An Enhanced Formation Channel for Galactic Dual-Line Gravitational-Wave Sources: von Zeipel-Lidov-Kozai effect in Triples Involving Sgr A*

TL;DR

This work identifies the von Zeipel-Lidov-Kozai (ZLK) mechanism in hierarchical triples with Sgr A* as a powerful formation channel for Galactic Center dual-line GW sources, where a wide NS–NS inner binary experiences ZLK-induced eccentricity/inclination oscillations that modulate both millihertz inspiral GWs and hectohertz spin GWs. By comparing ZLK and general-relativistic precession timescales and modeling the resultant GW signals, the authors show that ZLK can dominate the inner-binary dynamics and significantly extend the detectable parameter space, increasing the expected dual-line yield by roughly a factor of $\sim 3$ to an order of unity over a 4-year mission with LISA/TianQin/Taiji and Cosmic Explorer. The study provides a quantitative framework for multi-band GW observations in the Galactic Center, highlighting a concrete pathway to constrain neutron-star equations of state and GC dynamics, while noting simplifications (equal masses, quadrupole order, neglected environmental effects) that motivate future refinement. Overall, ZLK dynamics offer a tangible and impactful enhancement to dual-line GW astronomy in dense galactic nuclei.

Abstract

The dense Galactic Center environment is expected to host compact binary inspirals detectable by future space-borne gravitational wave (GW) observatories (e.g., LISA, TianQin, Taiji) in the millihertz band. Aided by information from these facilities, next-generation ground-based GW detectors (e.g., Cosmic Explorer, Einstein Telescope) can potentially capture gravitational radiation in the hectohertz band from rapidly spinning neutron star (NS) components in such binaries. These Galactic Center systems are thus anticipated to act as dual-line (i.e., low-frequency inspiral and high-frequency spin) GW sources. However, the formation channels of these systems remain largely unexplored. In this \textit{Letter}, we propose that the von Zeipel-Lidov-Kozai (ZLK) effect can enhance the formation of dual-line GW sources in hierarchical triples involving the Galactic supermassive black hole, Sgr A*. We show that ZLK-driven oscillations in the eccentricity and inclination of the inner binary can modulate the GW emission from both the binary inspiral and the individual NS spins. This effect boosts the expected dual-line source count by a factor of $\sim 3$, from rare to $\mathcal{O}(1)$ in 4 years, making dual-line observations substantially more probable. Our results demonstrate that the ZLK effect provides an important formation channel for Galactic dual-line GW sources.

Figures (3)

• Figure 1: Geometric configuration of the hierarchical triple system where an NS binary orbits Sgr A$^*$. The reference frame is chosen such that the outer orbital angular momentum $\boldsymbol{L}_{\rm o}$ aligns with the $Z$-axis. The inner binary orbital plane is tilted at inclination $\iota$ with respect to the outer orbit, with longitude of ascending node $\Omega$ and pericenter angle $\omega$ defining the orbital orientation. The vector $\boldsymbol{S}_1$ represents the primary NS spin. The detector inclination angle $\iota_{d}$ is defined between $\boldsymbol{L}_{\rm o}$ and $\boldsymbol{D}$, and the spin inclination angle $\iota_{s}$ between $\boldsymbol{L}_{\rm o}$ and $\boldsymbol{S}_1$. Initially, both $\boldsymbol{D}$ and $\boldsymbol{S}_1$ lie in the $Y$-$Z$ plane, and their $Y$-components are positive.
• Figure 2: SNR contours for continuous GW detection from rapidly spinning NSs at the Galactic Center, shown in the spin period–equatorial ellipticity parameter space ($P_{\rm s}$, $\epsilon$) for a 4-year observation of Cosmic Explorer. The green shaded region indicates the detectable parameter space (assuming an SNR threshold of $\rho_{\rm NS} = 5$). NSs spinning at $P_{\rm s}=10$ ms are detectable with ellipticities as small as $\epsilon \sim 10^{-8}$.
• Figure 3: Dual-line gravitational radiation excitation through the ZLK effect for the Galactic Center NS--NS systems. Green contours show LISA-detectable systems without the ZLK effect, bounded by $\rho_{\rm NS\text{–}NS} = 5$ (right) and $\rho_{\rm NS\text{–}NS} = 40$ (left) in the $a_{\rm i}$–$(1-e_{\rm i})$ parameter space. The light blue region indicates ZLK dominance, exemplified by a system with $e_{\rm i0} = 0.6$ and $P_{\rm i} = 7$ h. The magenta point represents a rapidly spinning NS component detectable by Cosmic Explorer (Fig. \ref{['fig:SNRforNS']}). Without ZLK, this system has $\rho_{\rm NS\text{–}NS} = 0.16$ (undetectable), but ZLK-driven eccentricity oscillations boost the SNR to 5.5 over 4 years. The dark green contour shows the ZLK-modified SNR threshold $\rho_{\rm ZLK} = 5$, which extends into regions of larger orbital separation and lower eccentricity than the standard detection boundary. Monte Carlo sampling indicates that this parameter‑space expansion increases the number of detectable sources by threefold. ZLK oscillations therefore promote wide binaries from unresolvable backgrounds into LISA's detection window, substantially improving dual‑line prospects and establishing the ZLK effect as a viable formation channel for Galactic Center dual-line systems.