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

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 AXP4 code, the generated pulse profile is suitably compared with the corresponding observed energy-resolved 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^). 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 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.