Diffusion time estimate

Starting from:

\frac{dE}{dt} = \nabla\cdot\frac{c \lambda}{\kappa_R\rho}\nabla E

We get:

t_{diff}\approx \frac{L^2}{c}\frac{\kappa_R \rho}{\lambda}

L is the size of our system, c is speed of light, kappa_R is the rosseland specific mean opacity, rho is density of the system, and lamba is a dimensional parameter that has to do with gradient length scales of the radiative energy.

Offner et al '09 gives,

\kappa_R=.23 \frac{cm^2}{g}

for T=10 K gas.