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

This paper explores the effects of strong magnetic fields on the Comptonscattering of relativistic electrons. Recent studies of upscattering and energyloss by relativistic electrons that have used the non-relativistic, magneticThomson cross section for resonant scattering or the Klein-Nishina crosssection for non-resonant scattering do not account for the relativistic quantumeffects of strong fields ($ > 4 \times 10^{12}$ G). We have derived asimplified expression for the exact QED scattering cross section for thebroadly-applicable case where relativistic electrons move along the magneticfield. To facilitate applications to astrophysical models, we have alsodeveloped compact approximate expressions for both the differential and totalpolarization-dependent cross sections, with the latter representing well theexact total QED cross section even at the high fields believed to be present inenvironments near the stellar surfaces of Soft Gamma-Ray Repeaters andAnomalous X-Ray Pulsars. We find that strong magnetic fields significantlylower the Compton scattering cross section below and at the resonance, when theincident photon energy exceeds $m_ec^2$ in the electron rest frame. The crosssection is strongly dependent on the polarization of the final scatteredphoton. Below the cyclotron fundamental, mostly photons of perpendicularpolarization are produced in scatterings, a situation that also arises abovethis resonance for sub-critical fields. However, an interesting discovery isthat for super-critical fields, a preponderance of photons of parallelpolarization results from scatterings above the cyclotron fundamental. Thischaracteristic is both a relativistic and magnetic effect not present in theThomson or Klein-Nishina limits.Comment: AASTeX format, 31 pages included 7 embedded figures, accepted for publication in The Astrophysical Journa