Transit Timing Variation of XO-3b: Evidence for Tidal Evolution of Hot Jupiter with High Eccentricity

Abstract: Observed transit timing variation (TTV) potentially reveals the period decay caused by star-planet tidal interaction which can explain the orbital migration of hot Jupiters. We report the TTV of XO-3b, using TESS observed timings and archival timings. We generate a photometric pipeline to produce light curves from raw TESS images and find the difference between our pipeline and TESS PDC is negligible for timing analysis. TESS timing presents a shift of 17.6 minutes (80 $\sigma$), earlier than the prediction from the previous ephemeris. The best linear fit for all timings available gives a Bayesian Information Criterion (BIC) value of 439. A quadratic function is a better model with a BIC of 56. The period derivative obtained from a quadratic function is -6.2$\times$10$^{-9}$$\pm$2.9$\times$10$^{-10}$ per orbit, indicating an orbital decay timescale 1.4 Myr. We find that the orbital period decay can be well explained by tidal interaction. The `modified tidal quality factor' $Q_{p}'$ would be 1.8$\times$10$^{4}$$\pm$8$\times$10$^{2}$ if we assume the decay is due to the tide in the planet; whereas $Q_{*}'$ would be 1.5$\times$10$^{5}$$\pm$6$\times$10$^{3}$ if tidal dissipation is predominantly in the star. The precession model is another possible origin to explain the observed TTVs. We note that the follow-up observations of occultation timing and radial velocity monitoring are needed for fully discriminating the different models.