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# sol6 - Astro 405/505 fall semester 2004 Homework 6th set...

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Astro 405/505, fall semester 2004 Homework, 6th set, solutions. Problem 1: Eddington limit We cannot assume that the mean free path of photons is very small. Instead we explicitely calculate the force density on a population of electrons with density n e exerted by radially streaming photons with flux F = n ph c = L 4 π R 2 The momentum transfer per scattering depends on the scattering angle as δp = c (1 - cos θ ) and thus we calculate the force density as F = d Ω c (1 - cos θ ) F n e d Ω = n e L σ T 4 π R 2 c Gravitation pulls the gas (hydrogen for simplicity) inward with a force density F g = - G M n e m p R 2 Dominance of gravity then requires F g + F < 0 M > L σ T 4 π G m p c = (1 M ) L 1 . 3 · 10 38 erg / s For pair plasma we have to replace the proton mass in the gravitational force density by two times the electron mass. The required mass is therefore around a factor 1.000 higher than for ordinary gas, or for a given mass the maximum luminosity is correspondingly less.

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