Cyclotron line formation by reflection on the surface of a magnetic neutron star

Accretion onto magnetic neutron stars results in X-ray spectra that often exhibit a cyclotron resonance scattering feature (CRSF) and, sometimes, higher harmonics of it. Two places are suspect for the formation of a CRSF: the surface of the neutron star and the radiative shock in the accretion column. Here we explore the first possibility: reflection at the neutron-star surface of the continuum produced at the radiative shock. It has been proposed that for high-luminosity sources, as the luminosity increases, the height of the radiative shock increases, thus a larger polar area is illuminated, and as a consequence the energy of the CRSF decreases because the dipole magnetic field decreases by a factor of two from the pole to the equator. We used a Monte Carlo code to compute the reflected spectrum from the atmosphere of a magnetic neutron star, when the incident spectrum is a power-law one. We restricted ourselves to cyclotron energies $\ll m_ec^2$ and used polarization-dependent scattering cross sections, allowing for polarization mode change. As expected, a prominent CRSF is produced in the reflected spectra if the incident photons are in a pencil beam, which hits the neutron-star surface at a point with a well-defined magnetic field strength. However, the incident beam from the radiative shock has a finite width and thus various magnetic field strengths are sampled. As a result of overlap, the reflected spectra have a CRSF, which is close to that produced at the magnetic pole, independent of the height of the radiative shock. Reflection at the surface of a magnetic neutron star cannot explain the observed decrease in the CRSF energy with luminosity in the high-luminosity X-ray pulsar V 0332+53.