If "c" is the mean sound speed, so that c^{2} represents
a mean gas temperature T, then:
 GM/(c^{2}R)
~ 1 gives
the equilibrium radius of a spherical star of mass M.
 GM/(c^{2}R) represents the ratio of E_{grav}
to E_{thermal} in a protostellar gas cloud.

GM/(c^{2}R)
~ 1 gives
the Jeans mass of a spherically symmetric protostellar gas cloud.
If, upon contraction, M is constant and P ~
r^{g}
, then
T ~
c^{2} ~ r^{g  1} ,
R ~ r^{ 1/3} ,
hence,
E_{grav}/E_{thermal} ~
r^{4/3  g} .
Note the significance of the exponent value g = 4/3
and, hence, the slope dlnT/dlnr = 1/3.
Go to rT Plot

