Apparent luminosity and pulsed fraction affected by gravitational lensing of accretion columns in bright X-ray pulsars

TL;DR

This paper models how gravitational lensing influences the observed luminosity and pulse profiles of super-critical X-ray pulsars, revealing that apparent luminosity deviations are typically around 20%, with pulse shape strongly affected by accretion geometry.

Contribution

It introduces a toy model simulation of accretion columns in X-ray pulsars, quantifying the effects of gravitational lensing on observed luminosity and pulse profiles, and correlates accretion column growth with increased pulsed fraction.

Findings

Apparent luminosity deviates by about 20% due to lensing.

Pulse profile shape is significantly affected by accretion geometry.

Increased accretion columns correlate with higher pulsed fractions.

Abstract

The luminosity of X-ray pulsars is their key parameter determining the geometry and physical conditions of the accretion flow both on the spatial scales of a binary system and on much smaller scales of emitting regions located close to the stellar surface. Traditionally, the luminosity of X-ray pulsars is estimated out of the X-ray energy flux averaged over the pulsed period and the estimated distance to the source. Due to the anisotropy of X-ray emission, the luminosity estimated on the base of the observed pulse profile can differ from the actual one. Super-critical X-ray pulsars with accretion columns are of particular interest because the X-ray flux from columns is a matter of strong gravitational lensing by a neutron star. Using toy model of an accretion column, we simulate beam patterns in super-critical X-ray pulsars, construct theoretical pulse profiles for different geometries and mutual orientations of pulsars and distant observers and show that despite strong light bending, the typical deviation of the apparent luminosity from the actual one is $\sim 20\%$ only, and in $\sim 90\%$ of cases, the apparent luminosity $0.8 L\lesssim L_{\rm app}\lesssim 1.25 L$. However, the shape of the pulse profiles is strongly affected by the geometry of the emitting region. We show that the appearance and growth of accretion columns tend to be accompanied by an increase of observed pulsed fraction, which is in agreement with the recent observations of bright X-ray transients.