Before proceeding, we need an understanding of how stars are formed.
Observations show that new stars appear to be forming in regions of dense interstellar clouds.
We can ask under what conditions the gravitational force, trying to contract the cloud, can overcome the gas forces that are trying to expand the cloud. The critical mass, above which such a cloud will collapse, is called the Jean's mass. where T and rho are the cloud temperature and density, m H the hydrogen atom mass and m the mean atomic weight of the cloud material relative to hydrogen. If, as the collapse proceeds, the cloud can radiate away the gravitational potential energy then sooner or later a smaller cloud may exceed a smaller Jean's mass caused by the higher density. Thus the cloud fragments, and these clumps may in turn fragment. So from one massive cloud we may expect the formation of a cluster of stars covering the whole mass spectrum, from short-lived massive stars weighing many tend of solar masses to brown dwarfs.