Download Molecular cloud

1/11
Nonlinear Hydromagnetic
Wave Support of a Stratified
Molecular Cloud
Takahiro Kudoh
Shantanu Basu
University of Western Ontario
Canada
2/11
Molecular cloud
Magnetic
field line
M  10 M SUN
3
MHD wave pressure
Cloud
Turbulence
Interstellar molecular clouds
have long been known to
yield supersonic line widths of
molecular spectral lines.
The MHD wave picture of the
turbulence has been
strengthened by the detection
of large-scale magnetic fields
within molecular clouds.
How do the MHD waves affect the global structure of the cloud?
MHD numerical simulation
3/11
Global MHD simulation: 1-dimensional
Most of the previous
simulations
Magnetic
field line
Magnetic field line
picks up the local region.
Low density and
Hot medium
hot gas
Our simulation
box
z
Periodic boundary box
Molecular cloud
M
 critical

Molecular
cloud
Self-gravity
If we want to study the global structure
Driving force
of the cloud, it is NOT a good setting
the problem.
Aofsinusoidal
driving force is input into
the molecular cloud.
Ideal MHD
Movie: Time evolution of density and
wave component of the magnetic field
n0 
0
m
 10 4 cm 3
Interface between cold cloud
and hot low-density gas
0.25pc
(z)
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Time evolution
of density
The density plots
at various times
are stacked with
time increasing
upward.
Note large oscillations
of outer cloud.
Driving is terminated
at t=40t0.
7.5 106 year
We input constant
driving force
amplitude during
this period.
Turbulent driving
amplitude increases
linearly with time
between t=0 and t=10t0.
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Snapshot of density
n0 
0
m
 10 4 cm 3
Shock waves
0.25pc
The density structure is complicated and has many shock waves.
7/11
Time averaged density
n0 
0
m
Time averaged quantities  t and
z t are for Lagrangian particles.
 10 4 cm 3
Time averaged density
The scale height is about
3 times larger than that
Initial condition
of the initial condition.
0.25pc
The time averaged density shows a smooth distribution.
8/11
An ensemble of clouds with different strengths of the driving force
[velocity dispersion]
Velocity dispersion vs. Scale of the clouds
cs 0  0.2km/s
The full mass position
The half mass position
 Z
1/ 2
Consistent with
observations
Time-averaged
gravitational equilibrium
H 0  0.05pc
[The scale of the cloud]
The coefficient of
Chandrasekhar-Fermi formula
 
| By |
B0

| vy |
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VA
=1 (for linear wave)
Surface of the cloud

=0.23
0.25pc
<1 at the surface of the cloud
A standing wave effect: By is small near the surface but vy is not.
10/11
Dissipation time of energy
The sum of the all
Kinetic energy
(lateral)
Dissipation time
t d  8t0  2.0 106 year
Ee
t / td
Magnetic energy
Kinetic energy
(vertical)
Note that the energy in transverse
modes remains much greater than
The time we stop driving force
that in generated longitudinal modes.
11/11
Summary
• Due to the effective pressure of MHD turbulence,
our one-dimensional cloud is lifted upward and
shows oscillations.
• It establishes a new time-averaged equilibrium
1/ 2
state, obeying   z where   1-D velocity
dispersion, z  scale of clouds.
• The coefficient of the Chandrasekhar-Fermi
formula must be modified near the cloud surface.
• The dissipation time of the cloud turbulence is
several crossing times of the cloud.
Thanks for the support of this research from CGPS and SHARCNET.