arXiv subjects

Vivien Parmentier

Publications and source records attributed to Vivien Parmentier.

At least 109 records · Page 6Linked to original sources

arXiv2022

A New Analysis of 8 Spitzer Phase Curves and Hot Jupiter Population Trends: Qatar-1b, Qatar-2b, WASP-52b, WASP-34b, and WASP-140b

With over 30 phase curves observed during the warm Spitzer mission, the complete data set provides a wealth of information relating to trends and three-dimensional properties of hot Jupiter atmospheres. In this work we present a comparative study of seven new Spitzer phase curves for four planets with equilibrium temperatures of T$_{eq}\sim$ 1300K: Qatar-2b, WASP-52b, WASP-34b, and WASP-140b, as well as the reanalysis of the 4.5 $\micron$ Qatar-1b phase curve due to the similar equilibrium temperature. In total, five 4.5 $\micron$ phase curves and three 3.6 $\micron$ phase curves are analyzed here with a uniform approach. Using these new results, in combination with literature values for the entire population of published Spitzer phase curves of hot Jupiters, we present evidence for a linear trend of increasing hot spot offset with increasing orbital period, as well as observational evidence for two classes of planets in apparent redistribution vs. equilibrium temperature parameter space, and tentative evidence for a dependence of hot spot offset on planetary surface gravity in our $\sim$ 1300 K sample. We do not find trends in apparent heat redistribution with orbital period or gravity. Non-uniformity in literature Spitzer data analysis techniques precludes a definitive determination of the sources or lack of trends.

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arXiv2022

3D radiative-transfer for exoplanet atmospheres. gCMCRT: a GPU accelerated MCRT code

Radiative-transfer (RT) is a key component for investigating atmospheres of planetary bodies. With the 3D nature of exoplanet atmospheres being important in giving rise to their observable properties, accurate and fast 3D methods are required to be developed to meet future multi-dimensional and temporal data sets. We develop an open source GPU RT code, gCMCRT, a Monte Carlo RT forward model for general use in planetary atmosphere RT problems. We aim to automate the post-processing pipeline, starting from direct global circulation model (GCM) output to synthetic spectra. We develop albedo, emission and transmission spectra modes for 3D and 1D input structures. We include capability to use correlated-k and high-resolution opacity tables, the latter of which can be Doppler shifted inside the model. We post-process results from several GCM groups including ExoRad, SPARC/MITgcm THOR, UK Met Office UM, Exo-FMS and the Rauscher model. Users can therefore take advantage of desktop and HPC GPU computing solutions. gCMCRT is well suited for post-processing large GCM model grids produced by members of the community and for high-resolution 3D investigations.

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arXiv2022

Confirmation of Water Absorption in the Thermal Emission Spectrum of the Hot Jupiter WASP-77Ab with HST/WFC3

Secondary eclipse observations of hot Jupiters can reveal both their compositions and thermal structures. Previous observations have shown a diversity of hot Jupiter eclipse spectra, including absorption features, emission features, and featureless blackbody-like spectra. We present a secondary eclipse spectrum of the hot Jupiter WASP-77Ab observed between $1-5$ $μ$m with the Hubble Space Telescope (HST) and the Spitzer Space Telescope. The HST observations show signs of water absorption indicative of a non-inverted thermal structure. We fit the data with both a one-dimensional free retrieval and a grid of one-dimensional self-consistent forward models to confirm this non-inverted structure. The free retrieval places a $3σ$ lower limit on the atmospheric water abundance of $\log(n_\mathrm{H_2O})>-4.78$ and can not constrain the CO abundance. The grid fit produces a slightly super-stellar metallicity and constrains the carbon-to-oxygen ratio to less than or equal to the solar value. We also compare our data to recent high-resolution observations of WASP-77Ab taken with the Gemini-South/IGRINS spectrograph and find that our observations are consistent with the best-fit model to the high-resolution data. However, the metallicity derived from the IGRINS data is significantly lower than that derived from our self-consistent model fit. We find that this difference may be due to disequilibrium chemistry, and the varying results between the models applied here demonstrate the difficulty of constraining disequilibrium chemistry with low-resolution, low wavelength coverage data alone. Future work to combine observations from IGRINS, HST, and JWST will improve our estimate of the atmospheric composition of WASP-77Ab.

