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 Σ, 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 ΣSFR, 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 ~0.004-0.01, consistent with low and approximately constant efficiencies inferred from observations. For Σ∈(100--1000) , we find ΣSFR∈(0.1--4) , generally following a ΣSFR∝ Σ² 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 ΣSFR-Σ relation in high density environments, provide strong evidence for the self-regulation of star formation.