2020A&A...634A.126W

Context. Subdwarf B stars (sdBs) play a crucial role in stellar evolution, asteroseismology, and far-UV radiation of early-type galaxies, and have been intensively studied with observation and theory. It has theoretically been predicted that sdBs with neutron star (NS) companions exist in the Galaxy, but none have been discovered yet. This remains a puzzle in this field. In a previous study (hereafter Paper I), we have studied the formation channels of sdB+NS binaries from main-sequence (MS) stars plus NS binaries by establishing a model grid, but it is still unclear how these binaries consisting of MS stars and NS binaries came to be in the first place. Aims. We systematically study the formation of sdB+NS binaries from their original zero-age main-sequence progenitors. We bridge the gap left by our previous study in this way. We obtain the statistical population properties of sdB+NS binaries and provide some guidance for observational efforts. Methods. We first used Hurley's rapid binary evolution code BSE to evolve 10⁷ primordial binaries to the point where the companions of NS+MS, NS+Hertzsprung gap star, and NS+Giant Branch star binaries have just filled their Roche lobes. Next, we injected these binaries into the model grid we developed in Paper I to obtain the properties of the sdB+NS populations. We adopted two prescriptions of NS natal kicks: the classical Maxwellian distribution with a dispersion of σ=265km/s, and a linear formula that assumes that the kick velocity is associated with the ratio of ejected to remnant mass. Different values of α_CE, where α_CE is the common-envelope ejection efficiency, were chosen to examine the effect of common-envelope evolution on the results. Results. In the Galaxy, the birthrate of sdB+NS binaries is about 10^–4yr^–1 and there are ∼7000-21000 such binaries. This contributes 0.3-0.5% of all sdB binaries in the most favorable case. Most Galactic sdB+NS binaries (≥60%) arise from the channel of stable mass transfer. The value of α_CE has little effect on the results, but when we use the linear formula prescription of NS natal kick, the number and birthrate doubles in comparison to the results we obtained with the Maxwellian distribution. The orbital periods of sdB+NS binaries from different formation channels differ significantly, as expected. This results in two peaks in the radial velocity (RV) semi-amplitude distribution: 100-150km/s for stable mass transfer, and 400-600km/s for common-envelope ejection. However, the two sdB+NS binary populations exhibit similar delay-time distributions, which both peak at about 0.2Gyr. This indicates that Galactic sdB+NS binaries are born in very young populations, probably in the Galactic disk. The sdB+NS binaries produced from the common-envelope ejection channel are potential sources of strong gravitational wave radiation (GWR), and about ∼100-300 could be detected by the Laser Interferometer Space Antenna (LISA) with a signal-to-noise ratio of 1.Conclusions. Most sdB+NS binaries are located in the Galactic disk with small RV semi-amplitudes. SdB+NS binaries with large RV semi-amplitudes are expected to be strong GWR sources, some of which could be detected by LISA in the future.