Radiative transfer and random walks

Energy is created at the center of the Sun in the form of gamma rays.
Energy flows from the surface of the Sun in the form of visible light.

What happens in between? How does the energy get out, and why is it changed from gamma rays to visible light?

Radiative Transfer

Radiation and matter interact with one another:

absorption - matter absorbs radiation - examples: ionization, excitation
emission - matter releases radiation - example: recombination
scattering - matter and radiation exchange energy - example: Thompson scattering between photons and electrons

This has the effect of reducing the average energy of the radiation, and randomizing the direction of motion.

With all this going on, how can the energy get out?

via a random walk

Let's say a particle moves, on average, a certain distance between interactions:

And that it takes a total number of steps (in a random direction):

Then, on average it will have moved a distance from its starting point:

or, to move a distance d it will need a number of steps:

In the inner portion of the Sun, this is how the energy moves outwards: it random walks its way out via radiative transfer.

Question #1: Why does it move outwards? Why not inwards?
Question #2: Gee this is inefficient. How long does it take the energy to get out?

l ~ 10^-3 m
d = R_sun
N ~ 10²²
t ~ 50,000 years!