LB-1 is inconsistent with the X-ray source population and pulsar-black hole binary searches in the Milky Way

If confirmed, a wide binary system consisting of a 70 M o˙ black hole (BH) and an 8 M o˙ main-sequence star (LB-1) is observed to reside in the Milky Way (MW). While we remain agnostic about the nature of LB-1, we show that long-term evolution of an 8 M o˙ star around a BH with mass between 5 and 70 M o˙ makes them visible as ultraluminous X-ray (ULX) sources in the sky. Given the expected ULX phase lifetime (≈0.1 Myr) and their lack of detection in the MW, we conclude that the frequency of an 8-20 M o˙ star to be in binary around a stellar mass BH should be less (f < 4 × 10-3). This is in tension with Liu et al., who claimed the detection frequency of an LB-1-like system to be around 8-20 M o˙ stars (f ≈ 3 × 10-2). Moreover, the 8 M o˙ star is likely to end as a neutron star (NS) born with a very small kick from an electron-capture supernova (ECSN), leaving behind a wide NS-BH binary. So far, less than 1% of all the detectable pulsars in the MW have been mapped and there has been no detection of any pulsars in binary systems around BHs, which sets an upper bound of about 100 possible pulsar-BH systems in the MW. We show whether the NS is born from ECSN, a frequency upper limit of (f ≈ 10-3) for stars with masses ≈8-20 M o˙ in the MW to have a BH companion. The rate discrepancy will further increase as more pulsars are mapped in the MW, yet these searches would not be able to rule out the Liu et al. detection frequency if NSs are instead born in core collapse SNe with the commonly inferred high kick velocities.