  Star formation rates in the centers of disk galaxies often vastly exceed
those at larger radii. We investigate the idea that these central starbursts
are self-regulated, with the momentum flux injected to the ISM by star
formation balancing the gravitational force confining the gas. 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,
the predicted star formation rate is Sigma_SFR=2 pi G Sigma^2 m_*/p_*
~0.1(Sigma/100Msun/pc^2)^2 Msun/kpc^2/yr 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 Sigma ~ 10^2-10^3 Msun/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 X_CO decreases weakly as Sigma and Sigma_SFR increase.
Star formation rates in dense, turbulent gas are also expected to depend on the
gravitational free-fall time; if the efficiency per free-fall time is
epsilon_ff ~ 0.01, the turbulent velocity dispersion driven by feedback is
expected to be v_z = 0.4 epsilon_ff p_*/m_* ~ 10 km/s, relatively independent
of Sigma or Sigma_SFR. Turbulence-regulated starbursts (controlled by kinetic
momentum feedback) are part of the larger scheme of self-regulation;
primarily-atomic low-Sigma outer disks may have star formation regulated by UV
heating feedback, whereas regions at extremely high Sigma may be regulated by
feedback of radiation that is reprocessed into trapped IR.