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arXiv2021

All along the line of sight: a closer look at opening angles and absorption regions in the atmospheres of transiting exoplanets

Transmission spectra contain a wealth of information about the atmospheres of transiting exoplanets. However, large thermal and chemical gradients along the line of sight can lead to biased inferences in atmospheric retrievals. In order to determine how far from the limb plane the atmosphere still impacts the transmission spectrum, we derive a new formula to estimate the opening angle of a planet. This is the angle subtended by the atmospheric region that contributes to the observation along the line of sight, as seen from the planet centre. We benchmark our formula with a 3D Monte-Carlo radiative transfer code and we define an opening angle suitable for the interpretation of JWST observations, assuming a 10-ppm noise floor. We find that the opening angle is only a few degrees for planets cooler than ca. 500 Kelvins, while it can be as large as 25 degrees for (ultra-)hot Jupiters and 50 degrees for hot Neptunes. Compared to previous works, our more robust approach leads to smaller estimates for the opening angle across a wide range scale heights and planetary radii. Finally, we show that ultra-hot Jupiters have an opening angle that is smaller than the angle over which the planet rotates during the transit. This allows for time-resolved transmission spectroscopy observations that probe independent parts of the planetary limb during the first and second half of the transit.

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arXiv2021

A solar C/O and sub-solar metallicity in a hot Jupiter atmosphere

Measurements of the atmospheric carbon (C) and oxygen (O) relative to hydrogen (H) in hot Jupiters (relative to their host stars) provide insight into their formation location and subsequent orbital migration. Hot Jupiters that form beyond the major volatile (H2O/CO/CO2) ice lines and subsequently migrate post disk-dissipation are predicted have atmospheric carbon-to-oxygen ratios (C/O) near 1 and subsolar metallicities, whereas planets that migrate through the disk before dissipation are predicted to be heavily polluted by infalling O-rich icy planetesimals, resulting in C/O < 0.5 and super-solar metallicities. Previous observations of hot Jupiters have been able to provide bounded constraints on either H2O or CO, but not both for the same planet, leaving uncertain the true elemental C and O inventory and subsequent C/O and metallicity determinations. Here we report spectroscopic observations of a typical transiting hot Jupiter, WASP-77Ab. From these, we determine the atmospheric gas volume mixing ratio constraints on both H2O and CO (9.5$\times 10^{-5}$ - 1.5$\times 10^{-4}$ and 1.2$\times 10^{-4}$ - 2.6$\times 10^{-4}$, respectively). From these bounded constraints, we are able to derive the atmospheric C/H (0.35$^{+0.17}_{-0.10}$ $\times$ Solar) and O/H (0.32 $^{+0.12}_{-0.08}$ $\times$ Solar) abundances and the corresponding atmospheric carbon-to-oxygen ratio (C/O=0.59$\pm$0.08; the solar value is 0.55). The sub-solar (C+O)/H (0.33$^{+0.13}_{-0.09}$ $\times$ Solar) is suggestive of a metal-depleted atmosphere relative to what is expected for Jovian-like planets while the near solar value of C/O rules out the disk-free migration/C-rich atmosphere scenario.

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arXiv2021

A unique hot Jupiter spectral sequence with evidence for compositional diversity

The emergent spectra of close-in, giant exoplanets ("hot Jupiters") are expected to be distinct from those of self-luminous objects with similar effective temperatures because hot Jupiters are primarily heated from above by their host stars rather than internally from the release of energy from their formation. Theoretical models predict a continuum of dayside spectra for hot Jupiters as a function of irradiation level, with the coolest planets having absorption features in their spectra, intermediate-temperature planets having emission features due to thermal inversions, and the hottest planets having blackbody-like spectra due to molecular dissociation and continuum opacity from the H- ion. Absorption and emission features have been detected in the spectra of a number of individual hot Jupiters, and population-level trends have been observed in photometric measurements. However, there has been no unified, population-level study of the thermal emission spectra of hot Jupiters such as has been done for cooler brown dwarfs and transmission spectra of hot Jupiters. Here we show that hot Jupiter secondary eclipse spectra centered around a water absorption band at 1.4 microns follow a common trend in water feature strength with temperature. The observed trend is broadly consistent with model predictions for how the thermal structures of solar-composition planets vary with irradiation level. Nevertheless, the ensemble of planets exhibits some degree of scatter around the mean trend for solar composition planets. The spread can be accounted for if the planets have modest variations in metallicity and/or elemental abundance ratios, which is expected from planet formation models. (abridged abstract)

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arXiv2021

Mapping the pressure-dependent day-night temperature contrast of a strongly irradiated atmosphere with HST spectroscopic phase curve

