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

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.

💡 Research Summary

The paper investigates a previously under‑explored formation channel for Galactic‑center dual‑line gravitational‑wave (GW) sources—systems that emit simultaneously in the millihertz band (binary inspiral) and the hectohertz band (continuous radiation from a rapidly spinning neutron star, NS). The authors focus on hierarchical triple systems in which a compact NS–NS binary orbits the supermassive black hole (SMBH) Sgr A* at the Milky Way’s core. By analytically and numerically studying the secular dynamics, they demonstrate that the von Zeipel–Lidov–Kozai (ZLK) mechanism, driven by the distant massive tertiary, can induce large-amplitude oscillations in the inner binary’s eccentricity (e) and inclination (i).

Key dynamical timescales are compared: the ZLK timescale (≈ 20 yr for the fiducial parameters) is far shorter than the 1‑post‑Newtonian relativistic precession (≈ 220 yr), de‑Sitter spin‑orbit precession (≈ 260 yr), and the precession of the outer orbit due to the SMBH spin (≈ 2.8 × 10³ yr). Consequently, ZLK dominates the evolution of the inner binary. When ZLK drives e up from an initial 0.6 to values ≳ 0.9, the GW luminosity is amplified by the factor F(e) ∝ (1‑e²)⁻⁷ᐟ², boosting the inspiral signal in the LISA/TianQin/Taiji band.

The high‑frequency component originates from a non‑axisymmetric, rapidly rotating NS. Using the standard quadrupole formula, the authors write the two polarizations h₊(t) and h×(t) in terms of the NS equatorial ellipticity ε, rotation frequency Ω_r (twice the spin frequency), moment of inertia I₃, and the angles between the spin axis, the outer orbital angular momentum, and the detector line‑of‑sight. Because the NS orbits the binary barycenter, which itself orbits Sgr A*, the NS position r_ns(t) introduces a time‑dependent Doppler shift. The observed GW frequency is therefore Ω_dr ≈ Ω_r