  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) simulations 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 ISM. 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,
indicating that both thermal and turbulent pressures are 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 an effective
equation of state that 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.
