Evidence of three mechanisms explaining the radius anomaly of hot Jupiters

¹ Physikalisches Institut, Universität Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
e-mail: christoph.mordasini@space.unibe.ch
² Max-Planck-Institut für Astronomie, Königstuhl 17, Heidelberg 69117, Germany
³ Institut für Astronomie und Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany

Received: 6 May 2020
Accepted: 4 September 2020

Abstract

Context. The anomalously large radii of hot Jupiters are still not fully understood, and all of the proposed explanations are based on the idea that these close-in giant planets possess hot interiors. Most of the mechanisms proposed have been tested on a handful of exoplanets.

Aims. We approach the radius anomaly problem by adopting a statistical approach. We want to infer the internal luminosity for the sample of hot Jupiters, study its effect on the interior structure, and put constraints on which mechanism is the dominant one.

Methods. We developed a flexible and robust hierarchical Bayesian model that couples the interior structure of exoplanets to the observed properties of close-in giant planets. We applied the model to 314 hot Jupiters and inferred the internal luminosity distribution for each planet and studied at the population level (i) the mass–luminosity–radius distribution and as a function of equilibrium temperature the distributions of the (ii) heating efficiency, (iii) internal temperature, and the (iv) pressure of the radiative–convective–boundary (RCB).

Results. We find that hot Jupiters tend to have high internal luminosity with 10⁴ L_J for the largest planets. As a result, we show that all the inflated planets have hot interiors with an internal temperature ranging from 200 up to 800 K for the most irradiated ones. This has important consequences on the cooling rate and we find that the RCB is located at low pressures between 3 and 100 bar. Assuming that the ultimate source of the extra heating is the irradiation from the host star, we also illustrate that the heating efficiency increases with increasing equilibrium temperature and reaches a maximum of 2.5% at ~1860 K, beyond which the efficiency decreases, which is in agreement with previous results. We discuss our findings in the context of the proposed heating mechanisms and illustrate that ohmic dissipation, the advection of potential temperature, and thermal tides are in agreement with certain trends inferred from our analysis and thus all three models can explain various aspects of the observations.

Conclusions. We provide new insights on the interior structure of hot Jupiters and show that with our current knowledge, it is still challenging to firmly identify the universal mechanism driving the inflated radii.