The Intensity Modulation of Fluorescent Line by a Finite Light Speed Effect in Accretion-Powered X-ray Pulsars

The X-ray line diagnostic method is a powerful tool for an investigation of plasma around accretion-powered X-ray pulsars. We point out an apparent intensity modulation of emission lines with their rotation period of neutron stars, due to the finite speed of light (we call this effect "finite light speed effect"), if the line emission mechanism is a kind of reprocessing, such as fluorescence or recombination after ionization by X-ray irradiation from pulsars. The modulation amplitude is determined by the size of the emission region, in competition with the smearing effect by the light crossing time in the emission region. This is efficient if the size of the emission region is roughly comparable to that of the rotation period multiplied by the speed of light. We apply this effect to a symbiotic X-ray pulsar, GX 1+4, a spin modulation of the intense iron line of which has been reported. The finite light speed effect can explain the observed intensity modulation, if its fluorescent region has a size of $\sim 10^{12}$ cm.