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.
Binary radio pulsars are generally believed to have been spun up to millisecond periods (i.e. recycling) via mass accretion from their donor stars, and they are the descendants of neutron star low-mass X-ray binaries. However, some studies indicate that the formation of pulsars from the accretion-induced collapse (AIC) of accreting white dwarfs (WDs) cannot be excluded. In this work, we use a population-synthesis code to examine if the AIC channel can produce eccentric binary millisecond pulsars (BMSPs) in the Galaxy. Our simulated results indicate that only when the natal MSPs receive a relatively strong kick ( 100 km s −1 ), can the AIC channel produce ∼10-180 eccentric (e > 0.1) BMSPs in the Galaxy, most of which are accompanied by a helium star. Such a kick seems to be highly unlikely in the conventional AIC process, hence the probability of forming eccentric BMSPs via the AIC channel can be ruled out. Even if a high kick is allowed, the AIC channel cannot produce eccentric BMSPs with an orbital period of 20 d. Therefore, we propose that the peculiar BMSP PSR J1903+0327 cannot be formed by the AIC channel. However, the AIC evolutionary channel may produce some fraction of isolated MSPs, and even submillisecond pulsars if they really exist.
We calculate the mass-radius relationship of quark stars with the magnetized densitydependent quark mass model in this work, considering two magnetic field geometries: a statistically isotropic, tangled field and a force-free configuration. In both cases, magnetic field production decreases in the case of maximum quark star mass. Furthermore, a tangled, isotropic magnetic field has a relatively smaller impact on the mass and radius, compared to the force-free configuration, which implies that the geometry of the interior magnetic field is at least as important as the field strength itself when the influence of the strong magnetic field on the mass and radius is assessed.
Rotochemical heating originates in the deviation from beta equilibrium due to spin-down compression, which is closely related to the dipole magnetic field. We numerically calculate the deviation from chemical equilibrium and thermal evolution of neutron stars with decaying magnetic fields. We find that the power-law long term decay of the magnetic field slightly affects the deviation from chemical equilibrium and surface temperature. However, the magnetic decay leads to older neutron stars that could have a different surface temperature with the same magnetic field strength. That is, older neutron stars with a low magnetic field (10 8 G) could have a lower temperature even with rotochemical heating in operation, which probably explains the lack of other observations on older millisecond pulsars with higher surface temperature, except millisecond pulsar J0437-4715.
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