$\texttt{AXP4}$, a Numerical Simulator of Pulse Profiles for Binary Accreting X-ray Pulsars $-$ I: Beam Geometries

TL;DR

This paper introduces a new numerical code, AXP4, to simulate pulse profiles of binary accreting X-ray pulsars, incorporating realistic beam geometries and general relativistic effects like light bending and gravitational red-shift.

Contribution

The work develops AXP4, a novel high-resolution numerical simulator that models pulse profiles with detailed beam geometries and relativistic effects, advancing previous models significantly.

Findings

Sharp, pointed-peak pulse profiles achieved with the model.

Relativistic light bending and red-shift effects significantly alter pulse profiles.

Application to various emission geometries demonstrates the model's versatility.

Abstract

The paper presents model pulse profiles from binary accreting X-ray pulsars using high-resolution numerical simulations for pencil and fan emission beam geometries, each with two different optical depths obtained using a new numerical code $\texttt{AXP4}$ developed in this work. Sharp, pointed-peak improvements are obtained in the known flat-top pulse profiles by extrapolating the model emission functions available in the literature over the full range of emission angles for a realistic description. The effect of general relativistic bending of light due to the strong gravity near the neutron star is taken into account, updating previous attempts with new analytic approximations for photon trajectories in curved space-time reported in the literature (including additional flux contribution from the dark unseen face of the pulsar). Incorporating the other general relativistic effect of gravitational red-shift is seen to redden the pulsar beam to increasingly lower energies along the X-ray observing band. Integrating this emission over a circular slab geometry for two antipodal hotspots lying flush at the neutron star polar caps presents smoothened, composite gravitationally bent pulse profiles to the observer. A comparison between the corresponding non-normalized flux profiles is included. For theoretical completeness and reference base, this treatment is applied to isotropic emitters with uniform injection and limb-darkened beams, as well. The possibility of the production of Einstein rings around a pulsar for a limiting value of the compactness parameter is a distinctive feature.