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

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 ∼ 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 ∼ 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. *

Astrophysics with the Laser Interferometer Space Antenna

“…Dynamically formed binaries are expected to feature several distinct sub-classes of formation channels that may also be distinguished by their eccentricities. In order of increasing characteristic formation frequency, these dynamical sub channels include: binaries dynamically ejected from their host cluster that merge as isolated binaries (f GW ≈ 10 −5 Hz), binaries that merge in cluster between strong dynamical encounters (f GW ≈ 10 −3 Hz), and finally binaries that merge in cluster through GW capture during single-single (f GW ≈ 10 −1 Hz) or few-body dynamical encounters encounters (f GW ≈ 1 Hz) (Breivik et al, 2016;Banerjee, 2018;Kremer et al, 2018a;Samsing and D'Orazio, 2018;D'Orazio and Samsing, 2018;Arca Sedda et al, 2021b;Samsing and D'Orazio, 2019;Kremer et al, 2019b;Zevin et al, 2019b;Banerjee, 2020;. Post-LISA-launch objective: Binaries formed through the ejected and in-cluster merger channels are expected to have eccentricities at GW frequencies of 10 −2 Hz of roughly 10 −3 and 10 −2 , respectively, which are expected to be measurable by LISA (Nishizawa et al, 2016).…”

The missing link in gravitational-wave astronomy: discoveries waiting in the decihertz range

“…The first 2 populations make up the broad peak at lower eccentricity, and the third results in the distribution at e 10 −2 seen for the gravitational-wave frequencies of f ref = 10.0 Hz and f ref = 1.0 Hz. At lower frequencies it is easier to distinguish between the ejected and in-cluster merger populations [133,326]; the dashed and dotted green lines differentiate the ejected and in-cluster populations, respectively, at f ref = 0.1 Hz. The peak near e ∼ 1 in the f ref = 10.0 Hz histogram is populated by systems that form in-band and merge on the timescale of days-years.…”

Parameter estimation of stellar-mass black hole binaries with LISA

“…We expect that 3 rd generation detectors (Einstein Telescope [52][53][54], Cosmic Explorer [55]) will be operational in parallel with LISA, with SNR figures reaching hundreds or thousands, thus significantly improving the PE over current observations. Given the current uncertainty in the population of SBHBs, we cannot reliably specify the properties of most detectable sources [19,39,45,[56][57][58][59]. In our study we focus on a fiducial system consistent with the population of currently observed SBHBs instead of working with a randomized catalog of sources.…”