Homework 2

Follow the photon until it has reached a radial

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Unformatted text preview: nd φ at each integration step). Follow the photon until it has reached a radial distance of 50 units from the origin. Repeat this for 10,000 trials, and plot the distribution of the number of steps required for each photon to reach the “surface”. What is the average of this distribution? How does this compare to (R/l)2? What about the minimum and maximum number of steps? Discuss how this distribution might be related to the lightcurve of an opaque body within which a sudden burst of energy is released. (c) [10 pt] The dominant source of opacity in the ionized interior of the Sun is Thompson scattering, where photons are scattered off of free electrons. The cross-section of this process is: 8π 8π 2 re = σT = r 3 e2 me c2 2 = 6.7×10−25 cm2 Show that the pathlength of a photon (distance travelled before scattering) with constant cross section is: l= A µmp 1 = ne σ T Z ρσT where µ = (Z/A)µe is the mean molecular weight, mp is the proton mass and Z/A the proton/nucleon fraction of ions (Note: you’ll have to relate the numbe...
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