Session P13: Gravitational Wave Parameter Estimation II: Eccentricity and Spins

Spin-eccentricity interplay in merging binary black holes

Orbital eccentricity and spin precession are precious observables to infer the formation history of binary black holes with gravitational-wave data. 

We present a post-Newtonian, multi-timescale analysis of the binary dynamics able to capture both precession and eccentricity over long inspirals. 

We show that the evolution of an eccentric binary can be reduced that of effective source on quasi-circular orbits, coupled to a post-Newtonian prescription for the secular evolution of the eccentricity. 

Our findings unveil an interplay between precession and eccentricity: the spins of eccentric binaries precess on shorter timescales and their nutation amplitude is altered compared to black holes on quasi-circular orbits, consequently affecting the so-called spin morphology. 

Even if binaries circularize by the time they enter the sensitivity window of our detectors, their spin orientations retain some memory of the past evolution on eccentric orbits, thus providing a new link between gravitational-wave detection and astrophysical formation. 

 At the same time, we point out that residual eccentricity should be considered a source of systematics when reconstructing the past history of black-hole binaries using the spin orientations.   

Understanding Eccentricity and Precession I: How well can we measure them?

The presence or absence of eccentricity and precession can be signatures of different formation channels for binary coalescences. Our ability to measure precession and eccentricity accurately and to distinguish between the two is essential for inferring the origin of gravitational wave (GW) signals. To this end, we present a two-part study on the distinguishability and measurability of these two key parameters. In this talk, we simulate eccentric-only and precessing-only signals with a state-of-the-art GW model across multiple masses and distances. We then analyze each signal with the same model in two secenarios: (1) assuming only eccentric, non-precessing systems and (2) assuming only quasi-circular, precessing systems. Finally, we assess our ability to measure both parameters as well as our inabiltiy to distinguish between the two.   

Understanding Eccentricity and Precession II: Can we measure accurately with incomplete models?

Eccentricity is a key observable to infer the origin of a gravitational wave (GW) source. While there have been many recent studies using eccentric state-of-the-art GW models, models incorporating both spin precession and eccentricity are only in their infancy. Understanding our ability to measure these parameters without all the physics incorporated into the models will be vital for inferring the formation of a binary. To this end, we present a two-part study on the distinguishability of these two key parameters. In this work, we focus on analyzing signals simulated from numerical relativity (NR) simulations of BBH mergers with both eccentricity and spin precession. We conduct two Bayesian parameter estimation analyses on these simulated signals: assuming only eccentric systems and only precessing systems. We then compare results to the corresponding NR generated quasi-circular precessing signals; we asses our ability to measure each parameter using eccentric-only or precession-only models. To illustrate the bias in different parts of parameter space, we analyze signals across masses and distances.   

Dissecting Gravitational-waves from Heavy Binary Black Holes in the Time Domain

Lying on the edge of the Laser Interferometer Gravitational-wave Observatory's (LIGO) sensitivity, the short-duration observable gravitational-wave signals from highly massive binary black holes are dominated by the merger phase of coalescence where the imprint of many physical effects remains poorly understood. In Miller et. al. 2024, we conduct parameter estimation in the time domain to trace the effect of spin precession cycle-by-cycle on the heaviest binary black hole confidently detected by LIGO to date, GW19051, finding that the inference of precession stems in the signal from the suppression of a weak portion of the pre-merger data with respect to the louder merger-ringdown. Here, we expand upon this framework and explore the utility of time-domain inference to locate the imprint of different underlying physical effects (e.g. spin precession, mass ratio, and eccentricity) on simulated merger-dominated waveforms. Establishing a consistent picture between a binary black hole's source dynamics and the resulting observed data is crucial for characterizing the growing number of LIGO observations, safeguarding against data quality issues and systematics, and ensuring the robustness of resultant astrophysical claims.   

Characterizing eccentricity in gravitational-wave data with time domain inference

Unambiguous evidence for eccentricity in gravitational-wave signals from compact binary coalescences is difficult to determine, particularly in high mass, merger dominated systems. Using cycle-by-cycle time domain inference as in Miller et. al. 2024, we explore the impact of eccentricity on merger dominated signals and contrast it to that of spin-precession.   

Detectability of Binary Black Hole Hyperbolic Encounters in Gravitational-Wave Detectors

Binary black hole (BBH) Hyperbolic Encounters involve  two black holes in a fly-by orbit, with emission of gravitational-wave (GW) bremsstrahlung. BBH hyperbolic encounters may be prevalent in dense stellar clusters, where collision rates are high. These encounters can be modeled by a small number of parameters: the relative velocity, total mass, and the impact parameter, a geometric property of the orbit. The corresponding GW signal would manifest in ground-based interferometers as a single-cycle transient. We present a study to  constrain detection rates for current and next generation ground-based GW detectors. We use waveforms from numerical simulations which cover a discrete grid of mass ratios ranging from q=1 (equal mass) to asymmetric mass ratio q = 16. We use BayesWave, a model-agnostic algorithm which characterizes features in the data regardless of an a priori assumed model. For this analysis, we have used shapelets, Morlet-Gabor and chirplets to reconstruct the injections, and compared their effectiveness.   

Inferring the Spins of the Black Hole Binary Population with Next-Generation Ground-Based Gravitational Wave Detectors

Precisely measuring the spins of black holes in binaries remains a significant challenge in gravitational wave astronomy. This spin information is crucial to address fundamental questions about the nature of astrophysical black holes, their formation pathways and the environments in which they form. But current measurements of back hole spins from gravitational waves are mostly uninformative, obfuscated by limited signal-to-noise ratios (SNRs) and short signal lengths. Future ground-based interferometers will alleviate these barriers, as better low-frequency sensitivity will allow us to more accurately infer spin parameters of individual binaries with longer inspirals and higher SNRs, and consequently constrain the spin distribution of the binary black hole population. However, the exact minimum frequency sensitivity cutoff for planned future instruments such as Cosmic Explorer and Einstein Telescope remains uncertain. In this talk, I will demonstrate how accurate spin inference is dependent upon minimum frequency cutoff in these future instrument networks. I will show how parameter estimation of spins for individual binary mergers improves with more low frequency content, and the consequent improvements for constraining spin distributions across the population of binary black holes.   

Precise measurement of neutron star spins with neutron star-black hole mergers

The precise measurement of neutron star (NS) spins can provide important insight into the formation and evolution of these systems. While traditional methods of NS spin measurement rely on pulsar observations, gravitational wave detections offer a complementary avenue. However, determining component spins with gravitational waves is hindered by the small dimensionless spins of the NS and the degeneracy in the mass and spin parameters. This degeneracy can be addressed by the inclusion of higher-order modes in the waveform, which are important for asymmetric systems that are not face-on. The talk focuses on the suitability of neutron star-black hole mergers, which are naturally asymmetric, for precise NS spin measurement. We explore the effects of the black hole masses and spins, higher-mode content, inclination angle, and detector sensitivity on the measurement of NS spin. We find that networks with next-generation observatories like the Cosmic Explorer and the Einstein Telescope can distinguish NS dimensionless spin of 0.04 (0.1) from zero at 1-σ confidence for events at ∼200 (∼900) Mpc. Networks with A+ and A# detectors achieve similar distinction at ∼20 (∼50) Mpc and ∼40 (∼110) Mpc, respectively.