Equivalent Width of Cyclotron Lines in Gamma-Ray Burst Spectra: Noncoherent Scattering

The X-ray astronomy satellite Ginga detected first- and second-harmonic cyclotron absorption lines at around 20 and 40 keV in the energy spectra of gamma-ray bursts. These gamma-ray bursts are readily interpreted as being phenomena in the teragauss magnetic fields of galactic neutron stars. In order to explain the cyclotron lines of these bursts, the multi-angle radiative transfers of the first- and the second-harmonic lines in a plane-parallel slab with a uniform magnetic field perpendicular to the slab were calculated, while taking into account noncoherent scattering in the cyclotron resonance (hereafter called noncoherent scattering) and the Lorentzian wing. Futhermore, this calculation code is also a preparation for studying the cyclotron lines of X-ray pulsars. It was found that, although the second harmonic is always absorptive, the behavior of the first harmonic is complex due to noncoherent scattering in cyclotron resonance and degradation of photons from the second harmonic. For example, the equivalent width of the first-harmonic line is positive (absorption line) when seen along the magnetic field line. However, the equivalent width decreases as the viewing angle theta relative to the magnetic field increases, and vanishes at theta ~ 80(deg) . Moreover, the equivalent width becomes negative (emission line) for theta >= 80(deg) . Consequently, the equivalent widths of the first- and second-harmonic lines can constrain the parameters of the transmission model, the optical depth tau_T and the viewing angle theta relative to the magnetic field.