Stars typically form in clusters having internal velocity dispersions, dv, of several
kilometers per second. assume that a uniform spherical molecular cloud of total mass m
and radius r forms a cluster of n stars with a star formation efficiency, e, and assume
that the stars are distributed uniformly throughout the cloud with a 3-dimensional
velocity dispersion of dv. (the parameter e is defined as the fraction of the cloud’s mass
that ends up in stars.) assume that the portion of the cloud that does not end up in stars is
blown completely away by the star formation process (e. g., by winds, jets, and
supernovae).
a. write down the condition that the resulting stellar cluster remain bound after the gas
has been dispersed to infinity. for both parts of this exercise, assume that n is a very
large number, so that the mass is very uniformly distributed.
b. evaluate what initial cloud density would be required to form a bound cluster if
e = 0.1, dv = 3 km/s, and m = 5 x 104 m8.