TY - JOUR

T1 - A simple law of star formation

AU - Padoan, Paolo

AU - Haugbølle, Troels

AU - Nordlund, Åke

PY - 2012

Y1 - 2012

N2 - 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, {\cal M}_a, and the sonic Mach number, {\cal M}_s. Using a very large set of deep adaptive-mesh-refinement simulations, we quantify the dependence of the SFR per free-fall time, epsilonff, on the above parameters. Our main results are (1) that epsilonff decreases exponentially with increasing t ff/t dyn, but is insensitive to changes in {\cal M}_s, for constant values of t ff/t dyn and {\cal M}_a. (2) Decreasing values of {\cal M}_a (stronger magnetic fields) reduce epsilonff, but only to a point, beyond which epsilonff increases with a further decrease of {\cal M}_a. (3) For values of {\cal M}_a characteristic of star-forming regions, epsilonff varies with {\cal M}_a by less than a factor of two. We propose a simple star formation law, based on the empirical fit to the minimum epsilonff, and depending only on t ff/t dyn: epsilonff ˜ epsilonwindexp (– 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.

AB - 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, {\cal M}_a, and the sonic Mach number, {\cal M}_s. Using a very large set of deep adaptive-mesh-refinement simulations, we quantify the dependence of the SFR per free-fall time, epsilonff, on the above parameters. Our main results are (1) that epsilonff decreases exponentially with increasing t ff/t dyn, but is insensitive to changes in {\cal M}_s, for constant values of t ff/t dyn and {\cal M}_a. (2) Decreasing values of {\cal M}_a (stronger magnetic fields) reduce epsilonff, but only to a point, beyond which epsilonff increases with a further decrease of {\cal M}_a. (3) For values of {\cal M}_a characteristic of star-forming regions, epsilonff varies with {\cal M}_a by less than a factor of two. We propose a simple star formation law, based on the empirical fit to the minimum epsilonff, and depending only on t ff/t dyn: epsilonff ˜ epsilonwindexp (– 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.

U2 - 10.1088/2041-8205/759/2/L27

DO - 10.1088/2041-8205/759/2/L27

M3 - Letter

VL - 759

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

M1 - L27

ER -