Bayesian Analysis of Hot-Jupiter Radius Anomalies: Evidence for Ohmic Dissipation?

Abstract

The cause of hot Jupiter radius inflation, where giant planets with T eq > 1000 K are significantly larger than expected, is an open question and the subject of many proposed explanations. Many of these hypotheses postulate an additional anomalous power which heats planets' convective interiors, leading to larger radii. Rather than examine these proposed models individually, we determine what anomalous powers are needed to explain the observed population's radii, and consider which models are most consistent with this. We examine 281 giant planets with well-determined masses and radii and apply thermal evolution and Bayesian statistical models to infer the anomalous power as a fraction of (and varying with) incident flux (F ) that best reproduces the observed radii. First, we observe that the inflation of planets below about M = 0.5 M J appears very different than their higher mass counterparts, perhaps as the result of mass loss or an inefficient heating mechanism. As such, we exclude planets below this threshold. Next, we show with strong significance that (F ) increases with T eq towards a maximum of ∼ 2.5% at T eq ≈ 1500 K, and then decreases as temperatures increase further, falling to ∼ 0.2% at T eff = 2500 K. This high-flux decrease in inflation efficiency was predicted by the Ohmic dissipation model of giant planet inflation but not other models. We also show that the thermal tides model predicts far more variance in radii than is observed. Thus, our results provide evidence for the Ohmic dissipation model and a functional form for (F ) that any future theories of hot Jupiter radii can be tested against.

Reinflation of Warm and Hot Jupiters

“…In this suite of models, we only include deposited heating if the incident stellar flux F ≥ 2.268 × 10 8 erg cm −2 s −1 , which corresponds to an equilibrium temperature T eq ≥ 1000 K. We do so because gas giants with T eq < 1000 K do not have anomalous radii (Demory & Seager 2011, Laughlin et al 2011, Miller & Fortney 2011, Thorngren & Fortney 2018. Weak deposited heating in warm Jupiter interiors is also expected from the inferred dependence of deposited power on T eq (Thorngren & Fortney 2018), which decreases to zero at T eq < 1000 K. This is also consistent with Ohmic dissipation and models of atmospheric heat transport, which expect that planets with T eq < 1000 K should not be inflated due to the small day-night forcing and low atmospheric ionization fraction (Youdin & Mitchell 2010, Menou 2012, Ginzburg & Sari 2016, Tremblin et al 2017. As a result, we assume that there is no deposited heating for planets with T eq < 1000 K, because otherwise warm Jupiters with anomalously large radii would have been discovered.…”

“…A variety of mechanisms have been propsed to explain the anomalous transit radii of hot Jupiters (Weiss et al 2013, Baraffe et al 2014, including tidal mechanisms (Bodenheimer et al 2001, Gu et al 2003, 2004, Jackson et al 2008, Ibgui & Burrows 2009, Miller et al 2009, Arras & Socrates 2010, Ibgui et al 2010, Leconte et al 2010, Gu et al 2019, modifications to the microphysics of hot Jupiters (Burrows et al 2007, Chabrier & Baraffe 2007, Leconte & Chabrier 2012, Kurokawa & Inutsuka 2015, incident stellar-fluxdriven hydrodynamic mechanisms , Youdin & Mitchell 2010, Tremblin et al 2017, Sainsbury-Martinez et al 2019, and Ohmic dissipation (Batygin & Stevenson 2010, Perna et al 2010, Batygin et al 2011, Huang & Cumming 2012, Menou 2012, Rauscher & Menou 2013, Wu & Lithwick 2013, Rogers & Showman 2014, Rogers & Komacek 2014, Ginzburg & Sari 2016. Studies of the radius distribution of hot Jupiters (Demory & Seager 2011, Laughlin et al 2011, Miller & Fortney 2011, Thorngren & Fortney 2018 have shown that radius anomalies only occur for gas giants with equilibrium temperatures in excess of 1000 K. Additionally, Laughlin et al (2011), Weiss et al (...…”

“…As a result, the mechanism that inflates hot Jupiters is directly tied to the incident flux from the host star. Recently, Thorngren & Fortney (2018) found that the fraction of irradiation that is converted to deposited heat must peak at an intermediate equilibrium temperature of ∼ 1600 K and fall off for both hotter and colder planets. predicted that warm Jupiters will re-inflate if their equilibrium temperature crosses the 1000 K heating threshold as their host stars evolve, provided that sufficient heat is deposited deep within the planet.…”

HATS-50b through HATS-53b: Four Transiting Hot Jupiters Orbiting G-type Stars Discovered by the HATSouth Survey*

“…It remains to be fully understood why giant exoplanets with similar masses present such a wide range of radii (see Thorngren & Fortney 2017). Particularly intriguing is, finally, the fact that the most recent studies of hot Jupiters' atmospheres have shown a wide range of different results, including Rayleigh scattering, Na and K absorption, detection of molecules, like H 2 O and titanium oxide, and flat Notes.…”

“…The four planets have densities comparable with models of core-free planets. One potential explanation could be that the planets are bloated, which would provide the incorrect impression of a core mass that is too small (Thorngren & Fortney 2017). An alternative explanation would be that relatively low opacities would allow gas runaway accretion also for lower core masses (Mordasini 2014;Ormel 2014).…”