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 = Rsun
- N ~ 1022
- t ~ 50,000 years!