How post-Newtonian dynamics shape the distribution of stationary binary black hole LISA sources in nearby globular clusters

We derive the observable gravitational wave (GW) peak frequency (f) distribution of binary black holes (BBHs) that currently reside inside their globular clusters (GCs), with and without 2.5 post-Newtonian (2.5 PN) effects included in the dynamical evolution of the BBHs. Recent Newtonian studies have reported that a notable number of nearby nonmerging BBHs, i.e., those BBHs that are expected to undergo further dynamical interactions before merger, in GCs are likely to be observable by LISA. However, our 2.5 PN calculations show that the distribution of log f for the nonmerging BBH population above similar to 10(-3.5) Hz scales as f (-34/9) instead of the f (-2/3) scaling found in the Newtonian case. This leads to a reduction of approximately 2 orders of magnitude in the expected number of GW sources at similar to 10(-3) Hz, which leads us to conclude that observing nearby BBHs with LISA is not as likely as has been claimed in the recent literature. In fact, our results suggest that it might be more likely that LISA detects the population of BBHs that will merge before undergoing further interactions. This interestingly suggests that the BBH merger rate derived from LIGO can be used to forecast the number of nearby LISA sources, as well as providing insight into the fraction of BBH mergers forming in GCs.