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Daniel Thorngren

Publications and source records attributed to Daniel Thorngren.

At least 37 records · Page 2Linked to original sources

High atmospheric metal enrichment for a Saturn-mass planet

Atmospheric metal enrichment (i.e., elements heavier than helium, also called "metallicity") is a key diagnostic of the formation of giant planets. The giant planets of the solar system exhibit an inverse relationship between mass and both their bulk metallicities and atmospheric metallicities. Extrasolar giant planets also display an inverse relationship between mass and bulk metallicity. However, there is significant scatter in the relationship and it is not known how atmospheric metallicity correlates with either planet mass or bulk metallicity. Here we show that the Saturn-mass exoplanet HD 149026b has an atmospheric metallicity 59 - 276 times solar (at 1 $σ$), which is greater than Saturn's atmospheric metallicity of ~7.5 times solar at >4 $σ$ confidence. This result is based on modeling CO$_2$ and H$_2$O absorption features in the thermal emission spectrum of the planet measured by JWST. HD 149026b is the most metal-rich giant planet known, with an estimated bulk heavy element abundance of 66 $\pm$ 2% by mass. We find that the atmospheric metallicities of both HD 149026b and the solar system giant planets are more correlated with bulk metallicity than planet mass.

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An unlikely survivor: a low-density hot Neptune orbiting a red giant star

Hot Neptunes, gaseous planets smaller than Saturn ($\sim$ 3-8 R$_\oplus$) with orbital periods less than 10 days, are rare. Models predict this is due to high-energy stellar irradiation stripping planetary atmospheres over time, often leaving behind only rocky planetary cores. We present the discovery of a 6.2 R$_\oplus$(0.55 R$_\mathrm{J}$), 19.2 M$_\oplus$(0.060 M$_\mathrm{J}$) planet transiting a red giant star every 4.21285 days. The old age and high equilibrium temperature yet remarkably low density of this planet suggests that its gaseous envelope should have been stripped by high-energy stellar irradiation billions of years ago. The present day planet mass and radius suggest atmospheric stripping was slower than predicted. Unexpectedly low stellar activity and/or late-stage planet inflation could be responsible for the observed properties of this system.

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Evidence for the volatile-rich composition of a 1.5-$R_\oplus$ planet

The population of planets smaller than approximately $1.7~R_\oplus$ is widely interpreted as consisting of rocky worlds, generally referred to as super-Earths. This picture is largely corroborated by radial-velocity (RV) mass measurements for close-in super-Earths but lacks constraints at lower insolations. Here we present the results of a detailed study of the Kepler-138 system using 13 Hubble and Spitzer transit observations of the warm-temperate $1.51\pm0.04~R_\oplus$ planet Kepler-138 d ($T_{\mathrm{eq, A_B=0.3}}$~350 K) combined with new Keck/HIRES RV measurements of its host star. We find evidence for a volatile-rich "water world" nature of Kepler-138 d, with a large fraction of its mass contained in a thick volatile layer. This finding is independently supported by transit timing variations, RV observations ($M_d=2.1_{-0.7}^{+0.6}~M_\oplus$), as well as the flat optical/IR transmission spectrum. Quantitatively, we infer a composition of $11_{-4}^{+3}$\% volatiles by mass or ~51% by volume, with a 2000 km deep water mantle and atmosphere on top of a core with an Earth-like silicates/iron ratio. Any hypothetical hydrogen layer consistent with the observations ($<0.003~M_\oplus$) would have swiftly been lost on a ~10 Myr timescale. The bulk composition of Kepler-138 d therefore resembles those of the icy moons rather than the terrestrial planets in the solar system. We conclude that not all super-Earth-sized planets are rocky worlds, but that volatile-rich water worlds exist in an overlapping size regime, especially at lower insolations. Finally, our photodynamical analysis also reveals that Kepler-138 c ($R_c=1.51 \pm 0.04~R_\oplus$, $M_c=2.3_{-0.5}^{+0.6}~M_\oplus$) is a slightly warmer twin of Kepler-138 d, i.e., another water world in the same system, and we infer the presence of Kepler-138 e, a likely non-transiting planet at the inner edge of the habitable zone.

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A strong H- opacity signal in the near-infrared emission spectrum of the ultra-hot Jupiter KELT-9b

We present the analysis of a spectroscopic secondary eclipse of the hottest transiting exoplanet detected to date, KELT-9b, obtained with the Wide Field Camera 3 aboard the Hubble Space Telescope. We complement these data with literature information on stellar pulsations and Spitzer/Infrared Array Camera and Transiting Exoplanet Survey Satellite eclipse depths of this target to obtain a broadband thermal emission spectrum. Our extracted spectrum exhibits a clear turnoff at 1.4$μ$m. This points to H$^{-}$ bound-free opacities shaping the spectrum. To interpret the spectrum, we perform grid retrievals of self-consistent 1D equilibrium chemistry forward models, varying the composition and energy budget. The model with solar metallicity and C/O ratio provides a poor fit because the H$^{-}$ signal is stronger than expected, requiring an excess of electrons. This pushes our retrievals toward high atmospheric metallicities ($[M/H]=1.98^{+0.19}_{-0.21}$) and a C/O ratio that is subsolar by 2.4$σ$. We question the viability of forming such a high-metallicity planet, and therefore provide other scenarios to increase the electron density in this atmosphere. We also look at an alternative model in which we quench TiO and VO. This fit results in an atmosphere with a slightly subsolar metallicity and subsolar C/O ratio ($[M/H]=-0.22^{+0.17}_{-0.13}$, log(C/O)$=-0.34^{+0.19}_{-0.34}$). However, the required TiO abundances are disputed by recent high-resolution measurements of the same planet.

