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 interstellar medium. 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 wide range of parameters, including surface density Σ, momentum injected per stellar mass formed (p _*/m _*), and angular velocity. The simulations are two-dimensional radial-vertical slices, and include both self-gravity and an external potential that helps to confine gas to the disk midplane. After the simulations reach a steady state in all relevant quantities, including the star formation rate Σ _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 midplane density, ε_ff(n ₀), is insensitive to the local conditions and to the star formation prescription in very dense gas. We measure ε_ff(n ₀) 0.004-0.01, consistent with low and approximately constant efficiencies inferred from observations. For Σ ∈ (100-1000) M pc^-2, we find Σ_SFR ∈ (0.1-4) M kpc^-2 yr^-1, generally following a Σ_SFR 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 Σ-Σ_SFR relation in high-density environments, provide strong evidence for the self-regulation of star formation.