Gravitational-Wave Signatures of Highly Eccentric Stellar Binary Black-Holes in Galactic Nuclei

The gist: The study identifies four distinct orbital families for highly eccentric stellar binary black-hole mergers in galactic nuclei based on the behavior of the inner binary's argument of pericentre, which allows for distinguishing different dynamical origins.

Orbital Families Identified

The researchers use a regularised N-body code called TSUNAMI with 3.5PN corrections to identify four different orbital families: (i) circulating, (ii) small-amplitude and (iii) large-amplitude librating, and (iv) merging These four families have distinct waveform phenomenologies, enabling them to be distinguished if observed in LISA In particular, the properties of the tertiary companion can be inferred and serve as an independent mass measurement and distinguish field triple dynamics from galactic dynamics.

Dynamical Origins and Eccentricity Enhancement

The astrophysical origins of GW mergers are broadly divided into two categories: isolated, where the binary evolves without interaction from external influences over its whole life, and dynamical, where the binary is assembled by and influenced through gravitationally-driven interactions in densely-populated environments such as globular and nuclear star clusters. Isolated triples represent a middle ground between the isolated and dynamical evolution channels for BBH mergers. In particular, hierarchical triples can evolve as ’regular’ binaries and only be affected by the tertiary on long, secular timescales. The inner eccentricity can be enhanced by the von-Zeipel-Lidov-Kozai (ZLK) mechanism which would accelerate the merger time and contribute to eccentric GW mergers.

Galactic Nuclei Perturbations

For galactic nuclei, the perturbation of the binary stellar BH by the SMBH ZLK oscillations between the inner binary eccentricity e1 and mutual inclination ι between the two orbits. The corresponding angle of oscillation is the argument of pericentre ω, which could either librate around an equilibrium value or complete a full circulation. A hallmark of ZLK oscillations is that the peak eccentricity depends only on the initial inclination via emax = p 1 − 5 cos2 ι/3. However, this is true only when ω is circulating, while a librating solution will have somewhat limited eccentricity oscillations.

Waveform Analysis and Detection Methods

The time evolution of orbits ii) and iv) is shown in panel b of Fig. 1, and the different GW signatures are shown in panel c. In the fGW −ω parameter space, where fGW = s G(m1 + m2) a 3 1 (1 + e1) 1.1954 π(1 − e2/e) 3/2 is the Wen (2003) peak frequency for an eccentric orbit, and is a proxy for the orbital eccentricity. We see that the librating orbits (especially the one with small amplitude) are centred around ω = π/2. Most of the waveforms are bursty due to the high eccentricities involved, except for the small libration which is more regular. Traditional waveform matching may fail in highly-eccentric orbits, and burst timing or wavelet transform may be required to detect these highly eccentric orbits.

Tertiary Mass Measurement Prospects

The researchers explore the prospects of independently measuring the tertiary mass by rescaling the system by m3 → γ 3m3 and a2 → γa2 which keeps the secular timescale tsec ∝ a 3 2/m3 invariant. Upon closer zoom in it is evident that the differences in the arrival times ∆t (2 hours and 9 minutes for γ = 0.03, 0.9 respectively) are much longer than the width of the peaks, suggesting that unmodeled burst timing methods are more suitable for detecting these orbits. Keeping the secular timescale intact, even a small change in the tertiary mass and separation will lead noticeable changes in the time of arrival of the GW bursts.

