In this paper we study the evolution of a primordial black hole binary (BHB) in a sample of over 1500 direct-summation $N-$body simulations of small-and intermediate-size isolated star clusters as proxies of galactic open clusters. The BHBs have mass
es in the range of the first LIGO/Virgo detections. Some of our models show a significant hardening of the BHB in a relatively short time. Some of them merge within the cluster, while ejected binaries, typically, have exceedingly long merger timescales. The perturbation of stars around BHB systems is key to induce their coalescence. The BHBs which merge in the cluster could be detected with a delay of a few years between space detectors, as future LISA, and ground-based ones, due to their relatively high eccentricity. Under our assumptions, we estimate a BHB merger rate of $R_{rm mrg} sim 2$ yr$^{-1}$ Gpc$^{-3}$. We see that in many cases the BHB triggers tidal disruption events which, however, are not linked to the GW emission. Open cluster-like systems are, hence, a promising environment for GWs from BHBs and tidal disruptions.
The first neutron star-neutron star (NS-NS) merger was discovered on August 17, 2017 through gravitational waves (GW170817) and followed with electromagnetic observations. This merger was detected in an old elliptical galaxy with no recent star forma
tion. We perform a suite of numerical calculations to understand the formation mechanism of this merger. We probe three leading formation mechanisms of double compact objects: classical isolated binary star evolution, dynamical evolution in globular clusters and nuclear cluster formation to test whether they are likely to produce NS-NS mergers in old host galaxies. Our simulations with optimistic assumptions show current NS-NS merger rates at the level of 10^-2 yr^-1 from binary stars, 5 x 10^-5 yr^-1 from globular clusters and 10^-5 yr^-1 from nuclear clusters for all local elliptical galaxies (within 100 Mpc^3). These models are thus in tension with the detection of GW170817 with an observed rate 1.5 yr^-1 (per 100 Mpc^3; LIGO/Virgo estimate). Our results imply that either (i) the detection of GW170817 by LIGO/Virgo at their current sensitivity in an elliptical galaxy is a statistical coincidence; or that (ii) physics in at least one of our three models is incomplete in the context of the evolution of stars that can form NS-NS mergers; or that (iii) another very efficient (unknown) formation channel with a long delay time between star formation and merger is at play.
