Maximally Star-forming Galactic Disks. I. Starburst Regulation Via Feedback-driven Turbulence

Star formation rates in the centers of disk galaxies often vastly exceed those at larger radii, whether measured by the surface density of star formation Σ_SFR, by the star formation rate per unit gas mass, Σ_SFR/Σ, or even by total output. In this paper, we investigate the idea that central starbursts are self-regulated systems in which the momentum flux injected to the interstellar medium (ISM) by star formation balances the gravitational force confining the ISM gas in the disk. For most starbursts, supernovae are the largest contributor to the momentum flux, and turbulence provides the main pressure support for the predominantly molecular ISM. If the momentum feedback per stellar mass formed is p_*/m_* ~ 3000 km s^-1, the predicted star formation rate is Σ_SFR ~ 2πGΣ² m_*/p_* ~ 0.1 M_sun kpc^-2 yr^-1(Σ/100 M_sun pc^-2)² in regions where gas dominates the vertical gravity. We compare this prediction with numerical simulations of vertically resolved disks that model star formation including feedback, finding good agreement for gas surface densities in the range Σ ~ 10²-10³ M_sun pc^-2. We also compare to a compilation of star formation rates and gas contents from local and high-redshift galaxies (both mergers and normal galaxies), finding good agreement provided that the conversion factor X _CO from integrated CO emission to H₂ surface density decreases modestly as Σ and Σ_SFR increase. Star formation rates in dense, turbulent gas are also expected to depend on the gravitational free-fall time at the corresponding mean ISM density ρ₀ if the star formation efficiency per free-fall time is ɛ_ff(ρ₀) ~ 0.01, the turbulent velocity dispersion driven by feedback is expected to be v_z = 0.4 ɛ_ff(ρ₀)p_*/m_* ~ 10 km s^-1, relatively independent of Σ or Σ_SFR. Turbulence-regulated starbursts (controlled by kinetic momentum feedback) are part of the larger scheme of self-regulation; primarily atomic low-Σ outer disks may have star formation regulated by ultraviolet heating feedback, whereas regions at extremely high Σ may be regulated by feedback of stellar radiation that is reprocessed into trapped infrared.