TOI-4504: Exceptionally large Transit Timing Variations induced by two resonant warm gas giants in a three planet system

Abstract: We present a joint analysis of TTVs and Doppler data for the transiting exoplanet system TOI-4504. TOI-4504 c is a warm Jupiter-mass planet that exhibits the largest known transit timing variations (TTVs), with a peak-to-node amplitude of $\sim$ 2 days, the largest value ever observed, and a super-period of $\sim$ 930 d. TOI-4504 b and c were identified in public TESS data, while the TTVs observed in TOI-4504 c, together with radial velocity (RV) data collected with FEROS, allowed us to uncover a third, non-transiting planet in this system, TOI-4504 d. We were able to detect transits of TOI-4504 b in the TESS data with a period of 2.4261$\pm 0.0001$ days and derive a radius of 2.69$\pm 0.19$ R${\oplus}$. The RV scatter of TOI-4504 was too large to constrain the mass of TOI-4504 b, but the RV signals of TOI-4504 c & d were sufficiently large to measure their masses. The TTV+RV dynamical model we apply confirms TOI-4504 c as a warm Jupiter planet with an osculating period of 82.54$\pm 0.02$ d, mass of 3.77$\pm 0.18$ M${\rm J}$ and a radius of 0.99$\pm 0.05$ R${\rm J}$, while the non-transiting planet TOI-4504 d, has an orbital period of 40.56$\pm 0.04$ days and mass of 1.42${-0.06}^{+0.07}$ M$_{\rm J}$. We present the discovery of a system with three exoplanets: a hot sub-Neptune and two warm Jupiter planets. The gas giant pair is stable and likely locked in a first-order 2:1 mean-motion resonance (MMR). The TOI-4504 system is an important addition to MMR pairs, whose increasing occurrence supports a smooth migration into a resonant configuration during the protoplanetary disk phase.