2011ApJ...730..106N

I model cyclotron lines by calculating a superposition of a large number of cyclotron line spectra emerging from different heights of a line-forming region of a non-uniform density and temperature of an electron-proton plasma threaded by a dipole magnetic field. In this paper, I mainly discuss the properties of the cyclotron lines in accreting X-ray pulsars with long spin periods (∼100-800 s). My simplified model succeeds in reproducing asymmetric line profiles, anharmonic ratios of line energy, relationship between the width and the depth of the line, and correlation between cyclotron line energy and X-ray intensity in the main pulse. In addition, I demonstrate that a shallower and broader fundamental (= first harmonic) line and a deeper second harmonic line as observed in accreting X-ray pulsars such as Vela X-1 and A0535+26 can be produced via a superposition of a large number of cyclotron lines formed at numerous different heights in a line-forming region with a dipole magnetic field. In this case, the ratio of the peak energy of the second harmonic absorption line to the fundamental can be larger than harmonic ratio 2. Furthermore, the width of the fundamental line is comparable to or larger than that of the second harmonic. These characteristics of the cyclotron lines are consistent with those observed in Vela X-1 and A0535+26.