Photodynamical modeling of TOI-4504 reveals its deeply resonant state and similarity to GJ 876

TL;DR

This study models the resonant orbital dynamics of the TOI-4504 planetary system, revealing its deeply resonant state, free eccentricities, and similarities to the GJ 876 system, with implications for planetary formation theories.

Contribution

It provides a detailed photodynamical analysis of TOI-4504, demonstrating its resonance state and eccentricity dynamics, and compares it to GJ 876 to understand planetary system evolution.

Findings

TOI-4504's planets are in a deep 2:1 resonance with significant free eccentricities.

The system's dynamics are similar to GJ 876 despite different host star masses.

Linear theory helps interpret the complex resonant and secular interactions.

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.