Planetary Desert around Compact Binaries: Dynamical Instability Triggered by Resonance-Induced Eccentricity Excitation

Compact binaries with orbital periods shorter than about 7 days show an absence of transiting planets, a feature known as the circumbinary planet desert". The physical mechanism behind this desert remains unclear. We investigate its origin by simulating the long-term dynamics of multi-planet circumbinary systems with evolving inner binaries. Our simulations are based on the single-averaged secular equations that average only over the binary orbital period and fully incorporate planet-planet interactions. When an eccentric binary decays via tides, an outer planet can be captured into resonance advection in eccentricity, a state in which its apsidal precession locks with that of the binary, driving extreme eccentricity growth. While such growth can occur in a binary-single planet system, the parameter space is limited and may not necessarily induce instability. In a multi-planet system, however, the excited orbit inevitably crosses those of its neighbors, which triggers violent planet-planet scatterings and produces collisions or ejections. Crucially, 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. Our results suggest that the resonance-induced instability provides a natural explanation for the observed circumbinary planet desert.

💡 Research Summary

The paper addresses the striking absence of transiting circumbinary planets (CBPs) around compact stellar binaries with orbital periods shorter than about seven days—a phenomenon known as the “circumbinary planet desert.” While several formation‑suppression or observational‑bias explanations have been proposed, the authors present a dynamical mechanism that operates during the tidal decay of the inner binary and naturally produces the observed desert.

The authors adopt the single‑averaged (SA) secular formalism, which averages only over the binary orbital period, allowing them to follow the long‑term evolution of planetary orbits while fully retaining planet‑planet gravitational interactions. The inner binary’s apsidal precession rate (𝜔̇_b) is dominated by general‑relativistic (1PN) precession and the non‑dissipative tidal bulge, both of which increase as the binary shrinks and circularizes under tidal dissipation. The outer planet’s precession rate (𝜔̇_p) is set by the quadrupole potential of the binary and decreases as the binary’s gravitational field weakens.

When the binary’s precession overtakes that of the planet, the condition 𝜔̇_b ≈ 𝜔̇_p is satisfied, producing an apsidal‑precession resonance. If three criteria are met—(i) adiabatic binary decay (the decay timescale far exceeds the secular precession timescale), (ii) the resonance is crossed from 𝜔̇_p > 𝜔̇_b to 𝜔̇_p < 𝜔̇_b, and (iii) the planet’s initial eccentricity is modest— the planet can be captured into “resonance advection.” In this state the two precession rates remain locked while the binary continues to shrink, driving a continuous and potentially extreme growth of the planet’s eccentricity (e_p). The authors analytically derive the parameter space where capture is possible and illustrate it with Figure 2, showing that the viable region shrinks for lower initial binary eccentricities and is bounded by the final binary separation a_b,f.

Single‑planet integrations (Figure 1) demonstrate that planets initially placed at intermediate distances (e.g., 1.24 AU and 2.13 AU for the chosen binary) undergo resonance capture, with e_p rising to ≳0.9 before the binary’s tidal evolution halts. Planets that are too close or too far never satisfy the resonance condition and retain low eccentricities.

The crucial insight of the paper is that, in realistic multi‑planet systems, the extreme eccentricity attained by the resonantly captured planet inevitably leads to orbit crossing with neighboring planets. The authors implement a “Ring+N‑body” code that adds the full Newtonian planet‑planet potential to the SA equations, allowing both angular‑momentum exchange (between binary and planets) and energy exchange (among planets). Once orbital crossing occurs, planet‑planet scattering, collisions, and ejections ensue, rapidly amplifying the localized instability of a single resonant planet into a global cascade that can clear the inner region of the system. This chain reaction explains why compact binaries end up devoid of detectable CBPs despite the fact that the binary’s tidal evolution alone would not necessarily destabilize a solitary planet.

The study therefore provides a coherent, quantitative framework linking tidal binary evolution, apsidal‑precession resonance, eccentricity excitation, and multi‑planet dynamical chaos. It accounts for the observed planet desert without invoking special formation conditions or observational selection effects. The authors also discuss broader implications, suggesting that similar resonance‑driven clearing could operate in other hierarchical systems (e.g., triples with a black‑hole binary) and that remnants of the clearing process—high‑eccentricity debris, scattered planetesimals, or transient dust—might be observable around tidally evolving binaries. Overall, the paper offers a compelling dynamical explanation for the paucity of planets around short‑period binaries and opens new avenues for both theoretical and observational follow‑up.