Many brown dwarfs are on ultra-short period and tidally-locked orbits around white dwarf hosts. Because of these small orbital separations, the brown dwarfs are irradiated at levels similar to hot Jupiters. Yet, they are easier to observe than hot Jupiters because white dwarfs are fainter than main-sequence stars at near-infrared wavelengths. Irradiated brown dwarfs are, therefore, ideal hot Jupiter analogs for studying the atmospheric response under strong irradiation and fast rotation. We present the 1.1--1.67$\rm μm$ spectroscopic phase curve of the irradiated brown dwarf (SDSS1411-B) in the SDSS J141126.20+200911.1 brown-dwarf white-dwarf binary with the near-infrared G141 grism of Hubble Space Telescope Wide Field Camera 3. SDSS1411-B is a $50~\rm M_{\rm Jup}$ brown dwarf with an irradiation temperature of 1300K and has an orbital period of 2.02864 hours. Our best-fit model suggests a phase-curve amplitude of 1.4$\%$ and places an upper limit of 11 degrees for the phase offset from the secondary eclipse. After fitting the white-dwarf spectrum, we extract the phase-resolved brown-dwarf emission spectra. We report a highly wavelength-dependent day-night spectral variation, with the water-band flux variation of about $360\pm70\% $ and a comparatively small J-band flux variation of $37\pm2\%$. By combining the atmospheric modeling results and the day-night brightness-temperature variations, we derive a pressure-dependent temperature contrast. We discuss the difference in the spectral features of SDSS1411-B and hot Jupiter WASP-43b, and the lower-than-predicted day-night temperature contrast of J4111-BD. Our study provides the high-precision observational constraints on the atmospheric structures of an irradiated brown dwarf at different orbital phases.

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arXiv2021

HST/WFC3 Complete Phase-resolved Spectroscopy of White Dwarf-Brown Dwarf Binaries WD 0137 and EPIC 2122

Brown dwarfs in close-in orbits around white dwarfs offer an excellent opportunity to investigate properties of fast-rotating, tidally-locked, and highly-irradiated atmospheres. We present Hubble Space Telescope Wide Field Camera 3 G141 phase-resolved observations of two brown dwarf-white dwarf binaries: WD 0137-349 and EPIC 212235321. Their 1.1 to 1.7 $μ$m phase curves demonstrate rotational modulations with semi-amplitudes of $5.27\pm0.02$% and $29.1\pm0.1$%; both can be well fit by multi-order Fourier series models. The high-order Fourier components have the same phase as the first order and are likely caused by hot spots located at the substellar points, suggesting inefficient day/night heat transfer. Both brown dwarfs' phase-resolved spectra can be accurately represented by linear combinations of their day- and night-side spectra. Fitting the irradiated brown dwarf model grids to the day-side spectra require a filling factor of ~50%, further supporting a hot spot dominating the emission of the day-sides. The night-side spectrum of WD 0137-349B is reasonably well fit by non-irradiated substellar models and the one of EPIC 212235321B can be approximated by a Planck function. We find strong spectral variations in the brown dwarfs' day/night flux and brightness temperature contrasts, which highlights the limitations of band-integrated measurements in probing heat transfer in irradiated objects. On the color-magnitude diagram, WD 0137-349B evolves along a cloudless model track connecting the early-L and mid-T spectral types, demonstrating that clouds and disequilibrium chemistry have a negligible effect on this object. A full interpretation of these high-quality phase-resolved spectra calls for new models that couple atmospheric circulation and radiative transfer under high-irradiation conditions.

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arXiv2021

Towards multi-dimensional analysis of transmission spectroscopy. Part II: Day-night induced biases in retrievals from hot to ultra-hot Jupiters

Hot Jupiters are very good targets for transmission spectroscopy analysis. Their atmospheres have a large scale height implying a high signal to noise ratio. As these planets orbit close to their stars, they often present strong thermal and chemical hetereogeneities between the day and the night side of their atmosphere. For the hottest ones, the thermal dissociation of several species occurs in their atmospheres which leads to a stronger chemical dichotomy between the two hemispheres. It has already been shown that the current retrieval algorithms, which are using 1D forward models, find biased molecular abundances in ultra hot Jupiters. Here, we quantify the effective temperature domain over which these biases are present. We use a set of 12 simulations of typical Hot Jupiters from Teq = 1000 K to Teq = 2100 K performed with the Substellar and Planetary Atmospheric Radiation and Circulation global climate model and generate transmission spectra that fully account for the 3D structure of the atmosphere with Pytmosph3R. These spectra are then analyzed using the 1D TauREx retrieval code. We find that for JWST-like data, accounting for non-isothermal vertical temperature profiles is required over the whole temperature range. We further find that 1D retrieval codes start to estimate wrong parameter values for planets with equilibrium temperatures greater than 1400 K if there are absorbers in the visible able to create a hot stratosphere. The high temperatures at low pressures indeed entail a thermal dissociation of species which creates a strong chemical day-night dichotomy. As a by-product, we demonstrate that when using synthetic observations to assess the detectability of a given feature or process using a Bayesian framework, it is valid to use non-randomized input data, as long as the anticipated observational uncertainties are correctly taken into account.

