Compton Scattering in Ultrastrong Magnetic Fields: Numerical and Analytical Behavior in the Relativistic Regime

Abstract

This paper explores the effects of strong magnetic fields onthe Compton scattering of relativistic electrons. Recent studies ofupscattering and energy loss by relativistic electrons that have used thenonrelativistic, magnetic Thomson cross section for resonant scatteringor the Klein-Nishina cross section for nonresonant scattering donot account for the relativistic quantum effects of strong fields(>4�10 12 G). We have derived a simplified expression forthe exact QED scattering cross section for the broadly applicablecase in which relativistic electrons move along the magnetic field.To facilitate applications to astrophysical models, we have alsodeveloped compact approximate expressions for both the differentialand total polarization-dependent cross sections, with the latterrepresenting well the exact total QED cross section even at the high fieldsbelieved to be present in environments near the stellar surfaces of softgamma repeaters and anomalous X-ray pulsars. We find that strongmagnetic fields significantly lower the Compton scattering crosssection below and at the resonance when the incident photon energyexceeds m e c 2 in the electron rest frame. Thecross section is strongly dependent on the polarization of the finalscattered photon. Below the cyclotron fundamental, mostly photons ofperpendicular polarization are produced in scatterings, a situation thatalso arises above this resonance for subcritical fields. However, aninteresting discovery is that for supercritical fields, a preponderance ofphotons of parallel polarization results from scatterings above thecyclotron fundamental. This characteristic is both a relativistic and amagnetic effect not present in the Thomson or Klein-Nishina limits.