Christoph Federrath, Ralf S. Klessen
We study the role of turbulence and magnetic fields 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, 2) sonic Mach number M, 3) turbulent forcing parameter b, which is a measure for the ratio of compressible-to-solenoidal modes in the velocity field, and 4) beta=2M_A^2/M^2 with the Alfv\'en Mach number M_A. We compare all six theories with MHD simulations, covering cloud masses of 300 to 4x10^6 M_sol and Mach numbers M=3-50 and M_A=1-infinity, with solenoidal (b=1/3), mixed (b=0.4) and compressive turbulent forcing (b=1). We find that the SFR increases by a factor of 4 between M=5 and 50 for compressive turbulent forcing and virial parameters of order unity. Comparing forcing parameters, we see that the SFR is more than 10x higher with compressive than solenoidal forcing for M=10 simulations. The SFR and fragmentation are both reduced by a factor of 2 in strongly magnetized, trans-Alfv\'enic 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=2-10% and local core-formation efficiencies epsilon=0.3-0.55 due to feedback. We conclude that the SFR is primarily controlled by interstellar turbulence, with a secondary effect coming from magnetic fields.
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http://arxiv.org/abs/1209.2856
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