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 (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
≈
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.