35) (red line). The total H$_2$ surface mass density threshold condition to become self-gravitating of our model, from Ec. (36) (blue line).
• Figure 4: Radial profiles of the star formation rate surface density, $\Sigma_\text{SFR}$, as a function of Galactocentric radius. The solid curve represents the upper bound value in Eq. (\ref{['eq:sfr_profile']}) and the solid red line represents the lower bound. The blue and green shaded regions correspond to data from Hi-GAL clumps and OBA stars, respectively Soler+2023. The purple and beige regions represent estimates based on pulsars, supernova remnants, and HII regions, as reported by Bacchini+2019 and Blitz_Rosolowsky_2006, respectively. The cyan region shows the adopted profile by Bacchini et al. (2019), while the dotted line is the prescription proposed by Blitz_Rosolowsky_2006.
• Figure 5: Comparison of the rates predicted by our model with the results of the EDGE-CALIFA survey Barrera-Ballesteros+21. The shaded contours enclose the 90, 80, and 50% data points of the sample and the dashed line represents their best fit. The solid curve is the upper bound value in Eq. (\ref{['eq:sfr_profile']}) and the solid red line is the lower bound.