What is the minimum mass of a cloud that can gravitationally collapse?

The so-called Jean's Mass defines the mass that is critically unstable to gravitational collapse for a given mass whose only internal support is thermal pressure.


       4 pi Rho          3/2         -3/2
MJ =  ---------  ( pi Vc)     (G Rho)
          3
where Rho is the gas density ( gm/cc), and Vc ( cm/sec) is the thermal sound speed in the gas which is given by
         2
1/2  m  V    = 3/2 K T
where m is the mass, in grams, of a typical gas atom, T is the gas temperature and K is Boltzman's Constant.

What this all means is that the minimum mass, in grams, that can collapse depends on its density and temperature:

                              1         3/2
MJ   proportional to        -----      T
                                1/2
                             Rho
which just means that cold clouds ( 10 - 20 K) yield the smallest masses after collapse, and the mass is also minimized by gas with the lowest density. Typical interstellar clouds have densities of about 1000 atoms/cc and lead to objects with about 0.1 - a few times the mass of the Sun, but brown dwarfs can also be produced with masses as low as 0.01 times the mass of the Sun.
Copyright 1997 Dr. Sten Odenwald
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