A Simple Law of Star Formation

Paolo Padoan; Troels Haugboelle; AAke Nordlund

doi:10.1088/2041-8205/759/2/L27

paper

A Simple Law of Star Formation

arXiv:1208.3758 · doi:10.1088/2041-8205/759/2/L27

Abstract

We show that supersonic MHD turbulence yields a star formation rate (SFR) as low as observed in molecular clouds (MCs), for characteristic values of the free-fall time divided by the dynamical time, $t_{ff} / t_{dyn}$ , the alfvénic Mach number, $M_{a}$ , and the sonic Mach number, $M_{s}$ . Using a very large set of deep adaptive-mesh-refinement simulations, we quantify the dependence of the SFR per free-fall time, $ε_{ff}$ , on the above parameters. Our main results are: i) $ε_{ff}$ decreases exponentially with increasing $t_{ff} / t_{dyn}$ , but is insensitive to changes in $M_{s}$ , for constant values of $t_{ff} / t_{dyn}$ and $M_{a}$ . ii) Decreasing values of $M_{a}$ (stronger magnetic fields) reduce $ε_{ff}$ , but only to a point, beyond which $ε_{ff}$ increases with a further decrease of $M_{a}$ . iii) For values of $M_{a}$ characteristic of star-forming regions, $ε_{ff}$ varies with $M_{a}$ by less than a factor of two. We propose a simple star-formation law, based on the empirical fit to the minimum $ε_{ff}$ , and depending only on $t_{ff} / t_{dyn}$ : $ε_{ff} \approx ε_{wind} exp (- 1.6 t_{ff} / t_{dyn})$ . 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.

ApJ Letters - in press

A Simple Law of Star Formation

Abstract

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