Lyman-\alpha Line Transfer

This is basically identical to the line transfer for ionizing radiation, except:

\sigma_H = 5.9\times 10^{-14} \sqrt{\frac{10^4 \text{K}}{T}}

and the energy per photon is instead the momentum per photon,

p_\gamma = \frac{h \nu}{c}.

To test, I've put neutral hydrogen of uniform density and temperature 10⁴ K in a uniform gravitational field opposed by radiation pressure. To balance, equate volumetric force:

F_g = n_H m_H g$ $F_\gamma = J \sigma_H n_H p_\gamma$ ,

with g = 980 \text{ cm/s}^2. Clearly the value of n_H doesn't affect the result, and I've chosen a small enough length scale that absorption doesn't matter and we can take \tau = 0 across the grid.

With a flux J = 5.09\times10^{13}, we get a result of (tweaking some decimals - flux in physics.data for this is actually 5.0999972\times10^{13}):

v \approx 0.1 \text{ cm/s} after ~0.1 seconds, when acceleration under only gravity would give v = g t = 980(0.1) = 98 \text{ cm/s}. Radiation pressure and gravity are clearly not perfectly matched, but it also seems clear that radiation pressure is working as it should.