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arXiv2021

The air over there: exploring exoplanet atmospheres

Atmospheric compositions for rocky exoplanets will depend strongly on the bulk planetary composition and the orbital position of the planet. Non-traditional gases may be present in the atmospheres of exceptionally hot planets. Atmospheres of more clement planets will depend on the abundances of volatiles acquired during planet formation and atmospheric removal processes, including escape, condensation, and reaction with the surface. While the observations of exoplanet atmospheres to date has focused on giant planets, a series of new space and ground-based observatories over the coming decade will revolutionize the precision and spectral resolution with which we are able to probe exoplanet atmospheres. This article consolidates lessons learned from the study of giant planet atmospheres, and points to the observations and challenges on the horizon for terrestrial planets.

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arXiv2021

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.

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arXiv2021

How Does Thermal Scattering Shape the Infrared Spectra of Cloudy Exoplanets? A Theoretical Framework and Consequences for Atmospheric Retrievals in the JWST era

Observational studies of exoplanets are suggestive of a ubiquitous presence of clouds. The current modelling techniques used in emission to account for the clouds tend to require prior knowledge of the cloud condensing species and often do not consider the scattering effects of the cloud. We explore the effects that thermal scattering has on the emission spectra by modelling a suite of hot Jupiter atmospheres with varying cloud single-scattering albedos (SSAs) and temperature profiles. We examine cases ranging from simple isothermal conditions to more complex structures and physically driven cloud modelling. We show that scattering from nightside clouds would lead to brightness temperatures that are cooler than the real atmospheric temperature if scattering is unaccounted for. We show that scattering can produce spectral signatures in the emission spectrum even for isothermal atmospheres. We identify the retrieval degeneracies and biases that arise in the context of simulated JWST spectra when the scattering from the clouds dominates the spectral shape. Finally, we propose a novel method of fitting the SSA spectrum of the cloud in emission retrievals, using a technique that does not require any prior knowledge of the cloud chemical or physical properties.

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arXiv2021

Simulating gas giant exoplanet atmospheres with Exo-FMS: Comparing semi-grey, picket fence and correlated-k radiative-transfer schemes

Radiative-transfer (RT) is a fundamental part of modelling exoplanet atmospheres with general circulation models (GCMs). An accurate RT scheme is required for estimates of the atmospheric energy transport and for gaining physical insight from model spectra. We implement three RT schemes for Exo-FMS: semi-grey, non-grey `picket fence', and real gas with correlated-k. We benchmark the Exo-FMS GCM using these RT schemes to hot Jupiter simulation results from the literature. We perform a HD 209458b-like simulation with the three schemes and compare their results. These simulations are then post-processed to compare their observable differences. The semi-grey scheme results show qualitative agreement with previous studies in line with variations seen between GCM models. The real gas model reproduces well the temperature and dynamical structures from other studies. After post-processing our non-grey picket fence scheme compares very favourably with the real gas model, producing similar transmission spectra, emission spectra and phase curve behaviours. Exo-FMS is able to reliably reproduce the essential features of contemporary GCM models in the hot gas giant regime. Our results suggest the picket fence approach offers a simple way to improve upon RT realism beyond semi-grey schemes.

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arXiv2021

Decomposing the Iron Cross-Correlation Signal of the Ultra-Hot Jupiter WASP-76b in Transmission using 3D Monte-Carlo Radiative Transfer

Ultra-hot Jupiters are tidally locked gas giants with dayside temperatures high enough to dissociate hydrogen and other molecules. Their atmospheres are vastly non-uniform in terms of chemistry, temperature and dynamics, and this makes their high-resolution transmission spectra and cross-correlation signal difficult to interpret. In this work, we use the SPARC/MITgcm global circulation model to simulate the atmosphere of the ultra-hot Jupiter WASP-76b under different conditions, such as atmospheric drag and the absence of TiO and VO. We then employ a 3D Monte-Carlo radiative transfer code, HIRES-MCRT, to self-consistently model high-resolution transmission spectra with iron (Fe I) lines at different phases during the transit. To untangle the structure of the resulting cross-correlation map, we decompose the limb of the planet into four sectors, and we analyse each of their contributions separately. Our experiments demonstrate that the cross-correlation signal of an ultra-hot Jupiter is primarily driven by its temperature structure, rotation and dynamics, while being less sensitive to the precise distribution of iron across the atmosphere. We also show that the previously published iron signal of WASP-76b can be reproduced by a model featuring iron condensation on the leading limb. Alternatively, the signal may be explained by a substantial temperature asymmetry between the trailing and leading limb, where iron condensation is not strictly required to match the data. Finally, we compute the $K_{p}-V_{sys}$ maps of the simulated WASP-76b atmospheres, and we show that rotation and dynamics can lead to multiple peaks that are displaced from zero in the planetary rest frame.

