Photodynamical analysis of the TOI-4504 system: Orbital precession brings planet d into transit to reveal its deeply resonant state and similarity to GJ 876
Abstract
The K-dwarf TOI-4504 hosts two giant planets in 2:1 mean-motion resonance, with orbital periods of 41.3 days (planet d) and 82.8 days (planet c). They exhibit among the largest known absolute transit-timing variations, with respective peak-to-node amplitudes up to 5 and 3 days. Newer TESS data show that the previously non-transiting planet d has now precessed into transiting, and we derive updated system parameters with significant discrepancies with the discovery paper. The revised parameters place planets d and c deep in the resonance and close to or in the fully-relaxed limit-cycle state, with the resonant and secular modes interfering nonlinearly to induce non-zero relaxed free eccentricities which precess at the same rate as the forced eccentricities and the longitude of conjunctions, in turn enabling precise measurement of the full eccentricities and apsidal angles. We discuss the predictions of linear theory and how it can be used to understand the true state of the system revealed by N-body integrations, and more generally why it is that the posteriors of systems more compact than 2:1 tend to suffer from significant eccentricity degeneracy. We show that the extraordinary dynamical states of the giant pairs orbiting TOI-4504 and the M-dwarf GJ 876 are remarkably similar, in spite of the significant difference in their host-star masses, and discuss the implications for damping timescales during the relatively gentle formation process of Type II migration.
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BibTeX
@article{almenara2026photodynamical,
title = {{Photodynamical analysis of the TOI-4504 system: Orbital precession brings planet d into transit to reveal its deeply resonant state and similarity to GJ 876}},
author = {J. Almenara and R. Mardling and A. Leleu and S. Udry and T. Forveille and Xavier Bonfils and F. Bouchy and C. Cadieux and J. Couturier and R. Díaz and Y. Eyholzer and E. Fontanet and T. Guillot and G. Hébrard and R. Hoogenboom and J. Korth and M. Lendl and A. Nigioni},
journal = {Astronomy \& Astrophysics - A\&A},
year = {2026},
month = oct,
doi = {10.1051/0004-6361/202658959},
eprint = {2603.05720},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05843475v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Photodynamical analysis of the TOI-4504 system: Orbital precession brings planet d into transit to reveal its deeply resonant state and similarity to GJ 876
AU - J. Almenara
AU - R. Mardling
AU - A. Leleu
AU - S. Udry
AU - T. Forveille
AU - Xavier Bonfils
AU - F. Bouchy
AU - C. Cadieux
AU - J. Couturier
AU - R. Díaz
AU - Y. Eyholzer
AU - E. Fontanet
AU - T. Guillot
AU - G. Hébrard
AU - R. Hoogenboom
AU - J. Korth
AU - M. Lendl
AU - A. Nigioni
PY - 2026
DA - 2026/10/29
JO - Astronomy & Astrophysics - A&A
DO - 10.1051/0004-6361/202658959
UR - https://hal.science/hal-05843475v1
AB - The K-dwarf TOI-4504 hosts two giant planets in 2:1 mean-motion resonance, with orbital periods of 41.3 days (planet d) and 82.8 days (planet c). They exhibit among the largest known absolute transit-timing variations, with respective peak-to-node amplitudes up to 5 and 3 days. Newer TESS data show that the previously non-transiting planet d has now precessed into transiting, and we derive updated system parameters with significant discrepancies with the discovery paper. The revised parameters place planets d and c deep in the resonance and close to or in the fully-relaxed limit-cycle state, with the resonant and secular modes interfering nonlinearly to induce non-zero relaxed free eccentricities which precess at the same rate as the forced eccentricities and the longitude of conjunctions, in turn enabling precise measurement of the full eccentricities and apsidal angles. We discuss the predictions of linear theory and how it can be used to understand the true state of the system revealed by N-body integrations, and more generally why it is that the posteriors of systems more compact than 2:1 tend to suffer from significant eccentricity degeneracy. We show that the extraordinary dynamical states of the giant pairs orbiting TOI-4504 and the M-dwarf GJ 876 are remarkably similar, in spite of the significant difference in their host-star masses, and discuss the implications for damping timescales during the relatively gentle formation process of Type II migration.
SN - 0004-6361
SN - 1432-0746
ER -