Cyclotron Line Formation in a Relativistic Outflow

There is mounting evidence that, if gamma-ray bursters are Galactic in origin, they are located in a Galactic corona at distances greater than 100 kpc. This has created a need to explore new models of cyclotron line formation. In most previous calculations the line-forming region was modeled as a static slab of plasma, optically thin to continuum scattering, and threaded by a magnetic field of the order $10^{12}$ gauss oriented normal to the slab. Such a model is appropriate, for example, for the magnetic polar cap of a neutron star with a dipole field. However, if bursters lie at distances farther than several hundred parsecs, the burst luminosity exceeds the magnetic Eddington luminosity, and the plasma in a line-forming region at the magnetic polar cap would be ejected relativistically along the field lines. Mitrofanov and Tsygan have modeled the dynamics of such an outflow, and Miller {\it et al.} have calculated the properties of the cyclotron second and third harmonics, approximating them as due to cyclotron absorption. Here we describe Monte Carlo calculations of cyclotron resonant scattering at the first three harmonics in a relativistic outflow from the magnetic polar cap, and show that such scattering can produce narrow lines like those observed by Ginga.