Characterizing Density and Gravitational Potential Fluctuations of the Interstellar Medium

TL;DR

The paper addresses how interstellar medium (ISM) substructure perturbs star formation and stellar orbits by quantifying surface-density fluctuations in high-fidelity TIGRESS-NCR MHD simulations. It develops analytic, small-complexity models for the 2D surface-density statistics (one-point PDFs and two-point power spectra) and their 3D extensions to density and gravitational potential using a separable vertical structure with a mixed sech$^2$/exponential profile; temporal behavior is captured by a dispersion relation with $\tau_0 \approx 5$ Myr and $v_{\mathrm{eff}} \approx 10$–$12$ km s$^{-1}$. The main empirical results are that the logarithmic surface-density fluctuations are Gaussian with a time-varying width, the power spectra follow steep power laws with $n_\delta \approx 2.2$ and $n_s \approx 2.8$, and most power resides at large scales; the vertical structure yields a mean potential and scale-dependent fluctuation amplitudes that can be efficiently used in stellar-dynamical calculations. Together, these parameterizations enable realistic incorporation of ISM perturbations into orbital dynamics and provide a framework for direct comparison with multi-wavelength observations, while also highlighting the role of anisotropy and non-Gaussianity in the ISM.

Abstract

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.

Figures (22)

• Figure 1: Snapshots of the gas surface density $\Sigma$ at different times in the R8 (top row) and LGR4 (bottom row) TIGRESS-NCR simulations.
• Figure 2: A snapshot of the linear surface density fluctuation $\delta$ (left) and logarithmic surface density fluctuation $s$ (right) for the R8 simulation at $t = 350\,$Myr. This is the same snapshot as in panel (c) of \ref{['fig:snapshots']}.
• Figure 3: Histograms of the values of the logarithmic density fluctuation $s(\mathbf{x},t)$ measured at the simulation grid scale for the R8 (left, purple) and LGR4 (right, orange) simulations. The solid curves show the time-averaged histograms, while the shaded regions indicate $\pm 1\sigma$ variations about the values in each bin. A Gaussian with standard deviation $\sigma_s$ (corresponding to the measured standard deviation in the time-averaged values) and mean $\mu_s = -\sigma_s^2 / 2$ is overplotted as a black dashed curve.
• Figure 4: The standard deviation in $s=\ln(\Sigma(\mathbf{x},t)/\overline{\Sigma}(t))$ as a function of time for the R8 (purple) and LGR4 (orange) simulations. The light purple and orange dashed lines show the value calculated from the time-averaged distributions shown in \ref{['fig:s_pdfs']} respectively.
• Figure 5: The standard deviation in $s \equiv \ln(\Sigma/\overline{\Sigma})$ as a function of scale for the R8 (purple) and LGR4 (orange) simulations. The left panel shows the standard deviation calculated after smoothing with a window function that is sharp in $k$-space (\ref{['eq:window_sharpk']}), while the right panel uses a window function that is sharp in real space (\ref{['eq:window_sharpreal']}). The dashed curves in each panel are calculated assuming the model isotropic power-law spectrum measured from fits to each simulation (see \ref{['eq:power_Sigma_spatial']} and \ref{['tab:power_k_measurements']} below).