Pressure-confined Jeans mass ($M_J\propto v^4/(G^{3/2}{P}^{1/2})$)

For a cloud supported by an effective speed of sound $v$ and confined by a surface pressure $P$, dimensional analysis fixes the gravitational instability mass scale to $v^4/(G^{3/2}{P}^{1/2})$. The dimensionless coefficient depends on the equilibrium model and the convention used for the instability threshold.