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(1) Resonance Capture and Advection
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Left panel: Phase-space portraits in terms of the canonical variables at a series of stages of the orbital evolution for the system in our fiducial model. γ is the ratio of apsidal precession rates of two orbits (evaluated at e_out=0). The existence of a separatrix (black line) divides phase space into circulation zones and libration zone. The orange curve represents the numerical solution of the outer binary's eccentricity vector.
Right panel: The orbital evolution of two orbits in a frame corotating with the inner binary eccentricity vector (the timestep corresponds to the one in the left panel). The black and orange lines refer to the black hole binary and outer stellar orbit, and the arrows represent the eccentricity vectors.
System setup ↑↑
Black hole binary (eccentric) + Tertiary star (quasi-circular) + Coplanar configuration
Results
During the orbital decay of a black hole binary (BHB), the system can be driven across the apsidal precession resonance, where the apsidal precession rate of the stellar orbit matches that of the inner BHB.
Following the resonance crossing, the system gets captured into a state of resonance advection until the merger of the BHB.
The above mechanism can produce extreme outer binary eccentricity (left panel of the movie) + apsidal alignment of two orbits (right panel of the movie).
More information can be found in Liu & Lai (2024)
(2) The Circumbinary Planet Desert: Dynamical Instability Triggered by Resonance-induced Eccentricity Excitation
Compact binaries with orbital periods shorter than about seven days show an absence of transiting planets, a feature known as the “circumbinary planet desert.” We investigate its origin by simulating the long-term dynamics of multiplanet circumbinary systems with evolving inner binaries.
Results
When an eccentric binary decays via tides, an outer planet can be captured into resonance advection in eccentricity, driving extreme eccentricity growth.
Such growth can occur in a binary-single planet system, but the parameter space is limited and may not necessarily induce instability.
In a multiplanet system, the excited orbit inevitably crosses those of its neighbors, which triggers violent planet–planet scatterings and produces collisions or ejections.
These mutual gravitational interactions amplify the “localized” instability of a single planet into a system-wide chain reaction, drastically reshaping the orbital architecture and potentially clearing out the inner regions of planetary systems.
More information can be found in Liu & Lai (2026)
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