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

Abstract

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.

Figures (3)

• Figure 1: Examples of different evolution of a triple systems. a. Sketch of the triple system with semi-major axes $a_1\ll a_2$ and other orbital angles sketched for the inner orbit. b. Dynamical evolution of a system at small libration (left panels) and at an initially librating orbit that is decoupled and than captured due to GW emissions (right panels). c. The phase space of $f_{\rm GW} - \omega$ for the four different orbits.
• Figure 2: Empirical GW strain polarisations for the different orbits from panel c. of Fig. \ref{['fig1']}.
• Figure 3: Circulating orbit for different mass and semi-major axis scaling. The SMBH mass is shifted by $m_3\to \gamma^3 m_3$ and the semi-major axis is shifted by $a_2\to \gamma a_2$, so $\gamma=0.03$ corresponds to $m_3=108 M_\odot$ a stellar mass BH. Top panel show the orbital evolution of the orbital elements. Bottom panel show the '+' strain polarisation, where the centre and right bottom panels are zoomed in versions of the strain data.