How Post-Newtonian Dynamics Shape the Distribution of Stationary Binary Black Hole LISA Sources in nearby Globular Clusters

TL;DR

This study investigates how Post-Newtonian effects influence the distribution of binary black hole sources in globular clusters, revealing a significant reduction in expected LISA-detectable sources compared to Newtonian predictions.

Contribution

It introduces 2.5PN dynamical modeling to refine predictions of gravitational wave source distributions in globular clusters, challenging previous Newtonian-based estimates.

Findings

2.5PN effects steepen the frequency distribution of non-merging BBHs.

Expected LISA sources at ~10^{-3} Hz are reduced by about two orders of magnitude.

LISA is more likely to detect BBHs that will merge before further interactions.

Abstract

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 (2.5PN) effects included in the dynamical evolution of the BBHs. Recent Newtonian studies have reported that a notable number of nearby non-merging 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 2.5PN calculations show that the distribution of $\log f$ for the non-merging BBH population above $\sim 10^{-3.5}$ Hz scales as $f^{-34/9}$ instead of the $f^{-2/3}$ scaling found in the Newtonian case. This leads to an approximately two-orders-of-magnitude reduction in the expected number of GW sources at $\sim 10^{-3}$ Hz, which lead 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.