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In a diffuse cloud, the centrifugal force does not play an important role.
Consider a gas parcel whose specific angular momentum is equal to .
When the gas element contracts till the distance from the center,
the centrifugal force per mass of
|
(4.87) |
works.
Contraction stops when the gravitational acceleration is balanced
by the centrifugal force.
Its radius (centrifugal radius) is expressed as
|
(4.88) |
Assuming that the disk is near the hydrostatic balance in -direction,
total column density is related to the volume density on the plane as
|
(4.89) |
We can show that a nondimensional ratio of specific angular momentum to the mass is equal to
the ratio of the free-fall time to the rotation period as follow:
|
(4.90) |
Many numerical simulations confirm that
the contracting disk in the runaway isothermal contraction phase has some `universality.'
The ratio of the free-fall time to the rotation period is approximately equal to
|
(4.91) |
regardless of the initial conditions (Matsumoto, Nakamura, & Hanawa 1997).
Thus,
.
Finally, we can see the centrifugal radius as
|
(4.92) |
increases with time in proportional to the mass ,
because gas element with large contracts later.
As the centrifugal radius increases with time, the launching point of the outflow
also expands with time.
Next: Entrainment Model
Up: Magneto-driven Model
Previous: Angular Momentum Transfer
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Kohji Tomisaka
2007-07-08