Next: Accretion Rate
Up: Free-fall Time
Previous: Problem
  Contents
Solve equation (2.16) and obtain equations (2.23)
and (2.24).
Figure:
Free-fall. x-axis and y-axis represent
and
.
![\begin{figure}\centering\leavevmode
\epsfxsize =.45\columnwidth \epsfbox{eps/r-t_ff.eps}\end{figure}](img335.png) |
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 ``free-fall time'' of the gas.
This gives the time-scale for the gas with density
to collapse.
In the actual interstellar space,
the gas pressure is not negligible.
However,
gives a typical time-scale for a gas cloud
to collapse and to form stars in it.
Next: Accretion Rate
Up: Free-fall Time
Previous: Problem
  Contents
Kohji Tomisaka
2007-07-08