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 ^ { -1 } .
Hence , gas averaged over \sim 100 pc regions follows P \propto \rho ^ { \alpha } with \alpha \approx 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 ^ { -1 } , comparable to observed values .
In our highest supernova rate model , superbubble blow-outs occur , and the turbulent pressure on large scales is \gtrsim 4 times higher than the thermal pressure .
We find a tight correlation between the thermal and turbulent pressures averaged over \sim 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 .