In a static equilibrium state the fluid velocity \(\vv\) vanishes. The momentum equation then becomes the hydrostatic equilibrium equation
Assuming the equilibrium is spherically symmetric, this simplifies to
Poisson’s equation can be integrated once to yield
where the second equality introduces the interior mass
The hydrostatic equilibrium equation thus becomes
The heat equation in the equilibrium state is
If the star is in thermal equilibrium then the left-hand side vanishes, and the nuclear heating rate balances the flux divergence term. Again assuming spherical symmetry, this is written
are the radiative and convective luminosities, respectively.