A SIMPLE LAW OF STAR FORMATION

Abstract

We show that supersonic MHD turbulence yields a star formation rate (SFR) as low as observed in molecular clouds, for characteristic values of the free-fall time divided by the dynamical time, t ff / t dyn , the Alfvénic Mach number, , and the sonic Mach number, . Using a very large set of deep adaptive-mesh-refinement simulations, we quantify the dependence of the SFR per free-fall time, ff , on the above parameters. Our main results are (1) that ff decreases exponentially with increasing t ff / t dyn , but is insensitive to changes in , for constant values of t ff / t dyn and . (2) Decreasing values of (stronger magnetic fields) reduce ff , but only to a point, beyond which ff increases with a further decrease of . (3) For values of characteristic of star-forming regions, ff varies with by less than a factor of two. We propose a simple star formation law, based on the empirical fit to the minimum ff , and depending only on t ff / t dyn : ff ≈ wind exp (− 1.6 t ff / t dyn ). Because it only depends on the mean gas density and rms velocity, this law is straightforward to implement in simulations and analytical models of galaxy formation and evolution.