Numerical $\texttt{AXP4}$ Simulations of Pulse Profiles for Binary Accreting X-ray Pulsars $-$ II: A Case Study of Centaurus X-3

TL;DR

This study compares simulated pulse profiles with observations of Centaurus X-3, estimating the emission region size and analyzing effects of gravitational light bending and luminosity variations to better understand accretion physics in X-ray pulsars.

Contribution

It introduces a method to estimate the neutron star's hotspot size using pulse profile simulations and observational data, incorporating gravitational light bending effects.

Findings

Hotspot radius estimated to be around 1 km after including light bending.

Pulse profile sensitivity to luminosity variations links accretion geometry to X-ray luminosity.

Simulation results align with standard neutron star models, validating the approach.

Abstract

The pulse shapes simulated in the accompanying paper Part $-$ I are compared with observations of a model binary accreting X-ray pulsar, Centaurus X-3. With known Cen X-3 inclination angles provided as input to the $\texttt{AXP4}$ code, the generated pulse profile is suitably compared with the corresponding observed energy-resolved $\textit{AstroSat}$/LAXPC pulse profile. The pulsed fraction is proposed as a robust, quantitative measure for estimating the size of the emission region of Centaurus X-3 by extending the simulations to include spherical caps of varying fractional surface coverage of the neutron star $-$ over the full range of $0-100\%$, up to very large caps (with polar half angle $> 30^{\circ}$). The hotspot radius thus derived drops by an order of magnitude from $12.27$ km to $1.36^{+0.29}_{-0.26}$ km, within the ballpark of the standard model value of $\sim$$1$ km, after including the effect of gravitational light bending, lending further weight to its routine emphasis in the literature. The energy- and luminosity-dependence of the composite gravitationally bent and slab-integrated pulse profiles is further studied. As the pulse profile is sensitive to luminosity variations, the correlation of the size of a finite polar cap and its dependence on X-ray luminosity $-$ through the rate and subsequently, the geometry of accretion $-$ is discussed. Although a single, model pulsar was chosen for this work to exhibit the depth of the physical and astrophysical prospects of such a probe, this exercise can be extended to a wide range of existing X-ray pulse profiles of known binary accreting pulsars available in galactic catalogs, especially, with the possible inclusion of accretion columns (with cylindrical co-ordinate transformation) in the future.