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

TL;DR

This paper identifies a finite light speed effect causing intensity modulation of emission lines in accretion-powered X-ray pulsars, explaining observed phenomena and providing a new diagnostic tool for plasma regions.

Contribution

It introduces the finite light speed effect as a cause of line intensity modulation and applies it to explain observations in GX 1+4.

Findings

Finite light speed effect can cause observable line intensity modulation.

The effect explains the modulation in GX 1+4 with a region size of about 10^{12} cm.

The modulation depends on the emission region size relative to light crossing time.

Abstract

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.