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

The cause of hot Jupiter radius inflation, where giant planets with $T_{\rm eq}$ $>1000$ K are significantly larger than expected, is an open question and the subject of many proposed explanations. Rather than examine these models individually, this work seeks to characterize the anomalous heating as a function of incident flux, $\epsilon(F)$, needed to inflate the population of planets to their observed sizes. We then compare that result to theoretical predictions for various models. We examine the population of about 300 giant planets with well-determined masses and radii and apply thermal evolution and Bayesian statistical models to infer the anomalous power as a function of incident flux that best reproduces the observed radii. First, we observe that the inflation of planets below about M=0.5 \;\rm{M}_\rm{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 $\epsilon(F)$ increases with $T_{\rm{eq}}$ towards a maximum of $\sim 2.5\%$ at $T_{\rm{eq}} \approx 1500$ K, and then decreases as temperatures increase further, falling to $\sim0.2\%$ at T_\rm{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 explicitly check the thermal tides model and find that it predicts far more variance in radii than is observed. Thus, our results provide evidence for the Ohmic dissipation model and a functional form for $\epsilon(F)$ that any future theories of hot Jupiter radii can be tested against.Comment: 14 pages, 14 figures, accepted to The Astronomical Journal. This revision revises the description of statistical methods for clarity, but the conclusions remain the sam

The Mass-Metallicity Relation for Giant Planets

Exoplanet discoveries of recent years have provided a great deal of new data for studying the bulk compositions of giant planets. Here we identify 47 transiting giant planets ($20 M_\oplus < M < 20 M_{\mathrm{J}}$) whose stellar insolation is low enough ($F_* < 2\times10^8\; \text{erg}\; \text{s}^{-1}\; \text{cm}^{-2}$, or roughly $T_\text{eff} < 1000$) that they are not affected by the hot Jupiter radius inflation mechanism(s). We compute a set of new thermal and structural evolution models and use these models in comparison with properties of the 47 transiting planets (mass, radius, age) to determine their heavy element masses. A clear correlation emerges between the planetary heavy element mass $M_z$ and the total planet mass, approximately of the form $M_z \propto \sqrt{M}$. This finding is consistent with the core accretion model of planet formation. We also study how stellar metallicity [Fe/H] affects planetary metal-enrichment and find a weaker correlation than has been previously reported from studies with smaller sample sizes. We confirm a strong relationship between the planetary metal-enrichment relative to the parent star $Z_{\rm planet}/Z_{\rm star}$ and the planetary mass, but see no relation in $Z_{\rm planet}/Z_{\rm star}$ with planet orbital properties or stellar mass. The large heavy element masses of many planets ($>50$ $M_{\oplus}$) suggest significant amounts of heavy elements in H/He envelopes, rather than cores, such that metal-enriched giant planet atmospheres should be the rule. We also discuss a model of core-accretion planet formation in a one-dimensional disk and show that it agrees well with our derived relation between mass and $Z_{\rm planet}/Z_{\rm star}$.Comment: Accepted to The Astrophysical Journal. This revision adds a substantial amount of discussion; the results are the sam

Removal of Hot Saturns in Mass-Radius Plane by Runaway Mass Loss

The hot Saturn population exhibits a boundary in mass-radius space, such that no planets are observed at a density less than $\sim$0.1 g cm$^{-3}$. Yet, planet interior structure models can readily construct such objects as the natural result of radius inflation. Here, we investigate the role XUV-driven mass-loss plays in sculpting the density boundary by constructing interior structure models that include radius inflation, photoevaporative mass loss and a simple prescription of Roche lobe overflow. We demonstrate that planets puffier than $\sim$0.1 g cm$^{-3}$ experience a runaway mass loss caused by adiabatic radius expansion as the gas layer is stripped away, providing a good explanation of the observed edge in mass-radius space. The process is also visible in the radius-period and mass-period spaces, though smaller, high-bulk-metallicity planets can still survive at short periods, preserving a partial record of the population distribution at formation.Comment: 10 pages, 5 figures, submitted to ApJ Letter

The effect of interior heat flux on the atmospheric circulation of hot and ultra-hot Jupiters

Many hot and ultra-hot Jupiters have inflated radii, implying that their interiors retain significant entropy from formation. These hot interiors lead to an enhanced internal heat flux that impinges upon the atmosphere from below. In this work, we study the effect of this hot interior on the atmospheric circulation and thermal structure of hot and ultra-hot Jupiters. To do so, we incorporate the population-level predictions from evolutionary models of hot and ultra-hot Jupiters as input for a suite of General Circulation Models (GCMs) of their atmospheric circulation with varying semi-major axis and surface gravity. We conduct simulations with and without a hot interior, and find that there are significant local differences in temperature of up to hundreds of Kelvin and in wind speeds of hundreds of m s$^{-1}$ or more across the observable atmosphere. These differences persist throughout the parameter regime studied, and are dependent on surface gravity through the impact on photosphere pressure. These results imply that the internal evolution and atmospheric thermal structure and dynamics of hot and ultra-hot Jupiters are coupled. As a result, a joint approach including both evolutionary models and GCMs may be required to make robust predictions for the atmospheric circulation of hot and ultra-hot Jupiters.Comment: Accepted at ApJL, 17 pages, 8 figure