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

TL;DR

This paper investigates how hierarchical triples of stellar-mass BBHs in the Galactic Centre, perturbed by a supermassive black hole, generate gravitational-wave signals in the LISA band. Using the TSUNAMI N-body code with up to 3.5PN corrections, the authors identify four dynamical families arising from von-Zeipel-Lidov-Kozai oscillations and compute quadrupole GW strains from instantaneous accelerations. They show that each family produces distinct, bursty GW morphologies that differ from isolated binaries, and demonstrate the limitations of secular approximations in highly eccentric regimes. The results imply that a population of tens of librating BBHs could exist near Sgr A*, yielding observable, configuration-dependent bursts in LISA that can help constrain formation channels and the dynamical environment of galactic nuclei.

Abstract

A significant fraction of compact-object mergers in galactic nuclei are expected to be eccentric in the Laser-Interferometer-Space-Antenna (LISA) frequency sensitivity range, $10^{-4} - 10^{-1}\ \rm Hz$. Several compact binaries detected by the LIGO-Virgo-KAGRA Collaboration may retain hints of residual eccentricity at $10$~Hz, suggesting dynamical or triple origins for a significant fraction of the gravitational-wave-observable population. In triple systems, von-Zeipel-Lidov-Kozai oscillations perturb both the eccentricity and the argument of pericentre, $ω$, of the inner black hole binary. The latter could be fully \textit{circulating}, where $ω$ cycles through $2π$, or may \textit{librate}, with $ω$ ranges about a fixed value with small or large variation. We use \texttt{TSUNAMI}, a regularised N-body code with up to 3.5 post-Newtonian (PN) term corrections, to identify four different families of orbits: (i) circulating, (ii) small and (iii) large amplitude librating, and (iv) merging orbits. We develop and demonstrate a new method to construct gravitational waveforms using the quadrupole formula utilising the instantaneous {\it total} acceleration of each binary component in \texttt{TSUNAMI}. We show that the four orbital families have distinct waveform phenomenologies, enabling them to be distinguished if observed in LISA. The orbits are also distinguishable from an isolated binary or from a binary perturbed by a different tertiary orbit, even if the secular timescale is the same. Future burst timing models will be able to distinguish the different orbital configurations. For efficient binary formation, about $\sim 50$ binaries can have librating orbits in the Galactic Centre.

Figures (10)

• Figure 1: Sketch of the hierarchical triple system (not to scale). The inner binary orbit (orange) is inclined with inclination $\iota_{\rm mut}$ to the SMBH orbital plane. The argument of pericentre $\omega$ is measured from the line of nodes (red) to the pericentre in the inner binary plane. The nodal angle $\Omega$ is measured from the tertiary SMBH to the line of nodes in the outer binary plane.
• Figure 2: $f_{\rm GW}$-$\omega$ phase portrait for the different orbital families.
• Figure 3: Representative of the circulating family of orbits. The initial conditions are $m_1=m_2=20$ M$_\odot$, $a_1 = 0.15\ \rm au$, $a_2=60\ \rm au$, $e_1 = 0.1$, $e_2=0.01$, $\iota_{\rm mut} = 82.85\ \rm deg$, $\Omega_2=\omega_2=\Omega=0$, $\Omega_2=\nu_1=\pi$ and $\nu_2=45\ \rm deg$. inner orbit at fixed point, $a_1=0.15$ au, $j_z=0.1$. Left column (top to bottom) eccentricity, mutual inclination and argument of pericentre versus time. Middle column: instantaneous separation $\rm dr$ and pericentre $r_p$, GW frequency $f_{\rm GW}$ and the strain polarisations versus time. Right column: scatter plots of eccentricity versus $\omega$, GW frequency versus $\omega$ and the two strain polarisations.
• Figure 4: Representative of the large amplitude libration orbital family. Similar to Fig. \ref{['circ']}, bit with different initial conditions (see table \ref{['Tab1']}).
• Figure 5: Representative of the small amplitude libration family, similar to Figs. \ref{['circ']} and \ref{['large_lib']}. Initial conditions are near the fixed point in phase space.