Chasing the Tides: Searching for Orbital Decay Signatures in Transit Timing Data and Tidal Models for 20 Hot Jupiters

TL;DR

This study analyzes transit timing variations for 20 hot Jupiters to search for tidal-decay signatures and interprets the results with MESA-based tidal-dissipation models. By fitting linear and quadratic ephemerides to 2930 transit times and performing Lomb-Scargle analyses, the authors identify significant orbital evolution only in WASP-12 b, TrES-1 b, and WASP-121 b, while most systems remain consistent with constant periods. They update the decay rate for WASP-12 b to $\dot{P}= -29.4 \pm 4.0$ ms yr$^{-1}$ with $Q'_{\star} = (1.72 \pm 0.18) \times 10^5$, find $\dot{P} = -14.9 \pm 0.6$ ms yr$^{-1}$ for TrES-1 b (implying $Q'_{\star} = 5.7 \times 10^2$, inconsistent with standard theory), and detect orbital growth for WASP-121 b at $+15.1 \pm 0.8$ ms yr$^{-1}$ (likely inertial-wave-driven). The paper also provides a detailed assessment of tidal-dissipation mechanisms (IGW, IW, and EQ tides) across host stars using MESA, and discusses apsidal motion and tidal-stability implications for the surveyed systems, highlighting the need for continued long-baseline, high-precision timing. Overall, the results constrain $Q'_{\star}$ across a diverse set of hosts and inform theoretical expectations for tidal evolution in close-in planetary systems.

Abstract

In this work, we present a transit timing variation analysis for 20 hot Jupiter systems, which we interpret with theoretical tidal dissipation models. For the majority of the sample, we conclude that a constant orbital period model represents the timing data best. Only WASP-12 b, TrES-1 b and WASP-121 b exhibit a changing orbital period, according to the most up-to-date results. We updated the orbital decay rate of WASP-12 b to $\dot{P} = -29.4 \pm 4.0 \mathrm{~ms~yr^{-1}}$ and the corresponding stellar tidal quality factor to $Q_*^{\prime} = 1.72 \pm 0.18 \times 10^5$. For TrES-1 b, the median quadratic model suggests a period decrease at a rate of $-14.9 \pm 0.6 \mathrm{~ms~yr^{-1}}$, but the corresponding $Q_*^{\prime} = 570 \pm 60$ does not agree with the theoretical estimates, which suggest $Q_*^{\prime} \sim 10^6$ due to internal gravity wave dissipation. Lastly, WASP-121 b exhibits orbital growth at a rate of $15.1 \pm 0.8 \mathrm{~ms~yr^{-1}}$, and theoretical results support outward migration due to strong inertial wave dissipation.

Figures (8)

• Figure 1: Orbital period versus the selection criteria parameters $\tau_a$ and $\tau_{\omega_\star}$ for objects from NASA Exoplanet Archive and TEPCat. The symbol size is proportional to the planetary (or brown dwarf) radius, while the color scale represents the planetary mass. The systems analyzed in this study are highlighted and labeled.
• Figure 2: Light curves of the objects in our sample, as listed in Table \ref{['tab:observations']}. Individual exposures are shown in black, while the EXOFAST models are plotted in red. Light curves excluded from the sample due to PNR, $\beta$ or 3$\sigma$ clipping criterion are displayed with a grey background.
• Figure 3: Linear residuals of the TTV diagrams for CoRoT-2 b, HAT-P-23 b, HATS-18 b, KELT-9 b and KELT-16 b based on observations from various sources: ETD data (blue empty circles), obtained and analyzed literature light curves (green squares), adopted literature transit times (empty black squares), this work (black and yellow circles) and TESS observations (purple circles).
• Figure 4: Same as Figure \ref{['fig:ttv_plot_1']}, but for Qatar-1 b, Qatar-4 b, TOI-1937A b, TOI-2109 b and TrES-1 b. Since $|\Delta {\rm BIC}| > 10$ for TrES-1 b case, we also present the median orbital decay model represented with the orange line and the shaded band indicating its $3\sigma$ uncertainty range.
• Figure 5: Top: WASP-12's tidal efficiency due to IGW $(Q_\text{IGW}^{'})$ as a function of stellar age for 9 different stellar evolution models. The dashed horizontal line displays $Q_\star^{\prime} = 1.72 \times 10^5$ from our median quadratic model. Middle: Critical mass of WASP-12 b for wave breaking in the stellar core $M_\text{crit}$ as a function of stellar age. The horizontal dashed line shows the planetary mass $M_{\rm p} = 1.47 ~M_{\rm J}$ from collins2017qatar1. Bottom: WASP-12's stellar effective temperature $T_\text{eff}$ as a function of stellar age. Here, dashed horizontal line shows $T_\text{eff} = 6265 ~K$ from leonardi2024. For each plot, we show the age reported by collins2017qatar1 (2.0 Gyr) as a vertical black dashed line, and the age from leonardi2024 ($3.05 \pm 0.22$ Gyr) as an orange dashed line at the nominal value. The gold-shaded region represents the 68% confidence interval.