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 is a plane-parallel slab. We also consider a cylindrical line-forming region. In both cases, the line-forming region contains an electron-proton plasma at the equilibrium Compton temperature, $T_c$, and is threaded with a uniform magnetic field with strength $\sim 10^{12}$ 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. Our findings have implications for accretion-powered pulsars and gamma-ray bursters. In particular, the absence of pronounced shoulders on each side of the cyclotron first harmonic line in the spectra of accretion-powered pulsars suggests that the line-forming region is either illuminated from below and outside, as would be the case if it were plasma suspended in the magnetosphere of the neutron star, or it has a large ($\tau_{To} \gtrsim 10$) optical depth. Also, the ability of a slab line-forming region in which the magnetic field is parallel to the slab to produce narrow lines with large $W_E$ suggests that the lines observed in the X-ray spectra of some gamma-ray bursts might be able to be formed in plasma trapped at the magnetic equator of a neutron star.