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Constraints on Population I/II neutron star-black hole binary formation by gravitational wave and radio observations

Two neutron star (NS)-black hole (BH) binaries, GW200105 and GW200115 found in the LIGO/Virgo O3b run have smaller BH mass of 6--9\,$M_{\odot}$ which is consistent with Population I and II origin. Our population synthesis simulations using $10^6$ Population I and II binaries with appropriate initial parameters show consistent binary mass, event rate, and no detection of radio pulsar (PSR) and BH binaries in our galaxy so far. Especially, we found possible progenitors of GW200105 and GW200115 which were formed at redshift $z=0.15$ and $z=1.6$ with binary mass of $(34M_{\odot},\, 9.2M_{\odot})$ and $(23.7M_{\odot},\, 10.6M_{\odot})$, respectively. The final masses of these binaries are $(6.85M_{\odot},\,2.14M_{\odot})$ and $(6.04M_{\odot},\,1.31M_{\odot})$ which look like $(9.0_{-1.7}^{+1.7}M_{\odot},\, 1.91_{-0.24}^{+0.33}M_{\odot})$ of GW200105 and $(5.9_{-2.5}^{+2.0}M_{\odot},\,1.44_{-0.29}^{+0.85}M_{\odot})$ of GW200115, respectively. We also estimate that 2.68-19.7 PSR-BH binaries in our galaxy will be observed by SKA. The existence of NS-BHs in our galaxy can be confirmed in future SKA era. Using the GW observation of NS-BH mergers and the radio observation of PSR-BHs in future, we can get more severe constraints on the NS-BH formation process.