Context. Binary population synthesis predicts the existence of subdwarf B stars (sdBs) with neutron star (NS) or black hole (BH) companions. Several works have been dedicated to finding such systems, but none has been confirmed yet. Theoretically, the formation of sdBs with white dwarf (WD) and main sequence (MS) companions has been well investigated, while those with NS or BH companions remain to be explored further. Aims. We systematically investigate the formation of sdB+NS binaries from binary evolution and aim to obtain some clues for a search for such systems. Methods. We started from a series of MS+NS systems and determined the parameter spaces for producing sdB+NS binaries from the stable Roche-lobe overflow (RLOF) channel and from the common envelope (CE) ejection channel. The parameters for sdB+NS binaries were obtained from detailed binary evolution calculation with the code called modules for experiments in stellar astrophysics (MESA), and the CE parameters were given by the standard energy budget for CE evolution. The MS star had an initial mass ranging from 0.8 to 5 M . Various NS accretion efficiencies and NS masses were examined to investigate the effects they have. We show the characteristics of the produced sdB+NS systems, such as the mass of components, orbital period, the semi-amplitude of the radial velocity (K), and the spin of the NS component. Results. sdB+NS binaries can be produced either from stable RLOF or from CE ejection. In the stable RLOF channel, sdBs can be formed when the donor starts mass transfer close to the tip of the giant branch if the donor has an initial mass ≤ 2.0M . For more massive donors, sdBs can be formed when the donor starts mass transfer during the Hertzsprung gap or near the end of the MS. The orbital period of sdB+NS binaries produced in this way ranges from several days to more than 1000 days and moves toward the short-period (∼ hr) side with increasing initial MS mass. The highest K is about 150km s −1 for an MS star of initially 5M . However, the sdB+NS systems that result from CE ejection have very short orbital periods and then high values of K (up to 800km s −1 ). Such systems are born in very young populations (younger than 0.3 Gyr) and are potential gravitational wave sources that might be resolved by the Laser Interferometer Space Antenna (LISA) in the future. Gravitational wave radiation may again bring them into contact on a timescale of only ∼ Myr. As a consequence, they are rare and hard to discover. The pulsar signal is likely a feature of sdB+NS systems caused by stable RLOF, and some NS components in sdB binaries may be millisecond pulsars. Various NS accretion efficiencies and NS masses change some properties of sdB+NS binaries, but not our general results.

As a candidate of dark matter, primordial black holes (PBHs) have attracted more and more attentions as they could be possible progenitors of the heavy binary black holes (BBHs) observed by LIGO/Virgo. Accurately estimating the merger rate of PBH binaries will be crucial to reconstruct the mass distribution of PBHs. It was pointed out the merger history of PBHs may shift the merger rate distribution depending on the mass function of PBHs. In this paper, we use 10 BBH events from LIGO/Virgo O1 and O2 observing runs to constrain the merger rate distribution of PBHs by accounting the effect of merger history. It is found that the second merger process makes subdominant contribution to the total merger rate, and hence the merger history effect can be safely neglected.

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