Structure and Evolution of Internally Heated Hot Jupiters

Hot Jupiters receive strong stellar irradiation, producing equilibrium temperatures of $1000 - 2500 \ \mathrm{Kelvin}$. Incoming irradiation directly heats just their thin outer layer, down to pressures of $\sim 0.1 \ \mathrm{bars}$. In standard irradiated evolution models of hot Jupiters, predicted transit radii are too small. Previous studies have shown that deeper heating -- at a small fraction of the heating rate from irradiation -- can explain observed radii. Here we present a suite of evolution models for HD 209458b where we systematically vary both the depth and intensity of internal heating, without specifying the uncertain heating mechanism(s). Our models start with a hot, high entropy planet whose radius decreases as the convective interior cools. The applied heating suppresses this cooling. We find that very shallow heating -- at pressures of$1 - 10 \ \mathrm{bars}$-- does not significantly suppress cooling, unless the total heating rate is$\gtrsim 10\%$of the incident stellar power. Deeper heating, at$100 \ \mathrm{bars}$, requires heating at only$1\%$of the stellar irradiation to explain the observed transit radius of$1.4 R_{\rm Jup}$after 5 Gyr of cooling. In general, more intense and deeper heating results in larger hot Jupiter radii. Surprisingly, we find that heat deposited at$10^4 \ \mathrm{bars}$-- which is exterior to$\approx 99\%$ of the planet's mass -- suppresses planetary cooling as effectively as heating at the center. In summary, we find that relatively shallow heating is required to explain the radii of most hot Jupiters, provided that this heat is applied early and persists throughout their evolution.Comment: Accepted at ApJ, 14 pages, 10 figure

Effects of dissociation/recombination on the day-night temperature contrasts of ultra-hot Jupiters

Secondary eclipse observations of ultra-hot Jupiters have found evidence that hydrogen is dissociated on their daysides. Additionally, full-phase light curve observations of ultra-hot Jupiters show a smaller day-night emitted flux contrast than that expected from previous theory. Recently, it was proposed by Bell & Cowan (2018) that the heat intake to dissociate hydrogen and heat release due to recombination of dissociated hydrogen can affect the atmospheric circulation of ultra-hot Jupiters. In this work, we add cooling/heating due to dissociation/recombination into the analytic theory of Komacek & Showman (2016) and Zhang & Showman (2017) for the dayside-nightside temperature contrasts of hot Jupiters. We find that at high values of incident stellar flux, the day-night temperature contrast of ultra-hot Jupiters may decrease with increasing incident stellar flux due to dissociation/recombination, the opposite of that expected without including the effects of dissociation/recombination. We propose that a combination of a greater number of full-phase light curve observations of ultra-hot Jupiters and future General Circulation Models that include the effects of dissociation/recombination could determine in detail how the atmospheric circulation of ultra-hot Jupiters differs from that of cooler planets.Comment: Accepted at Research Notes of the AA

Atmospheric Circulation of Hot Jupiters: Dayside-Nightside Temperature Differences. II. Comparison with Observations

The full-phase infrared light curves of low-eccentricity hot Jupiters show a trend of increasing fractional dayside-nightside brightness temperature difference with increasing incident stellar flux, both averaged across the infrared and in each individual wavelength band. The analytic theory of Komacek & Showman (2016) shows that this trend is due to the decreasing ability with increasing incident stellar flux of waves to propagate from day to night and erase temperature differences. Here, we compare the predictions of this theory to observations, showing that it explains well the shape of the trend of increasing dayside-nightside temperature difference with increasing equilibrium temperature. Applied to individual planets, the theory matches well with observations at high equilibrium temperatures but, for a fixed photosphere pressure of $100 \ \mathrm{mbar}$, systematically under-predicts the dayside-nightside brightness temperature differences at equilibrium temperatures less than $2000 \ \mathrm{K}$. We interpret this as due to as the effects of a process that moves the infrared photospheres of these cooler hot Jupiters to lower pressures. We also utilize general circulation modeling with double-grey radiative transfer to explore how the circulation changes with equilibrium temperature and drag strengths. As expected from our theory, the dayside-nightside temperature differences from our numerical simulations increase with increasing incident stellar flux and drag strengths. We calculate model phase curves using our general circulation models, from which we compare the broadband infrared offset from the substellar point and dayside-nightside brightness temperature differences against observations, finding that strong drag or additional effects (e.g. clouds and/or supersolar metallicities) are necessary to explain many observed phase curves.Comment: Accepted at ApJ, 16 pages, 11 figure

