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

Abstract

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. This work may cast some doubt on our ability to accurately determine the interior heavy element enrichment of normal, non-inflated close-in planets, because of our dearth of knowledge about these planet's previous orbital-tidal histories. Finally, we find that the end state of most close-in planetary systems is disruption of the planet as it moves ever closer to its parent star.

A transiting giant planet with a temperature between 250 K and 430 K

“…Similarly, we estimate 12 a mass loss rate of about 8 3 10 6 g s 21 , which is the lowest one among the known transiting gas giants; escape processes have therefore not affected the planet significantly since its origin. That CoRoT-9b has a much larger periastron distance than any other known transiting exoplanet also strongly constrains its composition, independently of hypotheses 11,13 on possible missing energy sources and associated radius inflation: An evolutionary model of CoRoT-9b (Fig. 3) shows a good match to the observed radius between 0 and 20 Earth masses of heavy elements, comparable to the composition of giant planets in our Solar System 6 .…”

Is tidal heating sufficient to explain bloated exoplanets? Consistent calculations accounting for finite initial eccentricity

“…4 and 5, we compare the constant time-lag model with the constant Q model used by various authors. In order to allow a direct and immediate comparison with these studies, we will choose the values of the couple (Δt p , Δt ) from the relations (k 2 Δt p = 3 2n obs Q p , k 2 Δt = 3 2n obs Q ), where (Q p , Q ) are the constant normalized quality factors used by Miller et al (2009). This ensures that the effective tidal dissipation function is the same in both calculations for a given planet with its measured orbital parameters.…”

“…Following Bodenheimer et al (2001) and Gu et al (2003), attempts have been made to explain the observed large radius of some transiting close-in gas giant exoplanets -the so-called "Hot Jupiters" -by means of tidal heating (Jackson et al 2008;Miller et al 2009;). All these models, however, use tidal models truncated to a low (2nd) order in eccentricity, in spite of initial eccentricities, as determined from the tidal evolution calculations, which can be as large as e = 0.8!…”

Multi-site campaign for transit timing variations of WASP-12 b: possible detection of a long-period signal of planetary origin

“…This mechanism, in turn, might be responsible for heating up the planet's interior and bloating its radius in consequence (Miller et al 2009). The orbit of WASP-12 b is expected to be circularised on short timescales if the tidal dissipation A&A 551, A108 (2013) Notes.…”