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 \alpha _ { \mathrm { vir } } ; ( 2 ) sonic Mach number \mathcal { M } ; ( 3 ) turbulent forcing parameter b , which is a measure for the fraction of energy driven in compressive modes ; and ( 4 ) plasma \beta = 2 \mathcal { M } _ { \mathrm { A } } ^ { 2 } / \mathcal { M } ^ { 2 } with the Alfvén Mach number \mathcal { M } _ { \mathrm { A } } .
We compare all six theories with MHD simulations , covering cloud masses of 300 to 4 \times 10 ^ { 6 } \mbox { $M _ { \sun } $ } and Mach numbers \mathcal { M } = 3 – 50 and \mathcal { M } _ { \mathrm { A } } = 1 – \infty , 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 \mathcal { M } = 5 and 50 for compressive turbulent forcing and \alpha _ { \mathrm { vir } } \sim 1 .
Comparing forcing parameters , we see that the SFR is more than 10 \times higher with compressive than solenoidal forcing for \mathcal { M } = 10 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 \mathrm { SFE } = 1 \% – 10 \% and local efficiencies \epsilon = 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 .