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.