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We use a Monte Carlo radiative transfer code to examine the dependence of theproperties of cyclotron resonant scattering lines on the spatial geometry andthe optical depth of the line-forming region. We focus most of our attention ona line-forming region that is a plane-parallel slab. We also consider acylindrical line-forming region. In both cases, the line-forming regioncontains an electron-proton plasma at the equilibrium Compton temperature,$T_c$, and is threaded with a uniform magnetic field with strength $\sim10^{12}$ gauss. We consider geometries in which the photon source illuminatesthe line-forming region from below, and in which the photon source is embeddedin the line-forming region. Our findings have implications foraccretion-powered pulsars and gamma-ray bursters. In particular, the absence ofpronounced shoulders on each side of the cyclotron first harmonic line in thespectra of accretion-powered pulsars suggests that the line-forming region iseither illuminated from below and outside, as would be the case if it wereplasma suspended in the magnetosphere of the neutron star, or it has a large($\tau_{To} \gtrsim 10$) optical depth. Also, the ability of a slabline-forming region in which the magnetic field is parallel to the slab toproduce narrow lines with large $W_E$ suggests that the lines observed in theX-ray spectra of some gamma-ray bursts might be able to be formed in plasmatrapped at the magnetic equator of a neutron star.Comment: 61 LaTex pages and 19 Postscript figures, AASTeX. Submitted to the  Astrophysical Journal 7 March 199

Effects of the Geometry of the Line‐forming Region on the Properties of Cyclotron Resonant Scattering Lines