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

¹ School of Physics, Astronomy, and Computational Sciences, MS 5C3, George Mason University, 4400 University Drive, Fairfax, VA, USA
e-mail: pbecker@gmu.edu
² Institut für Astronomie und Astrophysik, Abt. Astronomie, Universität Tübingen, Sand 1, 72076 Tübingen, Germany
³ Leibniz-Institut für Astrophysik Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
⁴ Department of Electronics and Computer Science, Nagano National College of Technology, 716 Tokuma, 381-8550 Nagano, Japan
⁵ ISDC Data Center for Astrophysics, Université de Genève, Chemin d’Ecogia 16, 1290 Versoix, Switzerland
⁶ AIM (UMR 7158 CEA/DSM – CNRS – Université Paris Diderot) Irfu/Service d’Astrophysique, 91191 Gif-sur-Yvette, France
⁷ European Space Agency, European Space Astronomy Centre, PO Box 78, 28691 Villanueva de la Cañada, Madrid, Spain
⁸ Space Science Division, Naval Research Laboratory, Washington, DC, USA
⁹ Dr. Karl Remeis-Observatory and Erlangen Centre for Astroparticle Physics, Sternwartstr. 7, 96049 Bamberg, Germany

Received: 17 February 2012
Accepted: 22 May 2012

Abstract

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, L_crit, such that radiation pressure decelerates the matter to rest in sources with X-ray luminosity L_X > L_crit. The formula for L_crit 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, , 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 (L_X > L_crit) and the group 2 sources are subcritical (L_X < L_crit), although the situation is less clear for those highly variable sources that cross over the line L_X = L_crit. 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 L_X. Our model provides a physical basis for the observed variation of the CRSF energy as a function of L_X 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.