Title:Validation of TOI-1221 b: A warm sub-Neptune exhibiting TTVs around a Sun-like star

Abstract:We present a validation of the long-period ($91.68278^{+0.00032}_{-0.00041}$ days) transiting sub-Neptune planet TOI-1221 b (TIC 349095149.01) around a Sun-like (m$_{\rm V}$=10.5) star. This is one of the few known exoplanets with period >50 days, and belongs to the even smaller subset of which have bright enough hosts for detailed spectroscopic follow-up. We combine TESS light curves and ground-based time-series photometry from PEST (0.3~m) and LCOGT (1.0~m) to analyze the transit signals and rule out nearby stars as potential false positive sources. High-contrast imaging from SOAR and Gemini/Zorro rule out nearby stellar contaminants. Reconnaissance spectroscopy from CHIRON sets a planetary scale upper mass limit on the transiting object (1.1 and 3.5 M$_{\rm Jup}$ at 1$\sigma$ and 3$\sigma$, respectively) and shows no sign of a spectroscopic binary companion. We determine a planetary radius of $R_{\rm p} = 2.91^{+0.13}_{-0.12} R_{\oplus}$, placing it in the sub-Neptune regime. With a stellar insolation of $S = 6.06^{+0.85}_{-0.77}\ S_{\oplus}$, we calculate a moderate equilibrium temperature of $T_{\rm eq} =$ 440 K, assuming no albedo and perfect heat redistribution. We find a false positive probability from TRICERATOPS of FPP $ = 0.0014 \pm 0.0003$ as well as other qualitative and quantitative evidence to support the statistical validation of TOI-1221 b. We find significant evidence (>$5\sigma$) of oscillatory transit timing variations, likely indicative of an additional non-transiting planet.