Effects of Helium Phase Separation on the Evolution of Giant Planets

We present the first models of Saturn and Jupiter to couple their evolution to both a radiative-atmosphere grid and to high-pressure phase diagrams of hydrogen with helium. The purpose of these models is to quantify the evolutionary effects of helium phase separation in Saturn's deep interior. We find that prior calculated phase diagrams in which Saturn's interior reaches a region of predicted helium immiscibility do not allow enough energy release to prolong Saturn's cooling to its known age and effective temperature. We explore modifications to published phase diagrams that would lead to greater energy release, and find a modified H-He phase diagram that is physically reasonable, leads to the correct extension of Saturn's cooling, and predicts an atmospheric helium mass fraction Y_atmos in agreement with recent estimates. We then expand our inhomogeneous evolutionary models to show that hypothetical extrasolar giant planets in the 0.15 to 3.0 Jupiter mass range may have T_effs 10-15 K greater than one would predict with models that do not incorporate helium phase separation.Comment: 4 pages. Contribution to 'The Search for Other Worlds', Oct 2003, University of Marylan

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

Understanding the Mass-Radius Relation for Sub-Neptunes: Radius as a Proxy for Composition

Transiting planet surveys like Kepler have provided a wealth of information on the distribution of planetary radii, particularly for the new populations of super-Earth and sub-Neptune sized planets. In order to aid in the physical interpretation of these radii, we compute model radii for low-mass rocky planets with hydrogen-helium envelopes. We provide model radii for planets 1-20 Earth masses, with envelope fractions from 0.01-20%, levels of irradiation 0.1-1000x Earth's, and ages from 100 Myr to 10 Gyr. In addition we provide simple analytic fits that summarize how radius depends on each of these parameters. Most importantly, we show that at fixed composition, radii show little dependence on mass for planets with more than ~1% of their mass in their envelope. Consequently, planetary radius is to first order a proxy for planetary composition for Neptune and sub-Neptune sized planets. We recast the observed mass-radius relationship as a mass-composition relationship and discuss it in light of traditional core accretion theory. We discuss the transition from rocky super-Earths to sub-Neptune planets with large volatile envelopes. We suggest 1.75 Earth radii as a physically motivated dividing line between these two populations of planets. Finally, we discuss these results in light of the observed radius occurrence distribution found by Kepler.Comment: 17 pages, 9 figures, 7 tables, submitted to Ap

Re-inflated Warm Jupiters Around Red Giants

Since the discovery of the first transiting hot Jupiters, models have sought to explain the anomalously large radii of highly irradiated gas giants. We now know that the size of hot Jupiter radius anomalies scales strongly with a planet's level of irradiation and numerous models like tidal heating, ohmic dissipation, and thermal tides have since been developed to help explain these inflated radii. In general however, these models can be grouped into two broad categories: 1) models that directly inflate planetary radii by depositing a fraction of the incident irradiation into the interior and 2) models that simply slow a planet's radiative cooling allowing it to retain more heat from formation and thereby delay contraction. Here we present a new test to distinguish between these two classes of models. Gas giants orbiting at moderate orbital periods around post main sequence stars will experience enormous increases their irradiation as their host stars move up the sub-giant and red-giant branches. If hot Jupiter inflation works by depositing irradiation into the planet's deep interiors then planetary radii should increase in response to the increased irradiation. This means that otherwise non-inflated gas giants at moderate orbital periods >10 days can re-inflate as their host stars evolve. Here we explore the circumstances that can lead to the creation of these "re-inflated" gas giants and examine how the existence or absence of such planets can be used to place unique constraints of the physics of the hot Jupiter inflation mechanism. Finally, we explore the prospects for detecting this potentially important undiscovered population of planets.Comment: Accepted by ApJ. 8 Figures and 8 page