The Jeans Mass
The Jeans mass is determined by asking when the magnitude of the
gravitational potential energy exceeds the magnitude of the gas kinetic energy.
It is given by
MJ = 3kTR / 2Gm
where k is the Boltzmann constant, T the temperature, R
the radius of the
cloud, G the gravitational constant, and m the average mass of a gas
particle. If the cloud's mass exceeds this value, gravity can overcome the
gas kinetic energy and initiate collapse. The corresponding Jeans density is
DJ = constant
x (T 3 /
m 3M 2)
where constant = 81k3 / 32πG3 and
M is the mass of the cloud.
If the cloud is compressed so that its density exceeds this value, it can begin to collapse.