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Eccentricity and spin precession are key observables in gravitational-wave astronomy, encoding precious information about the astrophysical formation of compact binaries together with fine details of the relativistic two-body problem. However, the two effects can mimic each other in the emitted signals, raising issues around their distinguishability. Since inferring the existence of both eccentricity and spin precession simultaneously is – at present – not possible, current state-of-the-art analyses assume that either one of the effects may be present in the data. In such a setup, what are the conditions required for a confident identification of either effect? We present simulated parameter inference studies in realistic LIGO/Virgo noise, studying events consistent with either spin precessing or eccentric binary black hole coalescences and recovering under the assumption that either of the two effects may be at play. We quantify how the distinguishability of eccentricity and spin precession increases with the number of visible orbital cycles, confirming that the signal must be sufficiently long for the two effects to be separable. The threshold depends on the injected source, with inclination, eccentricity, and effective spin playing crucial roles. In particular, for injections similar to GW190521, we find that it is impossible to confidently distinguish eccentricity from spin precession.

 

Orbital eccentricity is a key signature of dynamical binary black hole formation. The gravitational waves from a coalescing binary contain information about its orbital eccentricity, which may be measured if the binary retains sufficient eccentricity near merger. Dedicated waveforms are required to measure eccentricity. Several models have been put forward, and show good agreement with numerical relativity at the level of a few percent or better. However, there are multiple ways to define eccentricity for inspiralling systems, and different models internally use different definitions of eccentricity, making it difficult to compare eccentricity measurements directly. In this work, we systematically compare two eccentric waveform models,SEOBNREandTEOBResumS, by developing a framework to translate between different definitions of eccentricity. This mapping is constructed by minimizing the relative mismatch between the two models over eccentricity and reference frequency, before evolving the eccentricity of one model to the same reference frequency as the other model. We show that for a given value of eccentricity passed toSEOBNRE, one must input a 20%–50% smaller value of eccentricity toTEOBResumSin order to obtain a waveform with the same empirical eccentricity. We verify this mapping by repeating our analysis for eccentric numerical relativity simulations, demonstrating thatTEOBResumSreports a correspondingly smaller value of eccentricity thanSEOBNRE.

 

Abstract Orbital eccentricity is one of the most robust discriminators for distinguishing between dynamical and isolated formation scenarios of binary black hole 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 catalogs, 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.