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Solve equation (2.16) and obtain equations (2.23)
and (2.24).
Figure:
Freefall. xaxis and yaxis represent and
.

In the present case,
at , since the energy is negative.
Equation (2.19) shows us
becomes equal to zero (the gas collapses) if as well as at .
Equation (2.21) indicates
it occurs at the epoch of
where represents the average density
inside of , that is
.
This is called ``freefall time'' of the gas.
This gives the timescale for the gas with density to collapse.
In the actual interstellar space,
the gas pressure is not negligible.
However, gives a typical timescale for a gas cloud
to collapse and to form stars in it.
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Up: Freefall Time
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Kohji Tomisaka
20070708