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arXiv2021

The Dark World: A Tale of WASP-43b in Reflected Light with HST WFC3/UVIS

Optical, reflected light eclipse observations provide a direct probe of the exoplanet scattering properties, such as from aerosols. We present here the photometric, reflected light observations of WASP-43b using the HST WFC3/UVIS instrument with the F350LP filter (346-822nm) encompassing the entire optical band. This is the first reflected light, photometric eclipse using UVIS in scanning mode; as such we further detail our scanning extraction and analysis pipeline Arctor. Our HST WFC3/UVIS eclipse light curve for WASP-43 b derived a 3-σ upper limit of 67 ppm on the eclipse depth, which implies that WASP-43b has a very dark dayside atmosphere. With our atmospheric modeling campaign, we compared our reflected light constraints with predictions from global circulation and cloud models, benchmarked with HST and Spitzer observations of WASP-43b. We infer that we do not detect clouds on the dayside within the pressure levels probed by HST WFC3/UVIS with the F350LP filter (P > 1 bar). This is consistent with the GCM predictions based on previous WASP-43b observations. Dayside emission spectroscopy results from WASP-43b with HST and Spitzer observations are likely to not be significantly affected by contributions from cloud particles.

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arXiv2021

A Comprehensive Reanalysis of $\textit{Spitzer}$'s 4.5 $μ$m Phase Curves, and the Phase Variations of the Ultra-hot Jupiters MASCARA-1b and KELT-16b

We have developed an open-source pipeline for the analysis of \textit{Spitzer}/IRAC channel 1 and 2 time-series photometry, incorporating some of the most popular decorrelation methods. We applied this pipeline to new phase curve observations of ultra-hot Jupiters MASCARA-1b and KELT-16b, and we performed the first comprehensive reanalysis of 15 phase curves. We find that MASCARA-1b and KELT-16b have phase offsets of $6^{+11}_{-11}~^{\circ}$W and $38^{+16}_{-15}~^{\circ}$W, dayside temperatures of $2952^{+100}_{-97}$ K and $3070^{+160}_{-150}$ K, and nightside temperatures of $1300^{+340}_{-340}$ K and $1900^{+430}_{-440}$ K, respectively. We confirm a strong correlation between dayside and irradiation temperatures with a shallower dependency for nightside temperature. We also find evidence that the normalized phase curve amplitude (peak-to-trough divided by eclipse depth) is correlated with stellar effective temperature. In addition, while our different models often retrieve similar parameters, significant differences occasionally arise between them, as well as between our preferred model and the literature values. Nevertheless, our preferred models are consistent with published phase offsets to within $-8\pm21$ degrees ($-1.6\pm3.2$ sigma), and normalized phase curve amplitudes are on average reproduced to within $-0.01\pm0.24$ ($-0.1\pm1.6$ sigma). Finally, we find that BLISS performs best in most cases, but not all; we therefore recommend future analyses consider numerous detector models to ensure an optimal fit and to assess model dependencies.

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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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arXiv2021

TESS observations of the WASP-121 b phase curve

We study the red-optical photometry of the ultra-hot Jupiter WASP-121 b as observed by the Transiting Exoplanet Survey Satellite (TESS) and model its atmosphere through a radiative transfer simulation. Given its short orbital period of $\sim1.275$ days, inflated state and bright host star, WASP-121 b is exceptionally favorable for detailed atmospheric characterization. Towards this purpose, we use \texttt{allesfitter} to characterize its full red-optical phase curve, including the planetary phase modulation and the secondary eclipse. We measure the day and nightside brightness temperatures in the TESS passband as $3012\substack{+40 \\ -42}$ K and $2022\substack{+254 \\ -602}$ K, respectively, and do not find a statistically significant phase shift between the brightest and substellar points. This is consistent with an inefficient heat recirculation on the planet. We then perform an atmospheric retrieval analysis to infer the dayside atmospheric properties of WASP-121 b such as its bulk composition, albedo and heat recirculation. We confirm the temperature inversion in the atmosphere and suggest H$^-$, TiO and VO as potential causes of the inversion, absorbing heat at optical wavelengths at low pressures. Future HST and JWST observations of WASP-121 b will benefit from its first full phase curve measured by TESS.

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