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

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.

💡 Research Summary

The paper tackles the long‑standing question of why the Kennicutt–Schmidt (KS) relation exhibits nearly constant molecular gas depletion times (τ_dep ≈ 1–3 Gyr) in normal disks, yet shows a super‑linear dependence on total gas surface density (Σ_gas) when atomic gas is included. The authors adopt the “gas‑cycling framework” originally introduced by Semenov et al. (2017), which treats the interstellar medium (ISM) as continuously cycling between a non‑star‑forming (NSF) state and a star‑forming (SF) state. Three characteristic timescales are defined: τ₊, the average time a parcel of gas spends in the NSF state before becoming SF; τ₋, the average lifetime of SF gas before feedback, turbulence, or shear returns it to the NSF state; and τ∗, the depletion time of the SF gas itself (i.e., the time required to convert SF gas into stars). In steady state, the balance of mass fluxes yields a simple expression for the star‑forming fraction f_sf = τ₋/(τ₊+τ₋) and for the global depletion time τ_dep = τ∗ + N_c τ₊, where N_c = τ∗ τ₋/τ₊ is the typical number of cycles a gas parcel undergoes before being turned into stars.

To quantify these timescales, the authors run a suite of high‑resolution, idealized disk galaxy simulations covering three representative environments: a dwarf disk (NGC 300/M33‑like), a Milky Way‑mass disk, and a gas‑rich, high‑redshift starburst analog. Passive tracer particles are embedded in the gas to record the exact moments when each particle transitions between NSF and SF states and when it is destroyed by feedback. The analysis reveals that the formation timescale τ₊ closely matches the vertical turbulent crossing time of the disk, t_cross,⊥ = H/σ_v, where H is the scale height and σ_v the turbulent velocity dispersion. As Σ_gas increases, σ_v rises and H shrinks, driving τ₊ down from ~30 Myr in low‑density disks to ~3 Myr in dense starbursts. The lifetime of SF gas, τ₋, is found to be extremely short, 0.4–1 Myr, and only weakly dependent on Σ_gas; this reflects rapid dispersal by ionizing radiation, stellar winds, supernovae, and turbulent shear. The depletion time of the SF gas itself, τ∗, spans 200–2000 Myr and declines with increasing Σ_gas because denser gas forms stars more efficiently (higher ε_ff ≈ t_ff/τ∗ ≈ 1 %). Consequently, the global depletion time τ_dep is governed primarily by τ₊ and the number of cycles N_c, which itself depends on the ratio τ∗/τ₋. In environments with high Σ_gas, the short τ₊ reduces N_c, leading to modestly shorter τ_dep, while the near‑constant τ∗ maintains the observed ≈1–3 Gyr molecular depletion time across a wide range of galactic conditions.

The authors compare their results to alternative theoretical approaches. Models that tie τ_dep solely to free‑fall times at the mean ISM density fail to capture the strong influence of turbulence and shear on τ₊, leading to over‑estimated formation timescales. Equilibrium disk‑regulation models (e.g., Ostriker & Shetty) successfully reproduce many large‑scale observables but often assume a marginally stable disk without explicitly linking τ₊ to turbulent crossing times. By contrast, the present work demonstrates that the vertical turbulent crossing time is the dominant regulator of how quickly gas becomes star‑forming, while feedback‑driven dispersal sets τ₋, and local dense‑gas free‑fall sets τ∗. The authors encapsulate these findings in simple scaling relations: τ₊ ≈ t_cross,⊥, τ₋ ≈ t_feedback (∼0.5 Myr), and τ∗ ≈ t_ff(dense). These relations provide a physically transparent bridge between observable galactic‑scale quantities (Σ_gas, σ_v, H) and the microscopic gas‑cycle timescales that shape the KS relation.

In summary, the paper delivers a cohesive, multi‑scale picture: galactic‑scale dynamics (gravity, rotation, and turbulence) set the rate at which gas can collapse into star‑forming clouds (τ₊); local cloud physics (density, turbulence, and feedback) determines how efficiently that gas turns into stars (τ∗) and how quickly it is destroyed (τ₋). The interplay of these three timescales naturally reproduces both the near‑constant molecular depletion time and the super‑linear total‑gas KS slope observed in real galaxies. This framework not only clarifies the physical origin of the KS relation but also offers a practical tool for interpreting upcoming high‑resolution observations (e.g., ALMA, JWST) and for improving sub‑grid models in cosmological simulations.