Abstract

The role of turbulence and magnetic fields is studied for star formation in molecular clouds. 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 αvir; (2) sonic Mach number ; (3) turbulent forcing parameter b, which is a measure for the fraction of energy driven in compressive modes; and (4) plasma with the Alfvén Mach number . We compare all six theories with MHD simulations, covering cloud masses of 300 to 4 × 106 M☉ and Mach numbers –50 and –∞, 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 and 50 for compressive turbulent forcing and αvir ∼ 1. Comparing forcing parameters, we see that the SFR is more than 10 times higher with compressive than solenoidal forcing for simulations. The SFR and fragmentation are both reduced by a factor of two in strongly magnetized, trans-Alfvénic 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%–10% and local efficiencies = 0.3–0.7 due to feedback. We conclude that the SFR is primarily controlled by interstellar turbulence, with a secondary effect coming from magnetic fields.