Spectral formation in accreting X-ray pulsars: bimodal variation of the cyclotron energy with luminosity

Context. Accretion-powered X-ray pulsars exhibit significant variability of the cyclotron resonance scattering feature (CRSF) centroid energy on pulse-to-pulse timescales, and also on much longer timescales. Two types of spectral variability are observed. For sources in group 1, the CRSF energy is negatively correlated with the variable source luminosity, and for sources in group 2, the opposite behavior is observed. The physical basis for this bimodal behavior is currently not well understood. Aims. We explore the hypothesis that the accretion dynamics in the group 1 sources is dominated by radiation pressure near the stellar surface, and that Coulomb interactions decelerate the gas to rest in the group 2 sources. Methods. We derive a new expression for the critical luminosity, Lcrit, such that radiation pressure decelerates the matter to rest in sources with X-ray luminosity LX > Lcrit. The formula for Lcrit is based on a simple physical model for the structure of the accretion column in luminous X-ray pulsars that takes into account radiative deceleration, the energy dependence of the cyclotron cross section, the thermodynamics of the accreting gas, the dipole structure of the pulsar magnetosphere, and the diffusive escape of radiation through the column walls. We show that for typical neutron star parameters, \hbox{$\Lcrit = 1.5 \times 10^{37} B_{12}^{16/15}~{\rm erg\, s}^{-1}$}, where B12 is the surface magnetic field strength in units of 1012 G. Results. The formula for the critical luminosity is evaluated for five sources, using the maximum value of the CRSF centroid energy to estimate the surface magnetic field strength B12. The results confirm that the group 1 sources are supercritical (LX > Lcrit) and the group 2 sources are subcritical (LX < Lcrit), although the situation is less clear for those highly variable sources that cross over the line LX = Lcrit. We also explain the variation of the CRSF energy with luminosity as a consequence of the variation of the characteristic emission height. The sign of this dependence is opposite in the supercritical and subcritical cases, hence creating the observed bimodal behavior. Conclusions. We have developed a new model for the critical luminosity in accretion-powered X-ray pulsars that explains the bimodal dependence of the CRSF centroid energy on the X-ray luminosity LX. Our model provides a physical basis for the observed variation of the CRSF energy as a function of LX for both the group 1 (supercritical) and the group 2 (subcritical) sources as a result of the variation of the emission height in the column.