The Rhythm of the ISM: Tracing the Timescales of Gas Evolution and Star Formation across Galactic Environments

TL;DR

This paper demonstrates that kiloparsec-scale star formation scaling relations arise from a rapid ISM gas-cycle whose miniaturized timescales ($\tau_{+}$ for supply, $\tau_{-}$ for removal, and $\tau_{*}$ for local depletion) are governed by ISM turbulence and disk structure. By analyzing three isolated-galaxy simulations with 1 kpc patches and passive gas tracers, the authors measure these timescales and show that $\tau_{+}$ tracks the vertical turbulent crossing time $t_{cross,z}$, while $\tau_{*}$ shortens with increasing $\Sigma_{gas}$ due to higher densities and modestly higher $\epsilon_{ff}$, and $\tau_{-}$ remains very short ($\sim0.8$ Myr). The framework yields global depletion time $\tau_{dep}$ and star-forming gas fraction $f_{sf}$ relations that reproduce the observed trends, with $\tau_{dep} \propto \Sigma_{gas}^{-1.46}$ and $f_{sf} \propto \Sigma_{gas}^{0.65}$, connecting galaxy-scale star formation to ISM turbulence and vertical disk structure. The results imply that local environment, encapsulated by $\Sigma_{gas}$, largely sets kiloparsec-scale SF properties, while global galaxy differences emerge from the range of $\Sigma_{gas}$ sampled, and suggest extensions to higher-density or non-disk regimes where the gas cycle could operate differently.

Abstract

We investigate the physical origin of the star formation scaling relations between the gas depletion time, the star-forming gas mass fraction, and the gas surface density, $Σ_{\rm gas}$, on kiloparsec scales, all of which are the key ingredients of the observed Kennicutt-Schmidt relation. To elucidate these trends, we employ an analytical framework that explicitly connects these kiloparsec-scale properties to the timescales governing the rapid, continuous ISM gas cycle on the scales of individual star-forming regions, including the formation, dispersal, and local depletion of star-forming gas. Using a suite of idealized disk galaxy simulations spanning a range of environments from dwarf and Milky Way-mass systems to a gas-rich starburst analog, we measure the timescales of the gas cycle and relate them to the dynamical and turbulent properties of the interstellar medium (ISM). We find that star-forming regions form on a timescale close to the vertical turbulent crossing time of the galactic disk, $\sim$3-30 Myr, which decreases at higher $Σ_{\rm gas}$ due to the increase in turbulent velocities in the ISM and the decrease in the disk thickness. In contrast, the local star formation and dispersal of such gas are set by the local conditions. Specifically, the local depletion time, $\sim$200-2000 Myr, is decreasing at higher $Σ_{\rm gas}$, as star-forming gas becomes denser and more efficient in forming stars. The lifetime of such gas is very short, $\sim$0.4-1 Myr, and only weakly increases with $Σ_{\rm gas}$. Together, our results demonstrate how the star formation properties of galaxies on kiloparsec scales emerge directly from the interplay between the galaxy-scale dynamics, ISM turbulence, and the state of star-forming gas.

Figures (13)

