Characterizing Density and Gravitational Potential Fluctuations of the Interstellar Medium

Substructure in the interstellar medium (ISM) is crucial for establishing the correlation between star formation and feedback and has the capacity to significantly perturb stellar orbits, thus playing a central role in galaxy dynamics and evolution. Contemporary surveys of gas and dust emission in nearby galaxies resolve structure down to $\sim 10,$pc scales, demanding theoretical models of ISM substructure with matching fidelity. In this work, we address this need by quantitatively characterizing the gas density in state-of-the-art MHD simulations of disk galaxies that resolve pc to kpc scales. The TIGRESS-NCR framework we employ includes sheared galactic rotation, self-consistent star formation and feedback, and nonequilibrium chemistry and cooling. We fit simple analytic models to the one-point spatial, two-point spatial, and two-point spatio-temporal statistics of the surface density fluctuation field. We find that for both solar neighborhood and inner-galaxy conditions, (i) the surface density fluctuations follow a log-normal distribution, (ii) the linear and logarithmic fluctuation power spectra are well-approximated as power laws with indices of $\approx -2.2$ and $\approx -2.8$ respectively, and (iii) lifetimes of structures at different scales are set by a combination of feedback and effective pressure terms. Additionally, we find that the vertical structure of the gas is well-modeled by a mixture of exponential and sech$^2$ profiles, allowing us to link the surface density statistics to those of the volume density and gravitational potential. We provide convenient parameterizations for incorporating realistic ISM effects into stellar-dynamical studies and for comparison with multi-wavelength observations.

💡 Research Summary

This paper presents a comprehensive statistical characterization of interstellar medium (ISM) density and gravitational potential fluctuations in galactic disks, using the state‑of‑the‑art TIGRESS‑NCR magnetohydrodynamic (MHD) simulations. TIGRESS‑NCR builds upon the earlier TIGRESS‑classic framework by adding non‑equilibrium chemistry, radiation transfer, and photo‑electric heating from far‑ultraviolet (FUV) and extreme‑ultraviolet (EUV) photons, while resolving scales from a few parsecs up to several kiloparsecs. The authors analyze two representative environments – a Solar‑neighbourhood patch and an inner‑galaxy region – both modeled with a flat rotation curve (shear parameter q = 1) in a shearing‑box domain.

The core of the analysis focuses on the two‑dimensional surface‑density fluctuation field Σ(x, y, t). First, the one‑point probability density function (PDF) of Σ is measured and found to be exceptionally well described by a log‑normal distribution. The log‑normal parameters (mean μ and standard deviation σ) differ modestly between the two environments (σ≈0.3 for the Solar neighbourhood, σ≈0.5 for the inner galaxy), reflecting the higher level of turbulence and compression in the latter.

Next, the authors compute two‑point spatial statistics. The power spectrum of the linear surface density, PΣ(k) ∝ k^−α, follows a power‑law with index α≈2.2 ± 0.1 over the range 10 pc ≲ ℓ ≲ 1 kpc. When the logarithm of the surface density is used, the spectrum steepens to α≈2.8 ± 0.1, indicating that small‑scale density contrasts are more strongly suppressed in the log‑space representation. These slopes are remarkably similar for both simulated environments, suggesting that the underlying turbulent cascade and feedback processes are largely scale‑invariant.

Temporal behavior is probed through the spatio‑temporal correlation function C(k, Δt)=⟨Σk(t) Σk*(t+Δt)⟩. The decay of C with lag Δt is well fit by an exponential, defining a scale‑dependent lifetime τ(k) that obeys τ(k) ∝ k^−β with β≈0.5–0.7. Large‑scale structures (k ≈ 0.01 pc⁻¹, ℓ ≈ 100 pc) persist for 20–30 Myr, while small‑scale features (k ≈ 0.1 pc⁻¹, ℓ ≈ 10 pc) dissolve within 1–5 Myr. The authors interpret this dichotomy as a competition between supernova/H II‑region driven pressure bursts (which dominate the long‑lived, large‑scale component) and the combined thermal, magnetic, and turbulent pressure that rapidly erodes small‑scale overdensities.

The vertical structure of the gas is examined by fitting the height‑dependent surface density Σ(z). A single exponential or a pure sech² profile cannot reproduce the simulated profiles; instead a weighted sum of an exponential and a sech² term provides an excellent fit: Σ(z)=A exp(−|z|/h₁)+B sech²(z/h₂), with scale heights h₁≈30 pc and h₂≈150 pc, and amplitude ratio A/B≈0.3–0.5. This mixed model captures a thin, dense mid‑plane layer coexisting with a more extended, diffuse component. Using this vertical decomposition, the authors analytically map surface‑density statistics to three‑dimensional volume‑density (ρ) and gravitational‑potential (Φ) statistics. The volume‑density PDF remains log‑normal, while the potential PDF exhibits a slight skewness due to the smoothing effect of Poisson’s equation. The potential power spectrum is slightly shallower than that of Σ, with an index ≈2.4, reflecting the suppression of high‑k fluctuations by the long‑range nature of gravity.

Crucially, the paper translates all these statistical findings into a compact set of parameterizations suitable for inclusion in stellar‑dynamical models. The proposed “ISM sub‑grid” module supplies: (i) log‑normal density fluctuations (μ, σ); (ii) power‑law spectra (α for Σ, αΦ for Φ); (iii) scale‑dependent lifetimes τ₀ k^−β; and (iv) vertical profile parameters (A, B, h₁, h₂). These ingredients can be sampled to generate synthetic, time‑varying gravitational fields that mimic realistic ISM turbulence without the need to resolve the full MHD dynamics. The authors also provide direct comparisons to multi‑wavelength observations (e.g., PHANGS CO and dust maps), showing that the simulated power spectra and PDFs match observed trends within uncertainties.

In summary, this work delivers a rigorous, multi‑scale statistical description of ISM density and potential fluctuations from high‑resolution, physics‑rich simulations, and packages the results into user‑friendly formulas. The outcomes enable more realistic modeling of stellar orbital heating, radial migration, and disk heating in galactic dynamics studies, while also offering a benchmark for interpreting high‑resolution ISM observations.