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We explore the self-regulation of star formation using a large suite of highresolution hydrodynamic simulations, focusing on molecule-dominated regions(galactic centers and [U]LIRGS) where feedback from star formation driveshighly supersonic turbulence. In equilibrium the total midplane pressure,dominated by turbulence, must balance the vertical weight of the ISM. Underself-regulation, the momentum flux injected by feedback evolves until itmatches the vertical weight. We test this flux balance in simulations spanninga range of parameters, including surface density $\Sigma$, momentum injectedper stellar mass formed ($p_*/m_*$), and angular velocity. The simulations are2D radial-vertical slices, including both self-gravity and an externalpotential that confines gas to the disk midplane. After the simulations reach asteady state in all relevant quantities, including the star formation rate$\Sigma_{SFR}$, there is remarkably good agreement between the vertical weight,the turbulent pressure, and the momentum injection rate from supernovae. Gasvelocity dispersions and disk thicknesses increase with $p_*/m_*$. Theefficiency of star formation per free-fall time at the mid-plane density isinsensitive to the local conditions and to the star formation prescription invery dense gas. We measure efficiencies $\sim$0.004-0.01, consistent with lowand approximately constant efficiencies inferred from observations. For$\Sigma\in$(100--1000) \msunpc, we find $\Sigma_{SFR}\in$(0.1--4) \sfrunits,generally following a $\Sigma_{SFR}\propto \Sigma^2$ relationship. The measuredrelationships agree very well with vertical equilibrium and with turbulentenergy replenishment by feedback within a vertical crossing time. Theseresults, along with the observed $\Sigma_{SFR}-\Sigma$ relation in high densityenvironments, provide strong evidence for the self-regulation of starformation.

Maximally Star-Forming Galactic Disks II. Vertically-Resolved Hydrodynamic Simulations of Starburst Regulation