• Figure 1: Illustration explaining the gas cycling in our model. The removal timescale $\tau_{\rm -}$ represents the average lifetime of gas in the star-forming state before being dispersed by feedback or other dynamical processes. The supply timescale $\tau_{\rm +}$ is the average time gas spends in the non-star-forming state before becoming star-forming. Once in the star-forming state, gas is converted into stars on a timescale $\tau_{\rm *}$. We select the star-forming gas as the gas with $\alpha_{\rm vir} < \alpha_{\rm vir, sf} = 20$, which corresponds to $\epsilon_{\rm ff} > 0.002$ (dotted line; see the text). The dashed and dash-dotted lines show $\alpha_{\rm vir} = 10.7$ and $\alpha_{\rm vir} = 4.43$, respectively, which corresponds to $\epsilon_{\rm ff} = 0.01$ and $\epsilon_{\rm ff} = 0.05$ (see Equation \ref{['eq:epsff_P12']}). These $\alpha_{\rm vir}$ values roughly correspond to all, average, and the most active star formation. The environments in which these regimes occur are shown in Figure \ref{['fig:eff_map']} in purple, blue and orange, respectively. Importantly, the gas distribution in the $(n, \sigma_{\rm tot})$ plane determines how much gas lies below each of these $\alpha_{\rm vir}$ values. This distribution therefore affects the amount of gas in the star-forming state, the resulting star-formation efficiency, and ultimately the depletion time. As a consequence, the star-forming fraction and depletion time depend sensitively on the local environment.
• Figure 2: Slices of the three simulated galaxies used in this study, showing the star-forming regions identified with different $\epsilon_{\rm ff}$ values. Here $0.002 \le \epsilon_{\rm ff} < 0.01$ (purple), $0.01 \le \epsilon_{\rm ff} < 0.05$ (blue), and $\epsilon_{\rm ff} \ge 0.05$ (orange) correspond respectively to all, average, and the most active star formation. These selections are equivalent to applying virial-parameter cuts of $\alpha_{\rm vir} < 20$, $10.7$, and $4.43$ (see Equation \ref{['eq:epsff_P12']}). The contrast between the intermediate dwarf, $L_*$, and gas-rich galaxies (see Section \ref{['sec:sims']} for their descriptions) demonstrates that the fraction and spatial distribution of star-forming gas depend strongly on the kiloparsec-scale environment. For reference, the grayscale background shows $\Sigma_{\rm gas}$ smoothed on a scale smaller than 1 kpc for visual purposes, as it preserves some details of the underlying ISM structure.
• Figure 3: Relation between the star formation rate surface density, $\Sigma_{\rm SFR}$, and the total (left panel) and molecular (right panel) gas surface densities in our simulated galaxies, compared to observational constraints. We show 1-kpc–patch–averaged median relations for the intermediate dwarf (orange), $L_\star$ galaxy (purple), and gas-rich galaxy (blue), with shaded regions indicating the 16--84th percentile scatter. To illustrate the effect of our H i and H$_2$ selection, the purple dashed line in the left panel also shows the total gas KSR for the $L_\star$ galaxy, i.e., with $\Sigma_{\rm gas}$ instead of $\Sigma_{\rm H{\textsc{i}}+H_2}$. Dashed straight lines correspond to the constant depletion times $\tau_{\rm dep}$ of 0.1 (black), 1 (gray), and 10 Gyr (light gray). In the left panel, our $\Sigma_{\rm H{\textsc{i}}+H_2}$–$\Sigma_{\rm SFR}$ relations are compared to observations of nearby spiral galaxies from bigiel_star_2008bigiel_extremely_2010, and of the Milky Way from Misiriotis_2006. In the right panel, we compare the $\Sigma_{\rm H_2}$–$\Sigma_{\rm SFR}$ relations to observational measurements from leroy_molecular_2013ellison20sun23villanueva24wong24. Additionally, the right panel includes a dash–dotted olive contour indicating the range $\tau_{\rm dep,H_2} \sim 0.5–2$ Gyr, estimated from radial profiles of $\Sigma_{\rm SFR}$ and $\Sigma_{\rm H_2}$ compiled in Fig. 7 of Kennicutt_2012, as well as a dash-dotted teal contour showing the corresponding range reported for NGC300 kruijssen_fast_2019
• Figure 4: Comparison between the relations measured directly from the three simulations (left column) with those predicted using our gas-cycling framework outlined in Section \ref{['sec:model_overview']} (middle column) and by our simple model summarized in Section \ref{['sec:model_summary']} (right columns). Shown are the global depletion time, $\tau_{\rm dep}$ (top row), and the star-forming gas fraction, $f_{\rm sf}$ (bottom row), both as functions of the gas surface density, $\Sigma_{\rm gas}$. In the middle column, we show the predictions of our framework obtained by explicitly measuring the characteristic timescales of the gas cycle ($\tau_{\rm +}$, $\tau_{\rm -}$, and $\tau_{\rm *}$) using passive gas tracer particles and substituting them into Equations \ref{['eq:fsf']}--\ref{['eq:Nc']}. The right column shows model predictions based on simple, physically motivated prescriptions for $\tau_{\rm +}$, $\tau_{\rm -}$, and $\tau_{\rm *}$, which we derive in Sections \ref{['sec:tau_plus']}--\ref{['sec:tau_minus']}. Solid lines show the 1 kpc patch medians for the intermediate dwarf (orange), $L_*$ galaxy (purple), and gas-rich galaxy (blue), while the purple dashed line in the bottom right panel shows a prediction with $\tau_{\rm -}$ calculated with tracer particles for the $L_*$ galaxy (see the text for details). For easier visual comparison, the black dashed lines show power-law fits to the measured medians, $\tau_{\rm dep} \propto {\Sigma_{\rm gas}}^{-1.46}$ and $f_{\rm sf} \propto {\Sigma_{\rm gas}}^{0.65}$. Shaded regions indicate the 16--84th percentile scatter. The close match between the measured values and theoretical predictions demonstrates that the model successfully reproduces the dependence of star formation properties on gas surface density across a wide range of galactic environments.
• Figure 5: Dependence of the characteristic model timescales $\tau_{\rm +}$, $\tau_{\rm *}$, and $\tau_{\rm -}$ on gas surface density, $\Sigma_{\rm gas}$. The solid lines show the median values as measured in the simulation, while the purple dashed line shows predictions from the simple model, for the $L_*$ galaxy only (summarized in Section \ref{['sec:model_summary']}). As $\Sigma_{\rm gas}$ increases, gas enters denser star-forming regions, resulting in shorter average depletion and supply timescales, $\tau_{\rm *}$ and $\tau_{\rm +}$. This trend reflects the higher densities and more efficient compression of gas into the star-forming state at high $\Sigma_{\rm gas}$. In contrast, the removal timescale $\tau_{\rm -}$ increases with $\Sigma_{\rm gas}$, as denser gas is more resistant to dispersal by feedback or turbulent motions.