Inflating and Deflating Hot Jupiters: Coupled Tidal and Thermal Evolution of Known Transiting Planets

We examine the radius evolution of close-in giant planets with a planet evolution model that couples the orbital-tidal and thermal evolution. For 45 transiting systems, we compute a large grid of cooling/contraction paths forward in time, starting from a large phase space of initial semi-major axes and eccentricities. Given observational constraints at the current time for a given planet (semi-major axis, eccentricity, and system age) we find possible evolutionary paths that match these constraints, and compare the calculated radii to observations. We find that tidal evolution has two effects. First, planets start their evolution at larger semi-major axis, allowing them to contract more efficiently at earlier times. Second, tidal heating can significantly inflate the radius when the orbit is being circularized, but this effect on the radius is short-lived thereafter. Often circularization of the orbit is proceeded by a long period while the semi-major axis slowly decreases. Some systems with previously unexplained large radii that we can reproduce with our coupled model are HAT-P-7, HAT-P-9, WASP-10, and XO-4. This increases the number of planets for which we can match the radius from 24 (of 45) to as many as 35 for our standard case, but for some of these systems we are required to be viewing them at a special time around the era of current radius inflation. This is a concern for the viability of tidal inflation as a general mechanism to explain most inflated radii. Also, large initial eccentricities would have to be common. We also investigate the evolution of models that have a floor on the eccentricity, as may be due to a perturber. In this scenario we match the extremely large radius of WASP-12b. (Abridged)

💡 Research Summary

The paper tackles the long‑standing problem of why many close‑in giant exoplanets (“hot Jupiters”) exhibit radii larger than predicted by standard cooling‑contraction models. The authors construct a coupled evolution framework that simultaneously follows a planet’s internal thermal evolution and the tidal (orbital‑tidal) evolution of its orbit. For each of 45 well‑characterized transiting hot Jupiters they generate a large grid of forward‑integrated models, varying the initial semi‑major axis (a₀) and eccentricity (e₀) over a broad range. At each timestep the model computes the planet’s radius from a standard interior‑structure code, the tidal dissipation rate inside the planet (using a constant‑Q or similar prescription), and the resulting changes in a and e due to tidal torques. The tidal dissipation acts as an internal heat source (“tidal heating”) that can temporarily inflate the radius, while the orbital decay changes the incident stellar flux and the timescale for cooling.

Two key tidal effects emerge from the simulations. First, planets that begin their evolution farther from the star (larger a₀) can contract more efficiently early on because the stellar irradiation is weaker; this helps explain why some planets now have relatively modest radii despite being close‑in today. Second, when the orbit is still eccentric, tidal dissipation is strong; as the orbit circularizes, the released tidal energy is deposited in the interior, inflating the radius. This inflation, however, is short‑lived—once e drops near zero the heating shuts off and the planet resumes cooling.

By matching the present‑day observed semi‑major axis, eccentricity, and system age, the authors identify evolutionary tracks that reproduce the measured radii. They find that several planets previously considered anomalously large—HAT‑P‑7b, HAT‑P‑9b, WASP‑10b, and XO‑4b—can be explained with reasonable choices of a₀ and e₀ (typically e₀≈0.3–0.6). In the “standard case” (no imposed eccentricity floor) the number of planets whose radii can be matched rises from 24 out of 45 (as in earlier studies) to as many as 35. This is a substantial improvement, indicating that coupled tidal‑thermal evolution can account for a large fraction of the inflated population.

Nevertheless, the success relies on observing many systems during a relatively brief phase of tidal inflation. Because the heating episode lasts only a few hundred million years, the probability of catching a random planet in that window is low, raising doubts about tidal heating as a universal explanation. Moreover, the model requires that large initial eccentricities be common among hot Jupiters, a condition not yet confirmed observationally.

To address the limitation, the authors explore a scenario where an external perturber (another planet or a distant companion) maintains a non‑zero “eccentricity floor” (e_min > 0). In this case, tidal dissipation continues over much longer timescales, providing a sustained heat source. Using this approach they can reproduce the extreme radius of WASP‑12b (≈1.7 R_J), which is otherwise difficult to explain.

In summary, the paper demonstrates that a self‑consistent coupling of tidal orbital decay and internal thermal evolution can explain many, though not all, inflated hot Jupiters. It highlights two competing influences: early‑time efficient contraction due to a larger orbital distance, and short‑term tidal inflation during circularization. The work also underscores the need for better constraints on the initial eccentricity distribution of hot Jupiters and on the prevalence of additional companions that could maintain ongoing tidal heating. Future observations—precise eccentricity measurements, long‑term monitoring of orbital decay, and searches for perturbers—will be essential to test whether tidal heating is a dominant or merely a contributing factor in shaping the radii of close‑in giant exoplanets.