The cyclotron spectrum of anisotropic ultrarelativistic electrons: interpretation of X-ray pulsar spectra

The spectrum of cyclotron radiation produced by electrons with a strongly anisotropic velocity distribution is calculated taking into account higher harmonics. The motion of the electrons is assumed to be ultrarelativistic along the magnetic field and nonrelativistic across the field. One characteristic feature of the resulting spectrum is that harmonics of various orders are not equally spaced. The physical properties and observed spectra of four X-ray pulsars displaying higher cyclotron harmonics are analyzed. The cyclotron features in the spectra of all four pulsars can be interpreted only as emission lines. Moreover, the observed harmonics are not equidistant, and display certain other properties characteristic of emission by strongly anisotropic ultrarelativistic electrons. In addition, there are indirect theoretical arguments that the electrons giving rise to cyclotron features in the spectra of X-ray pulsars are ultrarelativistic and characterized by strongly anisotropic distributions. As a result, estimates of the magnetic fields of X-ray pulsars (which are usually derived from the energies of cyclotron lines) and certain other physical parameters require substantial revision.