arXiv subjects

Peter Gao

Publications and source records attributed to Peter Gao.

At least 91 records · Page 5Linked to original sources

arXiv2021

Spatially Resolved Modeling of Optical Albedos for a Sample of Six Hot Jupiters

Optical secondary eclipse measurements made by \emph{Kepler} reveal a diverse set of geometric albedos for hot Jupiters with equilibrium temperatures between $1550-1700$ K. The presence or absence of high altitude condensates, such as Mg$_2$SiO$_4$, Fe, Al$_2$O$_3$, and TiO$_2$, can significantly alter optical albedos, but these clouds are expected to be confined to localized regions in the atmospheres of these tidally locked planets. Here, we present 3D general circulation models and corresponding cloud and albedo maps for six hot Jupiters with measured optical albedos in this temperature range. We find that the observed optical albedos of K2-31b and K2-107b are best matched by either cloud free models or models with relatively compact cloud layers, while Kepler-8b and Kepler-17b's optical albedos can be matched by moderately extended ($f_{sed}$ = 0.1) parametric cloud models. HATS-11b has a high optical albedo, corresponding to models with bright Mg$_2$SiO$_4$ clouds extending to very low pressures ($f_{sed}$ = 0.03). We are unable to reproduce Kepler-7b's high albedo, as our models predict that the dayside will be dominated by dark Al$_2$O$_3$ clouds at most longitudes. We compare our parametric cloud model with a two-zone microphysical cloud model (\texttt{CARMA}). We find that even after accounting for the 3D thermal structure, no single cloud model can explain the full range of observed albedos within the sample. We conclude that a better knowledge of the vertical mixing profiles, cloud radiative feedback, cloud condensate properties, and atmospheric metallicities is needed in order to explain the unexpected diversity of albedos in this temperature range.

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arXiv2021

Gemini/GMOS Transmission Spectroscopy of the Grazing Planet Candidate WD 1856+534 b

WD 1856+534 b is a Jupiter-sized, cool giant planet candidate transiting the white dwarf WD 1856+534. Here, we report an optical transmission spectrum of WD 1856+534 b obtained from ten transits using the Gemini Multi-Object Spectrograph. This system is challenging to observe due to the faintness of the host star and the short transit duration. Nevertheless, our phase-folded white light curve reached a precision of 0.12 %. WD 1856+534 b provides a unique transit configuration compared to other known exoplanets: the planet is $8\times$ larger than its star and occults over half of the stellar disc during mid-transit. Consequently, many standard modeling assumptions do not hold. We introduce the concept of a `limb darkening corrected, time-averaged transmission spectrum' and propose that this is more suitable than $(R_{\mathrm{p}, λ} / R_{\mathrm{s}})^2$ for comparisons to atmospheric models for planets with grazing transits. We also present a modified radiative transfer prescription. Though the transmission spectrum shows no prominent absorption features, it is sufficiently precise to constrain the mass of WD 1856+534 b to be > 0.84 M$_\mathrm{J}$ (to $2 \, σ$ confidence), assuming a clear atmosphere and a Jovian composition. High-altitude cloud decks can allow lower masses. WD 1856+534 b could have formed either as a result of common envelope evolution or migration under the Kozai-Lidov mechanism. Further studies of WD 1856+534 b, alongside new dedicated searches for substellar objects around white dwarfs, will shed further light on the mysteries of post-main sequence planetary systems.

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arXiv2021

A New Sedimentation Model for Greater Cloud Diversity in Giant Exoplanets and Brown Dwarfs

The observed atmospheric spectrum of exoplanets and brown dwarfs depends critically on the presence and distribution of atmospheric condensates. The Ackerman & Marley (2001) methodology for predicting the vertical distribution of condensate particles is widely used to study cloudy atmospheres and has recently been implemented in an open-source python package virga. The model relies upon input parameter $f_{\text{sed}}$, the sedimentation efficiency, which until now has been held constant. The relative simplicity of this model renders it useful for retrieval studies due to its rapidly attainable solutions. However, comparisons with more complex microphysical models such as CARMA have highlighted inconsistencies between the two approaches, namely that the cloud parameters needed for radiative transfer produced by virga are dissimilar to those produced by CARMA. To address these discrepancies, we have extended the original Ackerman and Marley methodology in virga to allow for non-constant $f_{\text{sed}}$ values, in particular those that vary with altitude. We discuss one such parameterization and compare the cloud mass mixing ratio produced by virga with constant and variable $f_{\text{sed}}$ profiles to that produced by CARMA. We find that the variable $f_{\text{sed}}$ formulation better captures the profile produced by CARMA with heterogeneous nucleation, yet performs comparatively to constant $f_{\text{sed}}$ for homogeneous nucleation. In general, virga has the capacity to handle any $f_{\text{sed}}$ with an explicit anti-derivative, permitting a plethora of alternative cloud profiles that are otherwise unattainable by constant $f_{\text{sed}}$ values. The ensuing flexibility has the potential to better agree with increasingly complex models and observed data.

