Implications of Eccentric Observations on Binary Black Hole Formation Channels

Abstract

Orbital eccentricity is one of the most robust discriminators for distinguishing between dynamical and isolated formation scenarios of binary black holes mergers using gravitational-wave observatories such as LIGO and Virgo. Using state-of-the-art cluster models, we show how selection effects impact the detectable distribution of eccentric mergers from clusters. We show that the observation (or lack thereof) of eccentric binary black hole mergers can significantly constrain the fraction of detectable systems that originate from dynamical environments such as dense star clusters. After roughly 150 observations, observing no eccentric binary signals would indicate that clusters cannot make up the majority of the merging binary black hole population in the local Universe (95% credibility). However, if dense star clusters dominate the rate of eccentric mergers and a single system is confirmed to be measurably eccentric in the first and second gravitational-wave transient catalogues, clusters must account for at least 14% of detectable binary black hole mergers. The constraints on the fraction of detectable systems from dense star clusters become significantly tighter as the number of eccentric observations grows, and will be constrained to within 0.5 dex once 10 eccentric binary black holes are observed.

Signs of eccentricity in two gravitational-wave signals may indicate a sub-population of dynamically assembled binary black holes

“…The second and third columns provide the percentage of posterior support for 𝑒 10 > 0.1 and 𝑒 > 0.05 respectively. These two values are typical used as thresholds for 'detectable' binary eccentricity at 10 Hz using operational gravitational-wave detectors (e.g., Lower et al 2018;Samsing 2018;Rodriguez et al 2018b,a;Zevin et al 2019;Zevin et al 2021a), although the true threshold for eccentricity sensitivity is unique to each signal. The next two columns provide the natural log Bayes factors ln B for the hypotheses that 𝑒 10 ≥ 0.1 (0.05) against the hypothesis that 𝑒 10 < 0.1 (0.05).…”

“…In Zevin et al (2021a), the lower limit on this branching fraction, 𝛽 c , is shown to be 0.14 (0.27) at 95% credibility for a number of observations with 𝑒 10 ≥ 0.05, 𝑁 ecc = 1 (2), when the total number of observed BBHs is 𝑁 obs = 46.…”

“…Dense star clusters are arguably the most well-studied dynamical formation environment (see, e.g., Sigurdsson & Hernquist 1993;Portegies Zwart & McMillan 2000;O'Leary et al 2006;Samsing et al 2014;Morscher et al 2015;Gondán et al 2018;Samsing 2018;Rodriguez et al 2018a;Randall & Xianyu 2018a,b;Rodriguez et al 2018b;Fragione & Kocsis 2018;Fragione & Bromberg 2019;Bouffanais et al 2019). Simulations of compact binary formation in such environments lead us to expect that ∼ 5% (∼ 7%) of their binary black holes retain eccentricities 𝑒 10 ≥ 0.1(0.05) when their gravitational radiation frequency reaches 10 Hz; see Samsing et al (2014); Samsing (2018); Rodriguez et al (2018b,a); ; Kremer et al (2020b); Zevin et al (2021a) and references within. Observing eccentricity in the gravitational waveform of a BBH coalescence therefore indicates that the system was formed dynamically.…”

“…While these events have less statistically significant support for eccentricity, with no more than 38% of their posterior probability in the region of 𝑒 10 ≥ 0.05, their support relative to other GWTC-2 events (see Table 2) introduces the possibility that we may have ≥ 4 eccentric events in GWTC-2. If these events truly are eccentric-not just statistical fluctuations, or capturing the effects of spin-induced precession-then dense star clusters alone cannot account for the abundance of eccentric binaries (Zevin et al 2021a). This would mean that other channels capable of producing eccentric compact binaries must be contributing significant quantities of mergers to our catalogues.…”

EFPE: Efficient fully precessing eccentric gravitational waveforms for binaries with long inspirals

“…The physics of inspiral binaries is rich, including effects such as spin-induced precession [22,23], tidal interactions [24], and orbital eccentricity [25,26]. The simultaneous measurement of those effects is an important ingredient in discriminating between different black hole binary formation scenarios [27,28], and massive black hole binary evolution [29]. Efforts towards building waveforms for preccessing and/or eccentric waveforms have been carried out using various formalisms [23,[30][31][32][33][34][35][36].…”