Bloated hot Jupiters

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Why are some hot Jupiters so much larger than standard models would allow?

The debate on the “inflation” of hot Jupiters started right after the first transit detection. The first measured radius of HD 209458b, 1.35 RJup, was substantially higher than models were predicting for a hotter version of Jupiter (~1.1 RJup).

The first explanations focussed on the radius observations, pointing out that the radius could have been over-estimated, and that the transit geometry meant that the effective radius was increased by the fact that the starlight was crossing the limb at a grazing angle.

Indeed, more precise measurements of the transit depth decreased the radius estimate a bit, and model calculations indicated that the second effect amounted to up to a few percent of the radius. Still, the size of ‘209 remained about 20% larger than the models, or 60% in density.

This implied either a very young age for the system (belied by the mid-age characteristics of the host star itself), or a massive input of energy into the planet.

In their seminal models of ‘209, Showman & Guillot (2002) and Guillot & Showman (2002) showed that if 1% of the stellar irradiation somehow made its way into the planetary interior, the excess radius could be explained. Injecting this energy, however, is not trivial, because any heating done in the atmosphere near or above the level of the photosphere will simply increase the effective temperature, and send back the energy to space. The stellar irradiation must somehow be transferred to another form of energy, then buried below the photosphere. Atmospheric circulation seemed like a natural way of doing that, via the dissipation of some of the winds needed to carry the heat from the day side to the night side. In the Showman circulation models, 1% looked like a reasonable value for this energy injection. Calculating actual values requires knowing the exact dissipation mechanisms and efficiencies in the atmosphere, which even for solar-system planets are very difficult to measure or estimate from first principles.

Transiting planets other than ‘209 were then discovered, starting with the OGLE survey, and it turned out that normal-size hot Jupiters were common as well. The issue of radius inflation might have been limited to a few odd cases represented by ‘209.

This lead credence to another category of explanations: the injection of energy into the planet could be due to orbital perturbations by an unseen companion or by tidal interaction with the star. Models tailored to each case were able to explain the radii nicely (e.g. e.g. Jackson et al. 2008). But these models have little explanatory or predictive power, and none of the unseen perturbers were detected by long-term radial velocity monitoring or transit timing variations.

Other avenues were explored to explain the “bloated” hot Jupiters, more intrinsic to the planet itself: Burrows et al. (2008) proposed that heavy-element enrichement in the envelope could increase the opacities and delay the contraction, although the enrichment would need to be limited to the outer layer of the planet, otherwise the increased overall density would counterbalance the effect. Chabrier & Baraffe (2007) showed how a composition gradient within the planet due to gravitational settling could inhibit convection and slow down cooling, leading to delayed contraction as well.

Hot Jupiters are known to form on eccentric orbits, that are then circularised as the planet gets close enough to the star for tidal effects to become dominant. The process of circularisation injects a lot of heat into the planet, enough to inflate its radius substantially. However, further calculations show that it would be difficult for this process to explain the phenomenon as a whole, since the contraction of hot Jupiters would resume rapidly after the circularisation of the orbit. This process could explain individual cases but required too many coincidences to explain the observed rate of ccurrence of inflated planets.

As more transiting planets were discovered, most notably by the WASP and HATNet surveys, it gradually became clear that the radius inflation was closely correlated to the amount of star light received by the planet. Even better, the relation between inflation and incident flux showed a dependence on the mass of the planet, with heavier planets suffering less inflation, exactly as expected in the scenario of converting part of the star light into internal heat (in a heavier planet the same amount of heat results in a smaller radius change).

Relation between radius and incident irradiation for exoplanets, in three mass regimes. The yellow lines show models without energy injection. The gray zone show the expected relation for an energy injection of 2% to 6% of the incoming irradiation in the interior of the planet. (Figure from poster by Pont & Aigrain at the Exoclimes 2010 conference).

 

Neither of the two “intrinsic” scenarios (enhanced opacities and reduced convection) predicted such a dependence with stellar flux. The tidal scenarios predicted a link with closeness with the star, but not directly with incident flux. Because parent stars of transiting planets cover a wide range of temperatures, and because flux is such a steep function of temperature, the two effects (star-planet distance and incident flux) can be separated, and it is clear that incident flux is the primary factor.

Following this finding, three actual processes were proposed to inject a fraction of the irradiation energy into the planet:

(1) the “thermal tides”. Arras & Socrates (2010) showed that the interaction of the tidal gravity field and the asymmetry caused by the heating of the atmosphere on the day side produce work in the planet.

(2) the “mechanical greenhouse”. Youdin et al. (2010) proposes that any – unknown but plausible – process that produces vertical mixing in the atmosphere will also be able to transfer energy from the winds to the interior.

(3)  the “Ohmic dissipation”. Batygin et al. (2010) and Perna et al. (2010) show that if the atmospheres of hot Jupiters contain ions, for instance NaII, then the magnetic drag on these can transfer some of the wind energy to the interior.

On the other hand, Showman (2012) has performed some more detailed simulations of hot Jupiter atmospheric circulation, and find that direct dissipation of the winds and currents is able to transfer only a very small fraction of the incident stellar energy as heat in the interior, so that the initial unmodified “Showman” scenario would not be working quantitatively.

That is were we are at the end of 2011. With more than one hundred transiting hot Jupiter measured, there is not yet a single exception to the relation between incoming flux and inflation (i.e. a very large, cool planet, or a normal size, very hot planet), so that the general explanation in terms of the conversion of a fraction of the incoming irradiation as internal entropy seems solidly established. As far as the actual process is concerned, the jury is still out.

 

Feature Image: figure from poster by Pont & Aigrain at the Exoclimes 2010 conference.


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About Author

I am a professor of planetary science at the University of Exeter. My specialty is the study of exoplanets, in particular the observation and modelling of exoplanet atmospheres. I have done my PhD a the University of Geneva and worked in Chile, France and Switzerland.