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 of 70 $M_{\odot}$ black hole (BH) and an 8
$M_{\odot}$ main sequence star (LB-1) is observed to reside in the Milky Way
(MW). We show that long term evolution of an 8 $M_{\odot}$ star around a BH
with mass between 5-70 $M_{\odot}$ makes them visible as ultra-luminous X-ray
(ULX) sources in the sky. Given the expected ULX phase lifetime ($\approx0.1$
Myr) and their lack of detection in the MW, we conclude that the frequency of
an 8-20 $M_{\odot}$ star to be in binary around a stellar mass BH should be
less than ($f<2\times10^{-3}$). This is in tension with Liu et al. (2019)
claimed detection frequency of LB-1 like system around 8-20$M_{\odot}$ stars
($f\approx3\times10^{-2}$). Moreover, the 8 $M_{\odot}$ 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 are 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 if the NS is born from ECSN,
a frequency upper limit of ($f=5\times10^{-4}$) for stars with masses $\approx
8-20~M_{\odot}$ 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.
