Cyclotron resonant scattering and absorption

The relativistic cross-sections for first-order absorption and second-order scattering are compared to determine the conditions under which the absorption cross-section is a good approximation to the much more complex scattering cross-section for purposes of modeling cyclotron lines in gamma-ray bursts. Differences in both the cross-sections and the line profiles are presented for a range of field strengths, angles, and electron temperatures. The relative difference of the cross-sections at one line width from resonance was found to increase with field strength and harmonic number. The difference is also strongly dependent on the photon angle to the magnetic field. For the field strength, 1.7 x 10 to the 12th G, and the angle inferred from the Ginga burst features, absorption is an excellent approximation for the profiles at the first and second harmonics.