Double Hot Jupiter Formation through Mirrored ZLK Migration in Binary Star Systems: The Case of WASP-94

To date, only a handful of binary star systems are known with at least one confirmed planet orbiting each star. Such systems, however, offer a unique perspective on the stochasticity intrinsic to planet formation and evolution – particularly in twin binary star systems, which consist of near-equal-mass stars formed contemporaneously in the same birth environment. The WASP-94 system, which includes twin F-type stars, is a striking exemplar of such systems, containing two hot Jupiters: WASP-94 Ab is a transiting, spin-orbit misaligned giant planet with a 4-day orbital period, while WASP-94 Bb is non-transiting and has a tighter 2-day orbital period. In this work, we leverage N-body simulations to show that the current double hot Jupiter configuration of the WASP-94 system can be reproduced through mirrored von Zeipel-Lidov-Kozai migration. The upcoming Gaia astrometric data releases offer the potential to search for additional twin planetary systems, including double cold Jupiter systems that may serve as the progenitors for WASP-94-like configurations.

💡 Research Summary

The paper investigates the origin of the two hot Jupiters orbiting the twin F‑type stars of the WASP‑94 binary system, proposing that both planets formed at wide separations (≈ 7 AU and ≈ 6.5 AU) and later migrated inward through a “mirrored” von Zeipel‑Lidov‑Kozai (ZLK) mechanism. The authors argue that when the binary’s orbital plane is highly eccentric (e ≈ 0.88) and the initial planet‑binary mutual inclination is close to 90°, the secular perturbations from the distant stellar companion drive simultaneous ZLK oscillations for both planets. These oscillations pump each planet’s eccentricity to extreme values (e ≈ 0.99), bringing the pericenter close enough for strong tidal forces to act.

To test this scenario, the authors performed a suite of 144 N‑body integrations using the REBOUND code with the Gragg‑Bulirsch‑Stoer integrator, supplemented by REBOUNDx modules for post‑Newtonian relativity and equilibrium tides. The tidal model adopts a constant‑time‑lag formalism, with planetary tidal quality factors (Q) initially set to 3 × 10⁵ and later reduced to 10³ to accelerate circularization without altering the qualitative dynamics. General relativistic precession, stellar and planetary spin, and realistic Love numbers are also included.

The simulation that best matches the observed system starts with both planets on circular, coplanar orbits aligned with their host star’s spin, but inclined by ~84–93° relative to the binary plane. The binary itself is modeled as a 1690 AU, e = 0.88 orbit, placing the stars near apastron at the present epoch. The evolution proceeds in four phases:

1. ZLK Phase – Both planets experience coupled ZLK cycles, their eccentricities rising in tandem.
2. Tidal Acceleration Phase – The tidal Q of the inner planet (WASP‑94 Bb) is artificially lowered, speeding up its eccentricity damping by a factor of ~300. This shortens the time needed for the planet to circularize while still preserving the dynamical pathway.
3. Collision Phase – Once WASP‑94 Bb’s orbit has shrunk to a few stellar radii, the simulation forces a merger with its host star, reproducing the observed non‑transiting nature (i ≈ < 79° or > 101°).
4. Final Stabilization Phase – The remaining planet (WASP‑94 Ab) continues to undergo tidal dissipation, settling into a 3.95‑day, retrograde orbit (spin‑orbit angle λ ≈ 123°) that matches the measured values.

The final orbital elements, planetary masses, radii, and stellar spin periods are all within observational uncertainties. The authors emphasize that the mirrored ZLK pathway naturally yields a retrograde hot Jupiter around one star while the companion planet is lost to its host, explaining the asymmetry in the observed system.

Beyond the case study, the paper highlights the broader implications for binary star planet formation. It suggests that high binary eccentricity can compensate for less extreme mutual inclinations, and that mirrored ZLK migration may be a viable channel for producing double hot Jupiters in other wide binaries. The authors propose that upcoming Gaia data releases, which will provide precise astrometry and binary orbital parameters, can be used to identify additional twin systems—both with double hot Jupiters and with double cold Jupiters that could be progenitors of WASP‑94‑like configurations.

In summary, the work delivers a comprehensive dynamical model that reproduces the unique architecture of WASP‑94, demonstrates the feasibility of simultaneous ZLK‑driven migration in twin binaries, and outlines a roadmap for future observational tests using Gaia and radial‑velocity surveys. This advances our understanding of how stochastic dynamical processes shape planetary system outcomes in environments where initial conditions are nearly identical.