Hydrostatic equilibrium in optical depth
= Hydrostatic equilibrium in optical depth
In a plane-parallel atmosphere with $d\tau=-\kappa\rho\,dr$ and $dP/dr=-\rho g$, one has $dP/d\tau=g/\kappa$. If gravity and opacity vary slowly, the pressure at optical depth $\tau$ is approximately $P\simeq g\tau/\kappa$.