The Energy Dissipation Rate of Supersonic, Magnetohydrodynamic Turbulence in Molecular Clouds
M. M. Mac Low;
ApJ, 1999, 524, 169
ABSTRACT:Molecular clouds have broad line widths, which suggests turbulent supersonic motions in the clouds.
These motions are usually invoked to explain
why molecular clouds take much longer than a free-fall time to form
stars.
Classically, it was thought that supersonic hydrodynamical turbulence would
dissipate its energy quickly but that the introduction of strong magnetic fields
could maintain these motions.
A previous paper has shown, however, that
isothermal, compressible MHD and hydrodynamical turbulence decay at virtually
the same rate, requiring that constant driving occur to maintain the
observed turbulence.
In this paper, direct numerical computations of
uniform, randomly driven turbulence with the ZEUS astrophysical MHD code are
used to derive the value of the energy-dissipation coefficient, which is
found to be E&d2;_kin~=-η_vmk&d5;v^3_rms, with η_v=0.21/π,
where v_rms is the root-mean-square (rms) velocity in the region, E_kin is
the total kinetic energy in the region, m is the mass of the region, and k&d5;
is the driving wavenumber.
The ratio τ of the formal decay time
E_kin/E&d2;_kin of turbulence to the free-fall time of the gas can then be shown to be
τ(κ)=κ/M_rms 14πη_v, where M_rms is the rms Mach number, and κ is the
ratio of the driving wavelength to the Jeans wavelength.
It is likely that
κ<1 is required for turbulence to support gas against gravitational
collapse, so the decay time will probably always be far less than the free-fall
time in molecular clouds, again showing that turbulence there must be
constantly and strongly driven.
Finally, the typical decay time constant of the
turbulence can be shown to be t_0~=1.0 ℒ/v_rms, where ℒ is the driving
wavelength.
KEYWORDS: ism: clouds, ism: kinematics and dynamics, ism: magnetic fields, magnetohydrodynamics: mhd, turbulence
PERSOKEY:turbulence, ,
CODE: mac_low99