Transit Timing Variation of XO-3b: Evidence for Tidal Evolution of Hot Jupiter with High Eccentricity
Fan Yang, Xing Wei
Abstract
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 σ ), 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 × 10 −9 ± 2.9 × 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” <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>Q</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> would be 1.8 × 10 4 ± 8 × 10 2 if we assume the decay is due to the tide in the planet; whereas <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>Q</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> would be 1.5 × 10 5 ± 6 × 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.