TOI-3686: A Hot Jupiter and Sub-Neptune In A 2:1 Mean-Motion Resonance
Hot Jupiters are typically thought to be "lonely", but a small and growing subset of them have been found to have nearby planets in the same system. We present the discovery of a new member of this class of systems, TOI-3686. TOI-3686 c is a hot Jupiter with $P_\mathrm{orb} = 5.078$ days detected by NASA's TESS mission that shows peak-to-peak transit timing variations (TTVs) of 40 minutes, amongst the largest ever observed for a hot Jupiter. A subsequent search of the TESS data revealed the transits of a second planet, TOI-3686 b, a sub-Neptune with $P_\mathrm{orb} = 2.54$~days and peak-to-peak TTVs of 10 hours, $\sim 16\%$ of its orbital period. We characterized the system through photodynamical modeling of photometry from TESS and ground-based facilities, as well as radial velocity measurements from the NEID and MAROON-X spectrographs. We find that the two planets in the TOI-3686 system are deep in a 2:1 mean-motion resonance, making this the only hot Jupiter system currently known to be in a truly resonant configuration, which may be related to its $\lesssim1$~Gyr system age. Systems like TOI-3686 likely formed through a dynamically quiescent pathway and were captured into resonance after migration through a disk, and may represent the high-mass end of processes that occur in compact systems of smaller planets.