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Accretion-powered X-ray pulsars exhibit significant variability of theCyclotron Resonance Scattering Feature (CRSF) centroid energy on pulse-to-pulsetimescales, and also on much longer timescales. Two types of spectralvariability are observed. For sources in group 1, the CRSF energy is negativelycorrelated with the variable source luminosity, and for sources in group 2, theopposite behavior is observed. The physical basis for this bimodal behavior iscurrently not understood. We explore the hypothesis that the accretion dynamicsin the group 1 sources is dominated by radiation pressure near the stellarsurface, and that Coulomb interactions decelerate the gas to rest in the group2 sources. We derive a new expression for the critical luminosity such thatradiation pressure decelerates the matter to rest in the supercritical sources.The formula for the critical luminosity is evaluated for 5 sources, using themaximum value of the CRSF centroid energy to estimate the surface magneticfield strength. The results confirm that the group 1 sources are supercriticaland the group 2 sources are subcritical, although the situation is less clearfor those highly variable sources that cross over the critical line. We alsoexplain the variation of the CRSF energy with luminosity as a consequence ofthe variation of the characteristic emission height. The sign of the heightvariation is opposite in the supercritical and subcritical cases, hencecreating the observed bimodal behavior.

Spectral Formation in Accreting X-Ray Pulsars: Bimodal Variation of the Cyclotron Energy with Luminosity