The GHOSDT Simulations: II. Missing H$_2$ in Simulations of a Self-Regulated Interstellar Medium

TL;DR

The HI-to-H$_2$ transition in self-regulated ISM models underpredicts the molecular fraction at solar neighborhood conditions. By running GHOSDT with 500 Myr durations across a range of resolutions, magnetic-field treatments, feedback variations, and a sub-grid clumping model, the study demonstrates that unresolved small-scale density structure significantly boosts $R_{ m mol}$, bringing simulations closer to observations when included. The most effective approach, FC-m1, yields $R_{ m mol}\approx0.25$, aligning with the Solar-circle value but still below the observed median of $\approx0.42$, implying additional physics may be required. These results underscore the importance of high resolution, pre-SN feedback, magnetic fields, and, especially, sub-grid clumping for realistic H$_2$ formation in galactic patches, and motivate future CO post-processing to enable direct observational comparisons.

Abstract

Observations in the Galaxy and nearby spirals have established that the HI-to-H$_2$ transition at solar metallicity occurs at gas weight of $P_{\rm DE}/k_B\approx 10^4 \ \rm K \ cm ^{-3}$, similar to solar neighbourhood conditions. Even so, state-of-the-art models of a self-regulated interstellar medium underproduce the molecular fraction ($R_{\rm mol} \equiv M_{{\rm H}_2}/M_{HI}$) at solar neighbourhood conditions by a factor of $\approx2-4$. We use the GHOSDT suite of simulations at a mass resolution range of $100-0.25\ M_{\odot}$ (effective spatial resolution range of $\sim 20-0.05\ \rm pc$) run for 500 Myr to show how this problem is affected by modeling choices such as the inclusion of photoionizing radiation, assumed supernova energy, numerical resolution, inclusion of magnetic fields, and including a model for sub-grid clumping. We find that $R_{\rm mol}$ is not converged even at a resolution of 1 $M_{\odot}$, with $R_{\rm mol}$ increasing by a factor of 2 when resolution is improved from 10 to $1\ M_{\odot}$. Models excluding either photoionization or magnetic fields result in a factor 2 reduction in $R_{\rm mol}$. The only model that agrees with the observed value of $R_{\rm mol}$ includes our sub-grid clumping model, which enhances $R_{\rm mol}$ by a factor of $\sim3$ compared with our fiducial model. This increases the time-averaged $R_{\rm mol}$ to $0.25$, in agreement with the Solar circle value, and closer to the observed median value of $0.42$ in regions comparable to the solar neighbourhood in nearby spirals. Our findings show that small-scale clumping in the ISM plays a significant role in H$_2$ formation even in high-resolution numerical simulations.

Figures (5)

• Figure 1: Observational data from the PHANGS--ALMA survey Leroy2021Leroy2021bSun2022. Top panel: $R_{\rm mol}$ as a function of total hydrogen surface density. Middle panel: $R_{\rm mol}$ as a function of gas weight. Bottom panel: $R_{\rm mol}$ as a function of stellar mass surface density for data with $\log \left(\Sigma_{\rm H ,tot}\right/\left( M_{\odot}\ \rm pc^{-2} \right))=1\pm 0.1$. In all panels, the white line shows the median and the red shaded region shows the 25-75% range. The orange lines indicate the intersection of the median and interquartile range with the solar neighbourhood value of $\Sigma_{\star}=40\ M_{\odot}\ \rm pc^{-2}$.
• Figure 2: (a)-(e): The H$_2$-to-H$I$1.2ex mass ratio $R_{\rm mol}$ as a function of time for different simulation groups. (a): Resolution study. (b): Effect of magnetic fields. (c)-(d): Variations to feedback and simulations setup. (e): Effects of our clumping sub-grid model. (f): Time averaged values of $R_{\rm mol}$ for all simulations. Vertical dashed line and shaded region show the observed median and interquartile range for PHANGS-ALMA pixels with $\Sigma_{\rm H,tot}=10$ and $\Sigma_{\star}=40$$M_{\odot}\ \rm pc^{-2}$. Numbers indicate $R_{\rm mol}$ in % for each model.
• Figure 3: Normalized histogram of the total gas mass (violet) and H$_2$ mass (blue) in model m1 (solid lines) and FC-m1 (dashed lines). The black solid and dashed lines show the binned median H$_2$ mass fraction as a function of density for the same models. The shaded regions indicate the density range containing the 25-75% range of H$_2$ mass in the respective models.
• Figure 4: Top panel: $v_{\rm turb}$ as a function of density for models m100, m10, m1, and m0.25. Dashed colored lines show the corresponding solid curves scaled by $\left(m_{\rm g}/M_{\odot}\right)^{-1/6}$. Also shown is the sound speed for m1, which is essentially independent of resolution, and a power law of the form $n^{-1/6}$ for reference. Bottom panel: as top but for $f_c$. The dashed lines show the solid curves scaled according to Equation \ref{['eq: clump scale']}.
• Figure 5: Top panel: normalized mass-weighted density histograms of the total gas mass for simulations in our resolution study, averaged over simulation time 200-500 Myr. The dashed vertical line marks the H$I$1.2ex-to-H$_2$ transition density for our m1 model. Bottom panel: mass-weighted density histogram (solid black) and the modified histogram resulting from our sub-grid model (dashed black; see Section \ref{['section: clumping']}), both for model m1. Colored dashed lines show the modified histogram when applied to density bins with a width of 1 dex.