Vertical Tracer Mixing in Hot Jupiter Atmospheres

Aerosols appear to be ubiquitous in close-in gas giant atmospheres, and disequilibrium chemistry likely impacts the emergent spectra of these planets. Lofted aerosols and disequilibrium chemistry are caused by vigorous vertical transport in these heavily irradiated atmospheres. Here we numerically and analytically investigate how vertical transport should change over the parameter space of spin-synchronized gas giants. In order to understand how tracer transport depends on planetary parameters, we develop an analytic theory to predict vertical velocities and mixing rates ($K_\mathrm{zz}$) and compare the results to our numerical experiments. We find that both our theory and numerical simulations predict that, if the vertical mixing rate is described by an eddy diffusivity, then this eddy diffusivity $K_\mathrm{zz}$ should increase with increasing equilibrium temperature, decreasing frictional drag strength, and increasing chemical loss timescales. We find that the transition in our numerical simulations between circulation dominated by a superrotating jet and that with solely day-to-night flow causes a marked change in the vertical velocity structure and tracer distribution. The mixing ratio of passive tracers is greatest for intermediate drag strengths that corresponds to this transition between a superrotating jet with columnar vertical velocity structure and day-to-night flow with upwelling on the dayside and downwelling on the nightside. Lastly, we present analytic solutions for $K_\mathrm{zz}$ as a function of planetary effective temperature, chemical loss timescales, and other parameters, for use as input to one-dimensional chemistry models of spin-synchronized gas giant atmospheres.Comment: 25 pages, 12 figures, Accepted at Ap

Greater Climate Sensitivity and Variability on TRAPPIST-1e than Earth

The atmospheres of rocky exoplanets are close to being characterized by astronomical observations, in part due to the commissioning of the James Webb Space Telescope. These observations compel us to understand exoplanetary atmospheres, in the voyage to find habitable planets. With this aim, we investigate the effect that CO$_2$ partial pressure (pCO$_2$) has on exoplanets' climate variability, by analyzing results from ExoCAM model simulations of the tidally locked TRAPPIST-1e exoplanet, an Earth-like aqua-planet and Earth itself. First, we relate the differences between the planets to their elementary parameters. Then, we compare the sensitivity of the Earth analogue and TRAPPIST-1e's surface temperature and precipitation to pCO$_2$. Our simulations suggest that the climatology and extremes of TRAPPIST-1e's temperature are $\sim$1.5 times more sensitive to pCO$_2$ relative to Earth. The precipitation sensitivity strongly depends on the specific region analyzed. Indeed, the precipitation near mid-latitude and equatorial sub-stellar regions of TRAPPIST-1e is more sensitive to pCO$_2$, and the precipitation sensitivity is $\sim$2 times larger in TRAPPIST-1e. A dynamical systems perspective, which provides information about how the atmosphere evolves in phase-space, provides additional insights. Notably, an increase in pCO$_2$, results in an increase in atmospheric persistence on both planets, and the persistence of TRAPPIST-1e is more sensitive to pCO$_2$ than Earth. We conclude that the climate of TRAPPIST-1e may be more sensitive to pCO$_2$, particularly on its dayside. This study documents a new pathway for understanding the effect that varying planetary parameters have on the climate variability of potentially habitable exoplanets and on Earth.Comment: Accepted at Ap