A SEMIANALYTIC MODEL FOR CYCLOTRON LINE FORMATION

We present here a semi-analytic, physically motivated model for the fo rmation of the cyclotron first harmonic line, as well as higher harmon ic lines. The model is based upon three basic physical principles: (1) the radiative transfer is a smooth stochastic process, (2) the first harmonic feature forms from complete redistribution in a single block of resonant photon scatters, and (3) the higher harmonics are well-app roximated as ''true'' absorption features. The emergent spectral shape s are expressed as quadratures. This model includes the essential rela tivistic effects and is valid for weak fields (B much less than B(c) = 4.414 x 10(13) G) in static media where the first harmonic is optical ly thick in the line core but not in its wings. This is a regime that may be relevant for the many classical gamma-ray burst sources where l ow-energy absorption-like features have been observed. To illustrate t his model, we consider the line transfer using polarization-averaged s cattering profiles derived using nonrelativistic quantum mechanics but with relativistic kinematics. This model approximates well the corres ponding exact physical model as calculated using Monte Carlo methods, and is at least an order of magnitude faster to compute than the Monte Carlo simulations. As such, it can be used as a practical substitute for the more time consuming simulations to perform complete analysis o f cyclotron lines in potentially large numbers of classical gamma-ray burst sources. Since the semi-analytic model is based upon only a few simple physical principles, it should be easily adaptable to more gene ral physical situations, such as to line formation in dynamic media. O wing to its relative simplicity and speed, such a semi-analytic model offers the promise of liberating the researcher from large codes and t ime consuming simulations in the analysis of cyclotron line spectra.