tokens: find (their Table 1, with ). On the other hand, Hoang et al. ( 2018 ) find much higher merger fractions of up to for their nominal GC model, which are higher than the merger fractions of Petrovich Antonini ( 2017 ) and our merger fraction by 2 orders of magnitude. This large difference can be ascribed to different initial conditions. About half of the binaries in Hoang et al. ( 2018 ) merge due the gravitational wave emission only (i.e., even in the absence of the torque of the MBH). Moreover, Hoang et al. ( 2018 ) considered binaries much closer to the MBH ( to (∼10 −2 )) for which the octupole-order terms are important, in contrast to our simulations. The merger rate predicted by Hoang et al. ( 2018 ) is ∼1–, which is one (two) order(s) of magnitude larger than our GC rate estimate without VRR assuming a top-heavy (canonical) IMF. This can be ascribed to the following. 1. The merger fraction adopted by Hoang et al. ( 2018 ) is , which is 0.15/0.005 = 30 times larger than our adopted fraction. 2. The “conversion” factor from the merger fraction to the rate adopted by Hoang et al. ( 2018 ) is . We assumed a “conversion” factor of and for the canonical and top-heavy IMFs, respectively. These two points combined explain the different merger rates. In calculating their rates, Hoang et al. ( 2018 ) assumed that there exists a steady-state population of BH–BH binaries in the central 0.1 pc, with a number of corresponding to a merger rate of . This requires replenishment of the BH–BH binaries on a timescale of 100 Myr, which would be consistent with in situ star formation in a disk of massive O/B stars close to the MBH (e.g., Bartko et al. 2009 ). In our rate calculation, we assumed a global influx of compact objects, which is more appropriate in our situation given that we considered a binary population at larger distances from the MBH. VanLandingham et al. ( 2016 ) were the first to consider the combined effects of VRR and LK evolution by means of hybrid N -body methods. Due to computational limitations, the MBH masses were limited to up to . VanLandingham et al. ( 2016 ) found high merger fractions in their simulations. This is consistent with our results, in the sense that we find that the enhancement due to VRR is most significant for low MBH masses. More quantitatively, VanLandingham et al. ( 2016 ) found a merger fraction of in their simulation with (10k stars). This is very similar to our merger fraction of for the case and γ = 2 (adding the semisecular and non-semisecular fractions). This apparent agreement may be fortuitous, however, given that we did not consider a number of potentially important effects (see Section 6.1 ). In particular, DF is an important process in the simulations of VanLandingham et al. ( 2016 ); prior to their merger, most merging binaries sink inwards to the MBH. DF could therefore be important for bringing a binary from a regime with , where LK–VRR coupling is unimportant, to a region in which , where LK–VRR
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