The Star Formation Rate of Supersonic MHD Turbulence
Abstract
This work presents a new physical model of the star formation rate (SFR), verified with an unprecedented set of large numerical simulations of driven, supersonic, self-gravitating, magneto-hydrodynamic (MHD) turbulence, where collapsing cores are captured with accreting sink particles. The model depends on the relative importance of gravitational, turbulent, magnetic, and thermal energies, expressed through the virial parameter, alphavir, the rms sonic Mach number, MS,0, and the ratio of mean gas pressure to mean magnetic pressure, beta0. The SFR is predicted to decrease with increasing alphavir (stronger turbulence relative to gravity), to increase with increasing MS,0 (for constant values of alphavir), and to depend weakly on beta0 for values typical of star forming regions (MS,0 ~ 4-20 and beta0 ~ 1-20). In the unrealistic limit of beta0 -> infinity, that is in the complete absence of a magnetic field, the SFR increases approximately by a factor of three, which shows the importance of magnetic fields in the star formation process, even when they are relatively weak (super-Alfvenic turbulence). In this non-magnetized limit, our definition of the critical density for star formation has the same dependence on alphavir, and almost the same dependence on MS,0, as in the model of Krumholz and McKee, although our physical derivation does not rely on the concepts of local turbulent pressure and sonic scale. However, our model predicts a different dependence of the SFR on alphavir and MS,0 than the model of Krumholz and McKee. The star-formation simulations used to test the model result in an approximately constant SFR, after an initial transient phase. Both the value of the SFR and its dependence on the virial parameter found in the simulations are shown to agree very well with the theoretical predictions.