Formation Mechanism for Broad and Shallow Profiles of Cyclotron Lines in Accreting X-Ray Pulsars

We model cyclotron lines by calculating a superposition of the spectra of some cyclotron lines emerging from some individual line-forming regions with a uniform density, temperature, and magnetic field strength in each region. A whole line-forming region is composed of a series of a large number of individual different domains at the temperature, density, and magnetic field strength, which vary with height or location of each of the individual domains. We study the properties of the cyclotron lines formed by superposing some cyclotron lines emerging from different heights or locations of an accretion column or mound and present the influences of the superposition of the lines, a geometry of the line-forming region, and the variations in a density, temperature, and magnetic field on the shapes of cyclotron resonant scattering lines. Consequently, we found that broader and shallower cyclotron lines as commonly observed in accretion-powered pulsars are formed in such a line-forming region composed of a large number of domains. The resulting cyclotron lines also tend to have an asymmetric profile that is shallower toward lower energies due principally to the gradient in the widths of the original lines. We also find that the cyclotron absorption line can become broader, as it becomes deeper, regardless of the geometries, i.e., slabs or cylinders as a result of a superposition of individual lines.