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

We explore the self-regulation of star formation using a large suite of high resolution hydrodynamic simulations, focusing on molecule-dominated regions (galactic centers and [U]LIRGS) where feedback from star formation drives highly supersonic turbulence. In equilibrium the total midplane pressure, dominated by turbulence, must balance the vertical weight of the ISM. Under self-regulation, the momentum flux injected by feedback evolves until it matches the vertical weight. We test this flux balance in simulations spanning a range of parameters, including surface density $\Sigma$, momentum injected per stellar mass formed ($p_*/m_*$), and angular velocity. The simulations are 2D radial-vertical slices, including both self-gravity and an external potential that confines gas to the disk midplane. After the simulations reach a steady 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. Gas velocity dispersions and disk thicknesses increase with $p_*/m_*$. The efficiency of star formation per free-fall time at the mid-plane density is insensitive to the local conditions and to the star formation prescription in very dense gas. We measure efficiencies $\sim$0.004-0.01, consistent with low and 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 measured relationships agree very well with vertical equilibrium and with turbulent energy replenishment by feedback within a vertical crossing time. These results, along with the observed $\Sigma_{SFR}-\Sigma$ relation in high density environments, provide strong evidence for the self-regulation of star formation.