Positive correlation between the cyclotron line energy and luminosity in sub-critical X-ray pulsars: Doppler effect in the accretion channel

Abstract

Cyclotron resonance scattering features observed in the spectra of some X-ray pulsars show significant changes of the line centroid energy with the pulsar luminosity. Whereas for bright sources above the so called critical luminosity these variations are established to be connected with the appearance of the high accretion column above the neutron star surface, at low, sub-critical luminosities the nature of the variations (but with the opposite sign) has not been discussed widely. We argue here that the cyclotron line is formed when the radiation from a hotspot propagates through the plasma falling with a mildly relativistic velocity onto the neutron star surface. The position of the cyclotron resonance is determined by the Doppler effect. The change of the cyclotron line position in the spectrum with luminosity is caused by variations of the velocity profile in the line-forming region affected by the radiation pressure force. The presented model has several characteristic features: (i) the line centroid energy is positively correlated with the luminosity; (ii) the line width is positively correlated with the luminosity as well; (iii) the position and the width of the cyclotron absorption line are variable over the pulse phase; (iv) the line has a more complicated shape than widely used Lorentzian or Gaussian profiles; (v) the phase-resolved cyclotron line centroid energy and the width are negatively and positively correlated with the pulse intensity, respectively. The predictions of the proposed theory are compared with the variations of the cyclotron line parameters in the X-ray pulsar GX 304-1 over a wide range of sub-critical luminosities as seen by the INTEGRAL observatory.

Dramatic spectral transition of X-ray pulsar GX 304−1 in low luminous state

“…This is very different from the INTEGRAL spectra at higher luminosities of 2.2×10 37 and 0.2×10 37 erg s −1 (upper two sets of data points in Fig. 1, Mushtukov et al 2015b), which can be well fitted with the standard XRP power-law model modified by a high energy cutoff and a cyclotron absorption line at ∼ 60 and ∼ 50 keV, respectively.…”

“…Moreover, such a large decrease appears to be unrealistic in the context of the two models proposed so far to explain the observed correlation of line energy with flux. In the model by Mushtukov et al (2015b), the observed correlation is produced by the Doppler effect in the flow, whose velocity is affected by radiation pressure, which is more efficient at higher luminosities. The maximal relative shift here is limited by a factor of two, as the flow velocity changes from the free-fall with v ≈ 0.5c to zero.…”

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

“…The energy of the CRSF depends on the accretion rate in good agreement with theoretical predictions: a fit of the data using as best fit model Equation 2 yields E⋆ = 29.56 ± 0.05, with χ 2 = 1.8, assuming a harmonic ratio of 2 (solid line in the top panel of Fig 3). Mushtukov et al (2015) have proposed an alternative theory to explain the positive correlation between CRSF energy and luminosity in subcritical sources: the bulk of the radiation, emitted by the hotspot on the polar cap, travels upwards through the accretion channel interacting with the infalling matter and producing the CRSF at the resonant energies. The line appears redshifted by Doppler effect to the observer due to the velocity profile of the plasma falling towards the NS surface.…”

Discovery and modelling of a flattening of the positive cyclotron line/luminosity relation in GX 304−1 withRXTE

“…Note that an alternative explanation of the positive correlations between Ecyc − Fx and W − Fx at moderate Xray luminosities was recently proposed by Mushtukov et al (2015b). However, that model predicts the opposite sign of the second derivative in the Ecyc − Fx and W − Fx relations (cf.…”