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arXiv2021

Diving Beneath the Sea of Stellar Activity: Chromatic Radial Velocities of the Young AU Mic Planetary System

We present updated radial-velocity (RV) analyses of the AU Mic system. AU Mic is a young (22 Myr) early M dwarf known to host two transiting planets - $P_{b}\sim8.46$ days, $R_{b}=4.38_{-0.18}^{+0.18}\ R_{\oplus}$, $P_{c}\sim18.86$ days, $R_{c}=3.51_{-0.16}^{+0.16}\ R_{\oplus}$. With visible RVs from CARMENES-VIS, CHIRON, HARPS, HIRES, {\sc {\textsc{Minerva}}}-Australis, and TRES, as well as near-infrared (NIR) RVs from CARMENES-NIR, CSHELL, IRD, iSHELL, NIRSPEC, and SPIRou, we provide a $5σ$ upper limit to the mass of AU Mic c of $M_{c}\leq20.13\ M_{\oplus}$ and present a refined mass of AU Mic b of $M_{b}=20.12_{-1.57}^{+1.72}\ M_{\oplus}$. Used in our analyses is a new RV modeling toolkit to exploit the wavelength dependence of stellar activity present in our RVs via wavelength-dependent Gaussian processes. By obtaining near-simultaneous visible and near-infrared RVs, we also compute the temporal evolution of RV-``color'' and introduce a regressional method to aid in isolating Keplerian from stellar activity signals when modeling RVs in future works. Using a multi-wavelength Gaussian process model, we demonstrate the ability to recover injected planets at $5σ$ significance with semi-amplitudes down to $\approx$ 10\,m\,s$^{-1}$ with a known ephemeris, more than an order of magnitude below the stellar activity amplitude. However, we find that the accuracy of the recovered semi-amplitudes is $\sim$50\% for such signals with our model.

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arXiv2021

H-Alpha Variability of V1298 Tau c

The 23 Myr system V1298 Tau hosts four transiting planets and is a valuable laboratory for exploring the early stages of planet evolution soon after formation of the star. We observe the innermost planet, V1298 Tau c, during transit using LBT PEPSI to obtain high spectral resolution characterization of escaping material near the H-alpha line. We find no strong evidence for atmospheric material escaping at the orbital velocity of the planet. Instead, we find a deep stellar feature that is variable on the few percent level, similar to a previous observation of the planet and can be explained by stellar activity. We attempted to monitor the broadband optical transit with LBT MODS but do not achieve the precision needed to characterize the atmosphere or improve the ephemeris.

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arXiv2021

Haze Evolution in Temperate Exoplanet Atmospheres Through Surface Energy Measurements

Photochemical hazes are important opacity sources in temperate exoplanet atmospheres, hindering current observations from characterizing exoplanet atmospheric compositions. The haziness of an atmosphere is determined by the balance between haze production and removal. However, the material-dependent removal physics of the haze particles is currently unknown under exoplanetary conditions. Here we provide experimentally-measured surface energies for a grid of temperate exoplanet hazes to characterize haze removal in exoplanetary atmospheres. We found large variations of surface energies for hazes produced under different energy sources, atmospheric compositions, and temperatures. The surface energies of the hazes were found to be the lowest around 400 K for the cold plasma samples, leading to the lowest removal rates. We show a suggestive correlation between haze surface energy and atmospheric haziness with planetary equilibrium temperature. We hypothesize that habitable zone exoplanets could be less hazy, as they would possess high-surface-energy hazes which can be removed efficiently.

