A Warm Massive Pair of Planets around TOI-1232 Revealed with Transit-timing Variations and Doppler Spectroscopy*

TOI-1232 is a G dwarf star with a mass of 1.0 6 − 0.06 + 0.07 M ⊙ , a radius of 1.07 ± 0.05 R ⊙ , and a slightly higher metallicity than solar of Fe/H = 0.18 ± 0.05. The star hosts a transiting warm Jovian-mass planet, TOI-1232 b, with an orbital period of P b = 14.25 6 − 0.001 + 0.001 days, identified with data from multiple sectors of the TESS space telescope. The TESS light curve of TOI-1232 is complex, as it is contaminated by a background eclipsing binary with a period of 1.37 days. TOI-1232 b was firmly confirmed by ground-based transit follow-up campaigns from the Las Cumbres, Hazelwood, Brierfield, and ASTEP observatories. Additionally, the TESS transits of TOI-1232 b exhibit strong transit-timing variations (TTVs) with a superperiod of 235.5 ± 0.7 days and a semiamplitude of 27 minutes. Radial velocity (RV) follow-up with the FEROS spectrograph confirms the planetary nature of the transiting candidate, while a self-consistent N -body analysis of RVs and TTVs pinpoints the presence of a second outer Saturn-mass companion, TOI-1232 c with a period of P c = 30.35 6 − 0.012 + 0.010 days. The TOI-1232 warm-giant system is particularly important due to the evidence of two massive planets that reside near the 2:1 commensurability but are not locked in a mean-motion resonance. Thanks to TESS, we have revealed a handful of these rare systems. Hence, TOI-1232 is an important addition to understanding the formation and dynamical evolution of such compact, massive, warm giant planets.