Jeans mass ($M_J$)

The Jeans mass is the characteristic gas mass above which self-gravity overcomes pressure support. Up to the convention used to define the collapsing region,for an ideal gas of fixed composition.

During isothermal collapse, $T$ is constant and the Jeans mass decreases as ${\rho }^{-1/2}$. Successively denser regions can therefore become independently unstable and fragment to smaller masses.

For adiabatic monatomic gas, $T\propto {\rho }^{2/3}$ and the Jeans mass increases as ${\rho }^{1/2}$. Once cooling fails and collapse becomes adiabatic, further fragmentation is suppressed.