Exploration of Spin-down Rate of Neutron Star in High Mass X-ray Binaries

TL;DR

This study uses population synthesis to analyze neutron star spin-down in high-mass X-ray binaries, finding certain models better match observed populations and suggesting the subsonic propeller phase may not exist.

Contribution

It compares various spin-down models for neutron stars in high-mass X-ray binaries using population synthesis, identifying which models align with observations.

Findings

Certain spin-down models predict the observed number of HMXBs.

Subsonic propeller phase may not exist according to observed distributions.

Models by Wan et al., Dai et al., and Jia et al. fit the data reasonably.

Abstract

We use the evolutionary population synthesis method to investigate the statistical properties of the wind-fed neutron star (NS) compact ($P_{\rm orb}<10$ days) high-mass X-ray binaries (HMXBs) in our Galaxy, based on different spin-down models. We find that the spin-down rate in the supersonic propeller phase given \textbf{by assuming that the surrounding material is treated as forming a quasi-static atmosphere} or \textbf{by assuming that the characteristic velocity of matter and the typical Alfv$\acute{e}$n velocity of material in the magnetospheric boundary layer are comparable to the sound speed in the external medium} is too low to produce the observed number of compact HMXBs. We also find that the models suggested \textbf{by assuming that the infalling material is ejected with the corotation velocity at the magnetospheric radius when the magnetospheric radius is larger than the corotation radius} and \textbf{by simple integration of the magnetic torque over the magnetosphere} with a larger spin-down rate than that given by \citet{dav81} or \citet{is75} can predict a reasonable number of observed wind-fed NS compact HMXBs. Our calculated results indicate that subsonic propeller phase may not exist at all by comparing with the observed particular distributions of wind-fed NS compact HMXBs in the $P_s-P_{orb}$ diagram. However, the spin-down rate suggested by \citet{wan85,dai06,jia05} and that given by \citet{dav73} both seem reasonable to produce the observed distribution of wind-fed NS compact HMXBs in the $P_s-P_{orb}$ diagram. We cannot find which spin-down rate seems more reasonable from our calculations.