CYCLOTRON RESONANT SCATTERING AND ABSORPTION

We have made a detailed comparison of the relativistic cross sections for both first-order absorption and second-order scattering 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. This requires a full treatment of the spin-dependent relativistic natural line widths as well as the derivation of the spin-dependent cross sections. Differences in both the cross sections and the line profiles will be presented for a range of field strengths, angles, and electron temperatures. Although the scattering and absorption cross sections are equal at the resonance energies (to second order in alpha), we find that their relative difference at one line width from resonance increases with field strength and harmonic number. The difference is also strongly dependent on the photon angle to the magnetic field and can be traced to the fact that resonant scattering does not have a standard Lorentz profile. For the field strength, 1.7 x 10(12); G, and angle inferred from the Ginga burst features, absorption is an excellent approximation for the profiles at the first and second harmonics. However, scattering cross sections should be used to model lines accurately at higher harmonics and higher field strengths.