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