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arXiv2021

A Universal Cloud Composition on the Nightsides of Hot Jupiters

The day and nightside temperatures of hot Jupiters are diagnostic of heat transport processes in their atmospheres. Recent observations have shown that the nightsides of hot Jupiters are a nearly constant 1100 K for a wide range of equilibrium temperatures (T$_{eq}$), lower than those predicted by 3D global circulation models. Here we investigate the impact of nightside clouds on the observed nightside temperatures of hot Jupiters using an aerosol microphysics model. We find that silicates dominate the cloud composition, forming an optically thick cloud deck on the nightsides of all hot Jupiters with T$_{eq}$ $\leq$ 2100 K. The observed nightside temperature is thus controlled by the optical depth profile of the silicate cloud with respect to the temperature-pressure profile. As nightside temperatures increase with T$_{eq}$, the silicate cloud is pushed upwards, forcing observations to probe cooler altitudes. The cloud vertical extent remains fairly constant due to competing impacts of increasing vertical mixing strength with T$_{eq}$ and higher rates of sedimentation at higher altitudes. These effects, combined with the intrinsically subtle increase of the nightside temperature with T$_{eq}$ due to decreasing radiative timescale at higher instellation levels lead to low, constant nightside photospheric temperatures consistent with observations. Our results suggest a drastic reduction in the day-night temperature contrast when nightside clouds dissipate, with the nightside emission spectra transitioning from featureless to feature-rich. We also predict that cloud absorption features in the nightside emission spectra of hot Jupiters should reach $\geq$100 ppm, potentially observable with the James Webb Space Telescope.

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arXiv2021

Aerosols in Exoplanet Atmospheres

Observations of exoplanet atmospheres have shown that aerosols, like in the Solar System, are common across a variety of temperatures and planet types. The formation and distribution of these aerosols are inextricably intertwined with the composition and thermal structure of the atmosphere. At the same time, these aerosols also interfere with our probes of atmospheric composition and thermal structure, and thus a better understanding of aerosols lead to a better understanding of exoplanet atmospheres as a whole. Here we review the current state of knowledge of exoplanet aerosols as determined from observations, modeling, and laboratory experiments. Measurements of the transmission spectra, dayside emission, and phase curves of transiting exoplanets, as well as the emission spectrum and light curves of directly imaged exoplanets and brown dwarfs have shown that aerosols are distributed inhomogeneously in exoplanet atmospheres, with aerosol distributions varying significantly with planet equilibrium temperature and gravity. Parameterized and microphysical models predict that these aerosols are likely composed of oxidized minerals like silicates for the hottest exoplanets, while at lower temperatures the dominant aerosols may be composed of alkali salts and sulfides. Particles originating from photochemical processes are also likely at low temperatures, though their formation process is highly complex, as revealed by laboratory work. In the years to come, new ground- and space-based observatories will have the capability to assess the composition of exoplanet aerosols, while new modeling and laboratory efforts will improve upon our picture of aerosol formation and dynamics.

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arXiv2020

Into the UV: The Atmosphere of the Hot Jupiter HAT-P-41b Revealed

For solar-system objects, ultraviolet spectroscopy has been critical in identifying sources for stratospheric heating and measuring the abundances of a variety of hydrocarbon and sulfur-bearing species, produced via photochemical mechanisms, as well as oxygen and ozone. To date, less than 20 exoplanets have been probed in this critical wavelength range (0.2-0.4 um). Here we use data from Hubble's newly implemented WFC3 UVIS G280 grism to probe the atmosphere of the hot Jupiter HAT-P-41b in the ultraviolet through optical in combination with observations at infrared wavelengths. We analyze and interpret HAT-P-41b's 0.2-5.0 um transmission spectrum using a broad range of methodologies including multiple treatments of data systematics as well as comparisons with atmospheric forward, cloud microphysical, and multiple atmospheric retrieval models. Although some analysis and interpretation methods favor the presence of clouds or potentially a combination of Na, VO, AlO, and CrH to explain the ultraviolet through optical portions of HAT-P-41b's transmission spectrum, we find that the presence of a significant H- opacity provides the most robust explanation. We obtain a constraint for the abundance of H-, log(H-) = -8.65 +/- 0.62 in HAT-P-41b's atmosphere, which is several orders of magnitude larger than predictions from equilibrium chemistry for a 1700 - 1950 K hot Jupiter. We show that a combination of photochemical and collisional processes on hot hydrogen-dominated exoplanets can readily supply the necessary amount of H- and suggest that such processes are at work in HAT-P-41b and many other hot Jupiter atmospheres.

