set6 - electron-positron pairs instead of ordinary...

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Astro 405/505, fall semester 2004 Homework, 6th set, return before Monday, November 29, 4pm. Don’t forget to give your name. Problem 1: Eddington limit Suppose a compact source of radiation existed with luminosity L . Calculate the radiative force on matter at a distance R , assuming only Compton scattering in the Thomson regime. We may posit that the source should not evacuate itself, for there were no radiating particles if was that the case. Gravitation appears the appropriate means to overcome the radiative force. Derive a limit for the central mass based on the assumption that the gravitational force is stronger than the radiative force. Bonus question: How would the limit for the central mass look like if we were dealing with
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Unformatted text preview: electron-positron pairs instead of ordinary electron-proton plasma? Problem 2: Synchrotron-self-Compton scattering Suppose a spherical source of radius R contained relativistic electrons with differential number density n ( γ ) = n γ-s Θ( γ max-γ ) . Assume the magnetic field to be turbulent, so there is no preferred direction but the amplitude is constant. Calculate the spectrum of synchrotron emission and derive an estimate for the frequency at which the source turns optically thick. Calculate the density spectrum of synchrotron photons in the center of the system. Determine the spectrum of inverse Compton emission using the head-on approximation, given that photon density spectrum....
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