The Star Formation Rate of Supersonic MHD Turbulence
  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, alpha_vir, the rms sonic Mach
number, M_S,0, and the ratio of mean gas pressure to mean magnetic pressure,
beta_0. The SFR is predicted to decrease with increasing alpha_vir (stronger
turbulence relative to gravity), to increase with increasing M_S,0 (for
constant values of alpha_vir), and to depend weakly on beta_0 for values
typical of star forming regions (M_S,0 ~ 4-20 and beta_0 ~ 1-20). In the
unrealistic limit of beta_0 -> 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 alpha_vir, and almost the same dependence on M_S,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 alpha_vir and M_S,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.