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arXiv2020

The Venusian Lower Atmosphere Haze as a Depot for Desiccated Microbial Life: A Proposed Life Cycle for Persistence of the Venusian Aerial Biosphere

We revisit the hypothesis that there is life in the Venusian clouds to propose a life cycle that resolves the conundrum of how life can persist aloft for hundreds of millions to billions of years. Most discussions of an aerial biosphere in the Venus atmosphere temperate layers never address whether the life-small microbial-type particles-is free floating or confined to the liquid environment inside cloud droplets. We argue that life must reside inside liquid droplets such that it will be protected from a fatal net loss of liquid to the atmosphere, an unavoidable problem for any free-floating microbial life forms. However, the droplet habitat poses a lifetime limitation: Droplets inexorably grow (over a few months) to large enough sizes that are forced by gravity to settle downward to hotter, uninhabitable layers of the Venusian atmosphere. (Droplet fragmentation-which would reduce particle size-does not occur in Venusian atmosphere conditions.) We propose for the first time that the only way life can survive indefinitely is with a life cycle that involves microbial life drying out as liquid droplets evaporate during settling, with the small desiccated 'spores' halting at, and partially populating, the Venus atmosphere stagnant lower haze layer (33-48 km altitude). We, thus, call the Venusian lower haze layer a 'depot' for desiccated microbial life. The spores eventually return to the cloud layer by upward diffusion caused by mixing induced by gravity waves, act as cloud condensation nuclei, and rehydrate for a continued life cycle. We also review the challenges for life in the extremely harsh conditions of the Venusian atmosphere, refuting the notion that the 'habitable' cloud layer has an analogy in any terrestrial environment.

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arXiv2020

A Featureless Infrared Transmission Spectrum for the Super-Puff Planet Kepler-79d

Extremely low density planets ('super-puffs') are a small but intriguing subset of the transiting planet population. With masses in the super-Earth range ($1-10$ M$_{\oplus}$) and radii akin to those of giant planets ($>4$ R$_{\oplus}$), their large envelopes may have been accreted beyond the water snow line and many appear to be susceptible to catastrophic mass loss. Both the presence of water and the importance of mass loss can be explored using transmission spectroscopy. Here, we present new HST WFC3 spectroscopy and updated Kepler transit depth measurements for the super-puff Kepler-79d. We do not detect any molecular absorption features in the $1.1-1.7$ $μ$m WFC3 bandpass and the combination of Kepler and WFC3 data are consistent with a flat line model, indicating the presence of aerosols in the atmosphere. We compare the shape of Kepler-79d's transmission spectrum to predictions from a microphysical haze model that incorporates an outward particle flux due to ongoing mass loss. We find that photochemical hazes offer an attractive explanation for the observed properties of super-puffs like Kepler-79d, as they simultaneously render the near-infrared spectrum featureless and reduce the inferred envelope mass loss rate by moving the measured radius (optical depth unity surface during transit) to lower pressures. We revisit the broader question of mass loss rates for super-puffs and find that the age estimates and mass loss rates for the majority of super-puffs can be reconciled if hazes move the photosphere from the typically assumed pressure of $\sim 10$ mbar to $\sim 10 \; μ$bar.

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arXiv2020

A planet within the debris disk around the pre-main-sequence star AU Microscopii

AU Microscopii (AU Mic) is the second closest pre main sequence star, at a distance of 9.79 parsecs and with an age of 22 million years. AU Mic possesses a relatively rare and spatially resolved3 edge-on debris disk extending from about 35 to 210 astronomical units from the star, and with clumps exhibiting non-Keplerian motion. Detection of newly formed planets around such a star is challenged by the presence of spots, plage, flares and other manifestations of magnetic activity on the star. Here we report observations of a planet transiting AU Mic. The transiting planet, AU Mic b, has an orbital period of 8.46 days, an orbital distance of 0.07 astronomical units, a radius of 0.4 Jupiter radii, and a mass of less than 0.18 Jupiter masses at 3 sigma confidence. Our observations of a planet co-existing with a debris disk offer the opportunity to test the predictions of current models of planet formation and evolution.

