Effect of the heating rate on the stability of the three-phase interstellar medium

We investigate the impact of the far ultraviolet (FUV) heating rate on the stability of the three-phase interstellar medium using three-dimensional simulations of a $1$ kpc$^2$, vertically-extended domain. The FUV heating rate sets the range of thermal pressures across which the cold ($\sim10^2$ K) and warm ($\sim10^4$ K) neutral media (CNM and WNM) can coexist in equilibrium. Even absent a variable star formation rate regulating the FUV heating rate, the gas physics keeps the pressure in the two-phase regime: because radiative heating and cooling processes happen on shorter timescales than sound wave propagation, turbulent compressions tend to keep the interstellar medium within the CNM-WNM pressure regime over a wide range of heating rates. The thermal pressure is set primarily by the heating rate with little influence from the hydrostatics. The vertical velocity dispersion adjusts as needed to provide hydrostatic support given the thermal pressure: when the turbulent pressure $\langle\rho\rangle\sigma_z^2$ is calculated over scales $\gtrsim500$ pc, the thermal plus turbulent pressure approximately equals the weight of the gas. The warm gas volume filling fraction is $0.2<f_w<0.8$ over a factor of less than three in heating rate, with $f_w$ near unity at higher heating rates and near zero at lower heating rates. We suggest that cosmological simulations that do not resolve the CNM should maintain an interstellar thermal pressure within the two-phase regime.