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

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, L crit = 1.5 × 10 37 B 16/15 12 erg s −1 , where B 12 is the surface magnetic field strength in units of 10 12 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 B 12 . 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.

TheSwift-BAT monitoring reveals a long-term decay of the cyclotron line energy in Vela X-1

“…This correlation, observed for the first time in Her X-1 (Staubert et al 2007) is expected in the sub-critical accretion regime (L coul < L < Lcrit, see Becker et al 2012), where the deceleration of the material to rest at the stellar surface is accomplished by a shock dominated by Coulomb interactions. The ram pressure of the infalling plasma increases with the accretion rate driving the shock region down to regions of higher mag- where τ⋆ is the Thomson optical depth ( ∼ 20 for typical HMXB parameters, Becker et al 2012), R⋆ is the radius of the NS, M⋆ is the mass of the NS, E⋆ is the energy of the fundamental cyclotron line at the NS surface and Λ is a constant related to the interaction between the magnetic field and the surrounding medium (Lamb et al 1973). We adopt the values Λ = 1, suitable for spherical accretion, R⋆ = 10 km and M⋆ = 1.8M⊙ (Rawls et al 2011) as in Fürst et al (2014).…”

“…This difference could be related to a narrower accretion column in Vela X-1, that, following Eq. 23 in Becker et al (2012), is ∼ 0.4 km with respect to ∼ 1.3 km in Her X-1 and allows for a faster growth of the height of the mound. Indeed, the accreted mass per unit surface is ∼ 7.2 × 10 −10 M ⊙ km −2 year −1 in Vela X-1, a factor of ∼ 4 higher than ∼ 1.9 × 10 −10 M ⊙ km −2 year −1 in Her X-1.…”

RX J0440.9 + 4431: a persistent Be/X-ray binary in outburst

“…According to the discussion of Becker et al (2012), at low luminosity (L X < ∼ 10 34−35 erg s −1 ) matter strikes the NS surface after passing through a gas-mediated shock. At higher luminosity, the radiation pressure begins to affect the accretion process so that a radiative shock forms, and plasma deceleration takes place through Coulomb interactions in an vertically extended atmosphere.…”

Transient X-ray pulsar V 0332+53: pulse-phase-resolved spectroscopy and the reflection model

“…A study of the source pulse-averaged spectra showed that the cyclotron line energy, as well as parameters of the spectral continuum, significantly change with the source luminosity (Tsygankov et al 2006; Mowlavi et al 2006;Tsygankov et al 2010;Nakajima et al 2010) along the outburst. This behaviour was interpreted as a result of changes in the height of the accretion column where the cyclotron absorption line was assumed to originate (see, e.g., Mihara 1995;Schönherr et al 2007;Nishimura 2008Nishimura , 2014Becker et al 2012, and references therein). However, alternative scenario has recently been proposed by Poutanen et al (2013), where the line forms in the illuminated atmosphere of the neutron star.…”