Dependence of Interstellar Turbulent Pressure on Supernova Rate

Feedback from massive stars is one of the least understood aspects of galaxy formation. We perform a suite of vertically stratified local interstellar medium (ISM) models in which supernova rates and vertical gas column densities are systematically varied based on the Schmidt-Kennicutt law. Our simulations have a sufficiently high spatial resolution (1.95 pc) to follow the hydrodynamic interactions among multiple supernovae that structure the interstellar medium. At a given supernova rate, we find that the mean mass-weighted sound speed and velocity dispersion decrease as the inverse square root of gas density. The sum of thermal and turbulent pressures is nearly constant in the midplane, so the effective equation of state is isobaric. In contrast, across our four models having supernova rates that range from one to 512 times the Galactic supernova rate, the mass-weighted velocity dispersion remains in the range 4–6 km s. Hence, gas averaged over ∼100 pc regions follows P ∝ ρ with α ≈ 1, indicating that the effective equation of state on this scale is close to isothermal. Simulated H I emission lines have widths of 10–18 km s, comparable to observed values. In our highest supernova rate model, superbubble blow-outs occur, and the turbulent pressure on large scales is &4 times higher than the thermal pressure. We find a tight correlation between the thermal and turbulent pressures averaged over ∼100 pc regions in the midplane of each model, as well as across the four ISM models. We construct a subgrid model for turbulent pressure based on analytic arguments and explicitly calibrate it against our stratified ISM simulations. The subgrid model provides a simple yet physically motivated way to include supernova feedback in cosmological simulations. Subject headings: galaxies: formation — ISM: kinematics and dynamics — ISM: structure — methods: numerical — turbulence