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

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 0.8L ≲ Lapp ≲ 1.25L. 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.

Searching for the Highest Energy of Pulsation and Critical Luminosity of Swift J0243.6+6124 Observed by Insight-HXMT

“…The observed pulse profiles depend on luminosity, energy and the geometry of the rotating NS in the observer's reference frame. Many studies have shown that reflection by the NS surface and gravitational lensing effects result in more complex beam patterns than the simplified "pencil-fan" picture and thus more complex pulse profiles (see e.g., Poutanen et al 2013;Lutovinov et al 2015;Postnov et al 2015;Mushtukov et al 2018;Markozov & Mushtukov 2024), as usually observed.…”