Compact Binary Formation in Open Star Clusters II: Difficulty of Gaia NS formation in low-mass star clusters

Gaia mission offers opportunities to search for compact binaries not involved in binary interactions (hereafter inert compact binaries), and results in the discoveries of binaries containing one black hole (BH) or one neutron star (NS), called "Gaia BHs’’ and "Gaia NSs’', respectively. We have assessed if Gaia BHs and NSs can be formed in open clusters through dynamical interactions. In order to obtain a large number of inert compact binaries similar to Gaia BHs and NSs, we have performed gravitational $N$-body simulations for a large number of open clusters whose total mass is $1.2 \times 10^8 M_\odot$. These clusters have various masses, metallicities, densities, and binary fractions. We have found that open clusters form Gaia BHs ($10^{-6}$-$10^{-5} M_\odot^{-1}$) much more efficiently than Gaia NSs ($\lesssim 10^{-7} M_\odot^{-1}$) for any cluster parameters. This is quite inconsistent with observational results, because the reported numbers of Gaia BHs and NSs are $3$ and $21$, respectively. Additionally, we have switched off NS natal kicks for $10^4$ open clusters each weighing $10^3 M_\odot$ in order to retain a large number of NSs in open clusters. Then, open clusters form inert NS binaries originating from primordial binaries rather than formed through dynamical interactions. This means that Gaia NSs are formed dominantly on isolated fields, not in open clusters, if there is no NS natal kick. We have concluded that Gaia BHs can be dominantly formed in open clusters, however Gaia NSs cannot.