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Unformatted text preview: 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 R 2 h The momentum transfer per scattering depends on the scattering angle as p = h c (1- cos ) and thus we calculate the force density as F = I d h c (1- cos ) F n e d d = n e L T 4 R 2 c Gravitation pulls the gas (hydrogen for simplicity) inward with a force density F g =- GM n e m p R 2 Dominance of gravity then requires F g + F &lt; M &gt; L T 4 Gm 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.ordinary gas, or for a given mass the maximum luminosity is correspondingly less....
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