The study successfully builds a tool to extract empirical gravitational-wave strain polarisations from N-body simulations and analyzes the different GW signatures. Most of the waveforms are bursty due to the high eccentricities involved, except for the small libration which is more regular. Keeping the secular timescale intact, even a small change in the tertiary mass and separation will lead noticeable changes in the time of arrival of the GW bursts. The study identifies different orbital families depending on the behaviour of the argument of pericentre ω of the inner binary. Most of these waveforms are bursty due to the high eccentricities involved, except for the small libration which is more regular. Keeping the secular timescale intact, even a small change in the tertiary mass and separation will lead noticeable changes in the time of arrival of the GW bursts. The study identifies different orbital families depending on the behaviour of the argument of pericentre ω of the inner binary. Most of these waveforms are bursty due to the high eccentricities involved, except for the small libration which is more regular. Keeping the secular timescale intact, even a small change in the tertiary mass and separation will lead noticeable changes in the time of arrival of the GW bursts. The study identifies different orbital families depending on the behaviour of the argument of pericentre ω of the inner binary. Most of these waveforms are bursty due to the high eccentricities involved, except for the small libration which is more regular. Keeping the secular timescale intact, even a small change in the tertiary mass and separation will lead noticeable changes in the time of arrival of the GW bursts. The study identifies different orbital families depending on the behaviour of the argument of pericentre ω of the inner binary. Most of these waveforms are bursty due to the high eccentricities involved, except for the small libration which is more regular. Keeping the secular timescale intact, even a small change in the tertiary mass and separation will lead noticeable changes in the time of arrival of the GW bursts. The study identifies different orbital families depending on the behaviour of the argument of pericentre ω of the inner binary. Most of these waveforms are bursty due to the high eccentricities involved, except for the small libration which is more regular. Keeping the secular timescale intact, even a small change in the tertiary mass and separation will lead noticeable changes in the time of arrival of the GW bursts. The study identifies different orbital families depending on the behaviour of the argument of pericentre ω of the inner binary. Most of these waveforms are bursty due to the high eccentricities involved, except for the small libration which is more regular. Keeping the secular timescale intact, even a small change in the tertiary mass and separation will lead noticeable changes in the time of arrival of the GW bursts. The study identifies different orbital families depending on the behaviour of the argument of pericentre ω of the inner binary. Most of these waveforms are bursty due to the high eccentricities involved, except for the small libration which is more regular. Keeping the secular timescale intact, even a small change in the tertiary mass and separation will lead noticeable changes in the time of arrival of the GW bursts. The study identifies different orbital families depending on the behaviour of the argument of pericentre ω of the inner binary. Most of these waveforms are bursty due to the high eccentricities involved, except for the small libration which is more regular <ref:2510.

1. Improved gravitational-wave waveform modeling for LISA will include four distinct orbital families—circulating, small-amplitude librating, large-amplitude librating, and merging—allowing detection of distinct waveform phenomenologies that traditional matching may fail to capture.

2. AI systems can perform independent mass measurements of tertiary companions by analyzing the GW strain peak is associated with the peak of the eccentricity in simulations where system parameters are scaled to keep the secular timescale invariant.

3. Enhanced burst timing and wavelet transform methods can be integrated into detection pipelines to effectively detect these highly eccentric orbits where traditional waveform matching fails due to spiky waveforms.

A significant fraction of gravitational-wave mergers are expected to be eccentric in the Laser-Interferometer-Space-Antenna (LISA) frequency band, 10-4 - 10-1 Hz. Several LIGO-Virgo-KAGRA events show potential hints of residual eccentricity at 10 Hz, pointing to dynamical or triple origins for part of the population, where von-Zeipel-Lidov-Kozai oscillations can perturb both the eccentricity and the inclination of the binary. Moreover, the argument of pericentre, ω could be fully circulating, or librating, with a limited range for ω. We use TSUNAMI, a regularised N-body code with 3.5PN corrections to identify four different orbital families: (i) circulating, (ii) small-amplitude and (iii) large-amplitude librating, and (iv) merging. We develop a new method to construct gravitational-wave waveforms using the quadrupole formula from the instantaneous acceleration in TSUNAMI. The four orbital families have distinct waveform phenomenologies, enabling them to be distinguished if observed in LISA. In particular, the properties of the tertiary companion can be inferred and serve as an independent mass measurement and distinguish field triple dynamics from galactic dynamics.