Scaling

d\tau = n \sigma dl

\frac{dn}{dt} = n \sigma F

Test problem

2D version of Tripathi without atmosphere

\rho_c = 6\times 10^8 cm^{-3}

R_c=1.5\times 10^{10} cm

F=2\times 10^{14} cm^{-2} s^{-1}

T= 10^3 K

embedded in a lower density pressure balanced ambient with a density ratio

\chi=100

With a cross section for photo-ionization of 6.3e-18 and our clump's column density of 9e18, we would expect the clump to be optically thick

And with a flux of 2e14, we would expect photo-ionization of the column to take 4.5e4 seconds