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

By J. Leconte, G. Chabrier, Isabelle Baraffe, B. Levrard. 2010

257 citations recorded by the source corpus.

We present the consistent evolution of short-period exoplanets coupling the tidal and gravothermal evolution of the planet. Contrarily to previous similar studies, our calculations are based on the complete tidal evolution equations of the Hut (1981) model, valid at any order in eccentricity, obliquity and spin. We demonstrate both analytically and numerically that except if the system was formed with a nearly circular orbit (e < 0.2), consistently solving the complete tidal equations is mandatory to derive correct tidal evolution histories. We show that calculations based on tidal models truncated at 2nd order in eccentricity, as done in all previous studies, lead to quantitatively and sometimes even qualitatively erroneous tidal evolutions. As a consequence, tidal energy dissipation rates are severely underestimated in all these calculations and the characteristic timescales for the various orbital parameters evolutions can be wrong by up to three orders of magnitude. These discrepancies can by no means be justified by invoking the uncertainty in the tidal quality factors. Based on these complete, consistent calculations, we revisit the viability of the tidal heating hypothesis to explain the anomalously large radius of transiting giant planets. We show that even though tidal dissipation does provide a substantial contribution to the planet’s heat budget and can explain some of the moderately bloated hot-Jupiters, this mechanism can not explain alone the properties of the most inflated objects, including HD 209 458 b. Indeed, solving the complete tidal equations shows that enhanced tidal dissipation and thus orbit circularization occur too early during the planet’s evolution to provide enough extra energy at the present epoch. In that case either a third, so far undetected, low-mass companion must be present to keep exciting the eccentricity of the giant planet, or other mechanisms – stellar irradiation induced surface winds dissipating in the planet’s tidal bulges and thus reaching the convective layers, inefficient flux transport by convection in the planet’s interior – must be invoked, together with tidal dissipation, to provide all the pieces of the abnormally large exoplanet puzzle.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/a56afb926938ff9c30ead52d38ede3cf7ef9c4b5

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In Astronomy and Astrophysics

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Citations in the corpus

• Tidal obliquity evolution of potentially habitable planets (2011, background): “…the most recent studies on equilibrium tides, one representing the family of CPL models (Ferraz-Mello et al. 2008, FM08 in the following) and one representing the family of CTL models (Leconte et al. 2010, Lec10 in the following), to simulate the tidal evolution of terrestrial planets aroundLMSs.”
• Tidal dissipation in planet-hosting stars: damping of spin-orbit misalignment and survival of hot Jupiters (2011, background): “…stars could play an important role the evolution and survival of hot Jupiter systems (e.g., Lin et al. 1996; Rasio et al. 1996; Marcy et al. 1997; Sasselov 2003; DobbsDixon et al. 2004; Barker & Ogilvie 2009; Jackson et al. 2009; Levrard et al. 2009; Leconte et al. 2010; Matsumura et al. 2010).”
• GLIESE 581D IS THE FIRST DISCOVERED TERRESTRIAL-MASS EXOPLANET IN THE HABITABLE ZONE (2011, background): “In the Solar System, Rayleigh scattering reflects the bluer incoming starlight much more effectively, and hence a planet receiving the same flux as GJ581d would be uninhabitable for any CO2 pressure.”
• A dynamically-packed planetary system around GJ 667C with three super-Earths in its habitable zone (2013, background): “17 Guillem Anglada-Escudé et al.: Three HZ super-Earths in a seven-planet system Leconte et al. (2010) model and the Earth’s dissipation, we find that tidal heating of the HZ planets will be negligible for most cases.”
• Tidal Dissipation in Stars and Giant Planets (2014, background): “The extension of these equations to arbitrary e and i under the assumption of a common time lag can be found in Leconte et al. (2010) and Matsumura et al. (2010), and was first derived by Alexander (1973).”
• THE MASS OF KOI-94d AND A RELATION FOR PLANET RADIUS, MASS, AND INCIDENT FLUX (2013, background): “The emerging view, in particular advanced by Leconte et al. (2010) who used the most detailed tidal evolution equations, is that since radius inflation via orbital eccentricity damping is a transient phenomenon, it cannot be the “universal” radius inflation mechanism.”
• THE IMPRINT OF EXOPLANET FORMATION HISTORY ON OBSERVABLE PRESENT-DAY SPECTRA OF HOT JUPITERS (2016, background): “However, at the ages of several Gyrs at which hot Jupiters are typically observed this should no longer be important (Leconte et al. 2010).”
• TIDAL EVOLUTION OF CLOSE-IN PLANETS (2010, methodology): “More recently, Leconte et al. (2010) revisited this problem, and pointed out that the truncated tidal equations used in many previous studies could lead to an erroneous tidal evolution for moderate to high eccentricity (e & 0.2).”
• 3D climate modeling of close-in land planets: Circulation patterns, climate moist bistability and habitability (2013, background): “Indeed, the standard theory of equilibrium tides (Darwin 1880; Hut 1981; Leconte et al. 2010) predicts that a planet should synchronize on a timescale equal to τsyn = 1 3 r2g M p a6 GM2?”