1208.3758 (Paolo Padoan et al.)

A Simple Law of Star Formation    [PDF]

Paolo Padoan, Troels Haugboelle, AAke Nordlund

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, $t_{\rm ff}/t_{\rm dyn}$, the alfv\'{e}nic Mach number, ${\cal M}_{\rm a}$, and the sonic Mach number, ${\cal M}_{\rm s}$. Using a very large set of simulations, we quantify the dependence of the SFR per free-fall time, $\epsilon_{\rm ff}$, on the above parameters. Our main results are: i) $\epsilon_{\rm ff}$ decreases exponentially with increasing $t_{\rm ff}/t_{\rm dyn}$, but is insensitive to changes in ${\cal M}_{\rm s}$, for constant values of $t_{\rm ff}/t_{\rm dyn}$ and ${\cal M}_{\rm a}$. ii) Decreasing values of ${\cal M}_{\rm a}$ (stronger magnetic fields) reduce $\epsilon_{\rm ff}$, but only to a point, beyond which $\epsilon_{\rm ff}$ increases with a further decrease of ${\cal M}_{\rm a}$. iii) For values of ${\cal M}_{\rm a}$ characteristic of star-forming regions, $\epsilon_{\rm ff}$ varies with ${\cal M}_{\rm a}$ by less than a factor of two, thus we propose a simple star-formation law, based on the empirical fit to the minimum $\epsilon_{\rm ff}$, and depending only on $t_{\rm ff}/t_{\rm dyn}$: $\epsilon_{\rm ff} \approx \epsilon_{\rm wind} \exp(-1.6 \,t_{\rm ff}/t_{\rm dyn})$. This exponential law shows that MHD turbulence is very effective at slowing down the star-formation process in molecular clouds. Because it only depends on the mean gas density and rms velocity, it is straightforward to implement in simulations and analytical models of galaxy formation and evolution.

View original: http://arxiv.org/abs/1208.3758