Suppose you have a point mass M in space that is surrounded by a gas of particles mass m at temperature T. Let the gas distribution be spherically symmetric about M. What is the radial dependence of the equilibrium gas distribution? Wish to include the case were M=0.

This may be a trick question because I think the gas may evaporate over time and slowly cool. If this is so, then I want the answer to the question above for short time periods over which the evaporation is negligible.

Many thanks!