Effects of the geometry of the line-forming region on the properties of cyclotron resonant scattering lines

We use a Monte Carlo radiative transfer code to examine the dependence of the properties of cyclotron resonant scattering lines on the spatial geometry and the optical depth of the line-forming region. We focus most of our attention on a line-forming region that isa plane-parallel slab threaded by a uniform magnetic field oriented at an angle Psi to the slab normal. We also consider a cylindrical line-forming region with the magnetic field oriented along the cylinder axis. In both cases; the line-forming region contains an electron-proton plasma at the equilibrium Compton temperature, T-C, and the field strength is similar to 10(12) gauss. We consider geometries in which the photon source illuminates the line-forming region from below and in which the photon source is embedded in the line-forming region. The former may correspond to a line-forming region in the magnetosphere of a neutron star, illuminated from below, the latter to a line-forming region on or near the surface of a neutron star as in an accretion column. We calculate the cyclotron line spectra produced by line-forming regions having a range of Thomson optical depths from tau(To) - 8 x 10(-4) to tau(To) 10. Our findings have implications for accretion-powered pulsars and gamma-ray bursters. In particular, the absence of pronounced shoulders on both sides of the cyclotron first harmonic line in the spectra of accretion-powered pulsars suggests that the line-forming region is either illuminated from below or has a large optical depth (Thomson optical depth tau(To) greater than or similar to 10). However, we (like earlier workers) find that models in which the line-forming region is either a static slab or a static cylinder and has a large optical depth are unable to explain the modest equivalent widths W-E of the cyclotron lines in the observed spectra of accretion-powered pulsars. In addition, we find that approximating the injected photon spectrum as a Wien spectrum, an approximation made by almost all workers to date, is not valid because of the frequency dependence of the cyclotron scattering cross section below the cyclotron fundamental. Consequently, future work in this area should explore physical effects that have not been included so far, such as the plasma flow velocity in the accretion column and the injected photon spectrum resulting from energy deposition in the surface layers of the neutron star; more complicated geometries, such as accretion mounds and multiple component magnetic fields; and alternative models, such as cyclotron scattering in the magnetosphere. We find that slab line-forming regions in which the magnetic field is parallel to the slab are able to produce narrow lines with large equivalent widths W-E, suggesting that the lines observed in the X-ray spectra of some gamma-ray bursts might be able to be formed not only in plasma near the magnetic poles of a neutron star but also in plasma trapped at the magnetic equator of the star.