Maximally Star-Forming Galactic Disks. I. Starburst Regulation via Feedback-Driven Turbulence

Abstract

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 selfregulated 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 ∼ 2πGΣ 2 m * /p * ∼ 0.1 M ⊙ kpc −2 yr −1 (Σ/100 M ⊙ 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 ∼ 10 2 − 10 3 M ⊙ 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 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 ρ 0 ; if the star formation efficiency per free-fall time is ε ff (ρ 0 ) ∼ 0.01, the turbulent velocity dispersion driven by feedback is expected to be v z = 0.4 ε ff (ρ 0 )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 UV heating feedback, whereas regions at extremely high Σ may be regulated by feedback of stellar radiation that is reprocessed into trapped IR.

Dusty star-forming galaxies at high redshift

“…The range of X CO values for high-z SMGs ranges from lower than to higher than the typical z ∼ 0 ULIRG value, and provides some evidence that the X-factor is not strictly bimodal. Moreover, Magnelli et al (2012) find an inverse relationship between the conversion factor and and dust temperature, which is consistent with the empirical inverse powerlaw correlation between X CO and gas surface density uncovered by Tacconi et al (2008) and Ostriker & Shetty (2011). Turning toward more 'normal' disk galaxies at high-z, Daddi et al (2010b) utilize dynamical arguments to infer α CO = 3.6±0.8 M pc −2 (K km s −1 ) −1 (i.e.…”

“…These authors found that at high surface densities, one might expect the X-factor to drop, similar to the empirical findings of Ostriker & Shetty (2011). Narayanan et al (2011b) and Narayanan et al (2012a) coupled 3D non-local thermodynamic equilibrium (LTE) radiative transfer calculations and dust radiative transfer simulations with smoothed particle hydrodynamic (SPH) models of disk galaxies and galaxy mergers to derive a functional form for the CO-H 2 conversion factor across a variety of environments.…”

“…For example, Krumholz et al (2009b) suggest that if the SFR in a galaxy is determined by the fraction of gas in molecular form, the cloud surface density (which occupies a narrow distribution in galaxies like the Milky Way), and turbulence-regulated star formation efficiencies ( ), then a linear KS relation is expected (when normalizing by the cloud free fall time, t ff ). On the other hand, in starburst-dominated regimes, where supernova-driven turbulence dominates the velocity dispersion and gas dominates the vertical pressure, Shetty (2011) andFaucherGiguère et al (2013) find an index of ∼ 2 should describe the KS relation. These are simply two examples, and there 18 is often referred to as the 'star formation efficiency', and should be distinguished from alternative definitions for the star formation efficiency that appear in the literature as well:…”

“…The functional form for X CO is that of Equation 21, and can be arrived at either from empirical fits to observations (e.g. Ostriker & Shetty, 2011), or from the results of numerical simulations . When assuming a smoothly varying X CO (as opposed to a discontinuous one), the star formation relation is unimodal.…”

“…They showed that if one takes plausible values for the typical gas free fall time in galaxy disks, and luminous starbursts, the apparent bimodal relation exhibited in the Daddi et al (2010b) and Genzel et al (2010) data reduces to a single, unimodal relation. An alternative class of theories was presented by Shetty (2011), andNarayanan et al (2012b), who argued that the existence of a bimodal KS relation was an artifact of the usage of a bimodal CO-H 2 conversion factor, and that if a unimodal (either constant, or smoothly varying) X-factor was employed, the KS relation would no longer appear bimodal. Ostriker & Shetty (2011) fit observed data between X CO and Σ H2 presented in Tacconi et al (2008) to derive an empirical form for a smoothly varying X-factor, while Narayanan et al (2012b) utilized numerical simulations in order to derive a theoretical model form for the conversion factor (Equation 21).…”