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 \Sigma _ { SFR } , by the star formation rate per unit gas mass , \Sigma _ { SFR } / \Sigma , 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 _ { * } \sim 3000 { km s ^ { -1 } } , the predicted star formation rate is \Sigma _ { SFR } \sim 2 \pi G \Sigma ^ { 2 } m _ { * } / p _ { * } \sim 0.1 { M _ { \odot } } { % kpc } ^ { -2 } { yr } ^ { -1 } ( \Sigma / 100 { M _ { \odot } } { 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 \Sigma \sim 10 ^ { 2 } -10 ^ { 3 } { M _ { \odot } } { 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 H _ { 2 } surface density 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 at the corresponding mean ISM density \rho _ { 0 } ; if the star formation efficiency per free-fall time is { \varepsilon _ { ff } } ( \rho _ { 0 } ) \sim 0.01 , the turbulent velocity dispersion driven by feedback is expected to be v _ { z } = 0.4 { \varepsilon _ { ff } } ( \rho _ { 0 } ) p _ { * } / m _ { * } \sim 10 { km s ^ { -1 } } , 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 stellar radiation that is reprocessed into trapped IR .