Exploration of spin-down rate of neutron stars in high-mass X-ray binaries

Abstract

We use the evolutionary population synthesis method to investigate the statistical properties of the wind-fed neutron star (NS) compact (P 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 by assuming that the surrounding material is treated as forming a quasi-static atmosphere or by assuming that the characteristic velocity of matter and the typical Alfvén 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 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 by simple integration of the magnetic torque over the magnetosphere with a larger spin-down rate than that given by Davies & Pringle (1981) or Illarionov & Sunyaev (1975) 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 Wang & Robertson (1985); Dai, Liu & Li (2006);Jiang & Li (2005) and that given by Davidson & Ostriker (1973) 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.

Can the Subsonic Accretion Model Explain the Spin Period Distribution of Wind-Fed X-Ray Pulsars?

“…The darkness of each element represents the relative number of the X-ray binaries. The diamonds mark the observed wind-fed supergiant HMXBs with known P s and P orb , and the triangles represent disk-fed X-ray pulsars (data from Townsend et al 2011;Dai et al 2016, and references therein). According to our calculation, the wind-fed X-ray pulsars are clustered into the upper and lower subgroups, related to different regimes of quasi-spherical accretion.…”

“…Different from Dai et al (2006Dai et al ( , 2016, we consider the NS spin evolution both prior to and during the HMXB phase, in which the subsonic accretion may dominate. In Section 2 we describe our assumptions and theoretical considerations.…”

“…This paper aims to test the model of Shakura et al (2012) by comparing the expected spin period distribution based on population synthesis calculation with the observations of wind-fed HMXBs. Different from Dai et al (2006Dai et al ( , 2016, we consider the NS spin evolution both prior to and during the HMXB phase, in which the subsonic accretion may dominate. In Section 2 we describe our assumptions and theoretical considerations.…”

Spin evolution of neutron stars in wind-fed high mass X-ray binaries

“…From such a nascent neutron star, strong electro-magnetic radiation and relativistic particles are emitted and mass accretion onto the neutron star could be avoided; this evolutionally stage is called the ejector phase (Popov & Turolla 2012;Dai et al 2016).…”

“…In recent years, on the other hand, studies on linking magnetic field evolution and spin evolution of neutron stars have been advanced (Popov & Turolla 2012;Dai et al 2016;Wang & Tong 2020). Especially, around accreting neutron star from the stellar wind, wind matter should be decelerated by a shock formation and then the settling accretion matter forms thermally supported shell (Shakura et al 2012).…”