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arXiv2020

EarthFinder Probe Mission Concept Study: Characterizing nearby stellar exoplanet systems with Earth-mass analogs for future direct imaging

EarthFinder is a NASA Astrophysics Probe mission concept selected for study as input to the 2020 Astrophysics National Academies Decadal Survey. The EarthFinder concept is based on a dramatic shift in our understanding of how PRV measurements should be made. We propose a new paradigm which brings the high precision, high cadence domain of transit photometry as demonstrated by Kepler and TESS to the challenges of PRV measurements at the cm/s level. This new paradigm takes advantage of: 1) broad wavelength coverage from the UV to NIR which is only possible from space to minimize the effects of stellar activity; 2) extremely compact, highly stable, highly efficient spectrometers (R>150,000) which require the diffraction-limited imaging possible only from space over a broad wavelength range; 3) the revolution in laser-based wavelength standards to ensure cm/s precision over many years; 4) a high cadence observing program which minimizes sampling-induced period aliases; 5) exploiting the absolute flux stability from space for continuum normalization for unprecedented line-by-line analysis not possible from the ground; and 6) focusing on the bright stars which will be the targets of future imaging missions so that EarthFinder can use a ~1.5 m telescope.

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arXiv2020

Aerosol Composition of Hot Giant Exoplanets Dominated by Silicates and Hydrocarbon Hazes

Aerosols are common in the atmospheres of exoplanets across a wide swath of temperatures, masses, and ages. These aerosols strongly impact observations of transmitted, reflected, and emitted light from exoplanets, obfuscating our understanding of exoplanet thermal structure and composition. Knowing the dominant aerosol composition would facilitate interpretations of exoplanet observations and theoretical understanding of their atmospheres. A variety of compositions have been proposed, including metal oxides and sulphides, iron, chromium, sulphur, and hydrocarbons. However, the relative contributions of these species to exoplanet aerosol opacity is unknown. Here we show that the aerosol composition of giant exoplanets observed in transmission is dominated by silicates and hydrocarbons. By constraining an aerosol microphysics model with trends in giant exoplanet transmission spectra, we find that silicates dominate aerosol opacity above planetary equilibrium temperatures of 950 K due to low nucleation energy barriers and high elemental abundances, while hydrocarbon aerosols dominate below 950 K due to an increase in methane abundance. Our results are robust to variations in planet gravity and atmospheric metallicity within the range of most giant transiting exoplanets. We predict that spectral signatures of condensed silicates in the mid-infrared are most prominent for hot (>1600 K), low-gravity (<10 m s$^{-2}$) objects.

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arXiv2020

Keck/NIRC2 $L$'-Band Imaging of Jovian-Mass Accreting Protoplanets around PDS 70

We present $L$'-band imaging of the PDS 70 planetary system with Keck/NIRC2 using the new infrared pyramid wavefront sensor. We detected both PDS 70 b and c in our images, as well as the front rim of the circumstellar disk. After subtracting off a model of the disk, we measured the astrometry and photometry of both planets. Placing priors based on the dynamics of the system, we estimated PDS 70 b to have a semi-major axis of $20^{+3}_{-4}$~au and PDS 70 c to have a semi-major axis of $34^{+12}_{-6}$~au (95\% credible interval). We fit the spectral energy distribution (SED) of both planets. For PDS 70 b, we were able to place better constraints on the red half of its SED than previous studies and inferred the radius of the photosphere to be 2-3~$R_{Jup}$. The SED of PDS 70 c is less well constrained, with a range of total luminosities spanning an order of magnitude. With our inferred radii and luminosities, we used evolutionary models of accreting protoplanets to derive a mass of PDS 70 b between 2 and 4 $M_{\textrm{Jup}}$ and a mean mass accretion rate between $3 \times 10^{-7}$ and $8 \times 10^{-7}~M_{\textrm{Jup}}/\textrm{yr}$. For PDS 70 c, we computed a mass between 1 and 3 $M_{\textrm{Jup}}$ and mean mass accretion rate between $1 \times 10^{-7}$ and $5 \times~10^{-7} M_{\textrm{Jup}}/\textrm{yr}$. The mass accretion rates imply dust accretion timescales short enough to hide strong molecular absorption features in both planets' SEDs.

