The Star Formation Rate of Turbulent Magnetized Clouds: Comparing
  Theory, Simulations, and Observations
  We derive and compare six theoretical models for the star formation rate
(SFR) - the Krumholz & McKee (KM), Padoan & Nordlund (PN), and Hennebelle &
Chabrier (HC) models, and three multi-freefall versions of these, suggested by
HC - all based on integrals over the log-normal distribution of turbulent gas.
We extend all theories to include magnetic fields, and show that the SFR
depends on four basic parameters: (1) virial parameter alpha_vir; (2) sonic
Mach number M; (3) turbulent forcing parameter b, which is a measure for the
fraction of energy driven in compressive modes; and (4) plasma beta=2(M_A/M)^2
with the Alfven Mach number M_A. We compare all six theories with MHD
simulations, covering cloud masses of 300 to 4x10^6 solar masses and Mach
numbers M = 3 to 50 and M_A = 1 to infinity, with solenoidal (b=1/3), mixed
(b=0.4) and compressive turbulent (b=1) forcings. We find that the SFR
increases by a factor of four between M=5 and 50 for compressive forcing and
alpha_vir~1. Comparing forcing parameters, we see that the SFR is more than 10x
higher with compressive than solenoidal forcing for Mach 10 simulations. The
SFR and fragmentation are both reduced by a factor of two in strongly
magnetized, trans-Alfvenic turbulence compared to hydrodynamic turbulence. All
simulations are fit simultaneously by the multi-freefall KM and multi-freefall
PN theories within a factor of two over two orders of magnitude in SFR. The
simulated SFRs cover the range and correlation of SFR column density with gas
column density observed in Galactic clouds, and agree well for star formation
efficiencies SFE = 1% to 10% and local efficiencies epsilon = 0.3 to 0.7 due to
feedback. We conclude that the SFR is primarily controlled by interstellar
turbulence, with a secondary effect coming from magnetic fields.
