Hope College Physics Department Research Experiences for Undergraduates Summer 2012 Project Summary

We present new analytic formulae for the resonant Compton scattering cross section in strong magnetic fields. A new contribution is the employment of correct spin-dependent widths, which are typically significant when the kinematics allows access to the resonance. Our previous analytical developments focused on the limiting case of relativistic electron scattering, in which the angle of photon incidence is Lorentz contracted to effectually zero degrees, leading to considerable algebraic simplifications. Our new developments depart from the limiting case by considering a general angle of photon incidence required for mildly relativistic scattering. Our analytics employ Sokolov & Ternov electron basis states and spin-dependent resonant widths, which have been carefully developed for each contributing intermediate state as all possible Landau excitations of the intermediate state contribute to the scattering. The process of resonant Compton upscattering in high magnetic fields is critical to understanding the high-energy emission of magnetars and high field pulsars, as it is believed that resonant Compton upscattering within the magnetosphere of magnetars is the primary source of intense X-ray emissions of neutron stars. Our formulae will be incorporated in Monte Carlo simulations using full inner magnetosphere magnetar models to obtain realistic X-ray spectra to make comparisons with observed X-ray spectra from magnetars. Most recently, it is suggested that Compton upscattering may account for the observed high-energy tails in magnetar groups of Soft Gamma-ray Repeaters and Anomalous X-ray pulsars. Necessary to modeling these observations is a detailed description of electron cooling rates. Compton scattering efficiently cools electrons, initially accelerated into the highly relativistic regime, into the mildly relativistic regime. As our general formulae are applicable to the high-energy regime, they are necessary for modeling high-energy tails. Our improved analytics are also applicable to the wider astronomical community, such as accretion models, which require a general cross section to produce improved estimates of the Eddington luminosities of neutron stars.

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