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arXiv2020

Optical to near-infrared transmission spectrum of the warm sub-Saturn HAT-P-12b

We present the transmission spectrum of HAT-P-12b through a joint analysis of data obtained from the Hubble Space Telescope Space Telescope Imaging Spectrograph (STIS) and Wide Field Camera 3 (WFC3) and Spitzer, covering the wavelength range 0.3-5.0 $μ$m. We detect a muted water vapor absorption feature at 1.4 $μ$m attenuated by clouds, as well as a Rayleigh scattering slope in the optical indicative of small particles. We interpret the transmission spectrum using both the state-of-the-art atmospheric retrieval code SCARLET and the aerosol microphysics model CARMA. These models indicate that the atmosphere of HAT-P-12b is consistent with a broad range of metallicities between several tens to a few hundred times solar, a roughly solar C/O ratio, and moderately efficient vertical mixing. Cloud models that include condensate clouds do not readily generate the sub-micron particles necessary to reproduce the observed Rayleigh scattering slope, while models that incorporate photochemical hazes composed of soot or tholins are able to match the full transmission spectrum. From a complementary analysis of secondary eclipses by Spitzer, we obtain measured depths of $0.042\%\pm0.013\%$ and $0.045\%\pm0.018\%$ at 3.6 and 4.5 $μ$m, respectively, which are consistent with a blackbody temperature of $890^{+60}_{-70}$ K and indicate efficient day-night heat recirculation. HAT-P-12b joins the growing number of well-characterized warm planets that underscore the importance of clouds and hazes in our understanding of exoplanet atmospheres.

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arXiv2020

Deflating Super-Puffs: Impact of Photochemical Hazes on the Observed Mass-Radius Relationship of Low Mass Planets

The observed mass-radius relationship of low-mass planets informs our understanding of their composition and evolution. Recent discoveries of low mass, large radii objects ("super-puffs") have challenged theories of planet formation and atmospheric loss, as their high inferred gas masses make them vulnerable to runaway accretion and hydrodynamic escape. Here we propose that high altitude photochemical hazes could enhance the observed radii of low-mass planets and explain the nature of super-puffs. We construct model atmospheres in radiative-convective equilibrium and compute rates of atmospheric escape and haze distributions, taking into account haze coagulation, sedimentation, diffusion, and advection by an outflow wind. We develop mass-radius diagrams that include atmospheric lifetimes and haze opacity, which is enhanced by the outflow, such that young (~0.1-1 Gyr), warm (T$_{eq}$ $\geq$ 500 K), low mass objects ($M_c$ < 4M$_{\rm Earth}$) should experience the most apparent radius enhancement due to hazes, reaching factors of three. This reconciles the densities and ages of the most extreme super-puffs. For Kepler-51b, the inclusion of hazes reduces its inferred gas mass fraction to <10%, similar to that of planets on the large radius side of the sub-Neptune radius gap. This suggests that Kepler-51b may be evolving towards that population, and that some warm sub-Neptunes may have evolved from super-puffs. Hazes also render transmission spectra of super-puffs and sub-Neptunes featureless, consistent with recent measurements. Our hypothesis can be tested by future observations of super-puffs' transmission spectra at mid-infrared wavelengths, where we predict that the planet radius will be half of that observed in the near-infrared.

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arXiv2020

The Intrinsic Temperature and Radiative-Convective Boundary Depth in the Atmospheres of Hot Jupiters

In giant planet atmosphere modelling, the intrinsic temperature $T_\mathrm{int}$ and radiative-convective boundary (RCB) are important lower boundary conditions. Often in one-dimensional radiative-convective models and in three-dimensional general circulation models it is assumed that $T_\mathrm{int}$ is similar to that of Jupiter itself, around 100 K, which yields a RCB around 1 kbar for hot Jupiters. In this work, we show that the inflated radii, and hence high specific entropy interiors, of hot Jupiters suggest much higher $T_\mathrm{int}$ values. Assuming the effect is primarily due to current heating (rather than delayed cooling), we derive an equilibrium relation between $T_\mathrm{eq}$ and $T_\mathrm{int}$, showing that the latter can take values as high as 700 K. In response, the RCB moves upward in the atmosphere. Using one-dimensional radiative-convective atmosphere models, we find RCBs of only a few bars, rather than the kilobar typically supposed. This much shallower RCB has important implications for the atmospheric structure, vertical and horizontal circulation, interpretations of phase curves, and the effect of deep cold traps on cloud formation.

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