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Constraining the Densities of the Three Kepler-289 Planets with Transit Timing Variations

Kepler-289 is a three-planet system containing two sub-Neptunes and one cool giant planet orbiting a young, Sun-like star. All three planets exhibit transit timing variations (TTVs), with both adjacent planet pairs having orbital periods close to the 2:1 orbital resonance. We observe two transits of Kepler-289c with the Wide-field InfraRed Camera (WIRC) on the 200" Hale Telescope at Palomar Observatory, using diffuser-assisted photometry to achieve space-like photometric precision from the ground. These new transit observations extend the original four-year Kepler TTV baseline by an additional 7.5 years. We re-reduce the archival Kepler data with an improved stellar activity correction and carry out a joint fit with the Palomar data to constrain the transit shapes and derive updated transit times. We then model the TTVs to determine the masses of the three planets and constrain their densities and bulk compositions. Our new analysis improves on previous mass and density constraints by a factor of two or more for all three planets, with the innermost planet showing the largest improvement. Our updated atmospheric mass fractions for the inner two planets indicate that they likely have hydrogen-rich envelopes, consistent with their location on the upper side of the radius valley. We also constrain the heavy element composition of the outer saturn-mass planet, Kepler-289c, for the first time, finding that it contains 30.5 $\pm$ 6.9 $M_{\oplus}$ of metals. We use dust evolution models to show that Kepler-289c must have formed beyond 1~au, and likely beyond 3~au, and then migrated inward.

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Cleaning our Hazy Lens: Exploring Trends in Transmission Spectra of Warm Exoplanets

Relatively little is understood about the atmospheric composition of temperate to warm exoplanets (equilibrium temperature $T_{\rm eq}<$ 1000 K), as many of them are found to have uncharacteristically flat transmission spectra. Their flattened spectra are likely due to atmospheric opacity sources such as planet-wide photochemical hazes and condensation clouds. We compile the transmission spectra of 25 warm exoplanets previously observed by the Hubble Space Telescope and quantify the haziness of each exoplanet using a normalized amplitude of the water absorption feature ($A_{\rm H}$). By examining the relationships between $A_{\rm H}$ and various planetary and stellar forcing parameters, we endeavor to find correlations of haziness associated with planetary properties. We adopt new statistical correlation tests that are more suitable for the small, non-normally distributed warm exoplanet sample. Our analysis shows that none of the parameters hold statistically significant correlation with $A_{\rm H}$ ($p \le 0.01$) with the addition of new exoplanet data, including the previously identified linear trends between $A_{\rm H}$ and $T_{\rm{eq}}$ or hydrogen-helium envelope mass fraction (f$_{\rm{HHe}}$). This suggests that haziness in warm exoplanets is not simply controlled by any single planetary/stellar parameter. Among all the parameters we investigated, planet gravity ($g_{\rm p}$), atmospheric scale height ($H$), planet density ($ρ_{\rm p}$), orbital eccentricity ($e$), and age of the star ($t_{\rm age}$) hold tentative correlations with $A_{\rm H}$. Specifically, lower $H$, higher $g_{\rm p}$, $ρ_{\rm p}$, $e$, or $t_{\rm age}$ may lead to clearer atmospheres. We still need more observations and laboratory experiments to fully understand the complex physics and chemistry involved in creating hazy warm exoplanets.

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Kepler-167e as a Probe of the Formation Histories of Cold Giants with Inner Super-Earths

The observed correlation between outer giant planets and inner super-Earths is emerging as an important constraint on planet formation theories. In this study we focus on Kepler-167, which is currently the only system known to contain both inner transiting super-Earths and a confirmed outer transiting gas giant companion beyond 1 au. Using long term radial velocity monitoring, we measure the mass of the gas giant Kepler-167e ($P=1071$ days) to be $1.01^{+0.16}_{-0.15}$ M$_{\rm J}$, thus confirming it as a Jupiter analog. We re-fit the $Kepler$ photometry to obtain updated radii for all four planets. Using a planetary structure model, we estimate that Kepler-167e contains $66\pm19$ M$_{\oplus}$ of solids and is significantly enriched in metals relative to its solar-metallicity host star. We use these new constraints to explore the broader question of how systems like Kepler-167 form in the pebble accretion framework for giant planet core formation. We utilize simple disk evolution models to demonstrate that more massive and metal-rich disks, which are the most favorable sites for giant planet formation, can also deliver enough solids to the inner disk to form systems of super-Earths. We use these same models to constrain the nature of Kepler-167's protoplanetary disk, and find that it likely contained $\gtrsim 300$ M$_{\oplus}$ of dust and was $\gtrsim 40$ au in size. These values overlap with the upper end of the observed dust mass and size distributions of Class 0 and I disks, and are also consistent with the observed occurrence rate of Jupiter analogs around sun-like stars.

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Thermal Phase Curves of XO-3b: an Eccentric Hot Jupiter at the Deuterium Burning Limit

We report \textit{Spitzer} full-orbit phase observations of the eccentric hot Jupiter XO-3b at 3.6 and 4.5 $μ$m. Our new eclipse depth measurements of $1770 \pm 180$ ppm at 3.6 $μ$m and $1610 \pm 70$ ppm at 4.5 $μ$m show no evidence of the previously reported dayside temperature inversion. We also empirically derive the mass and radius of XO-3b and its host star using Gaia DR3's parallax measurement and find a planetary mass $M_p=11.79 \pm 0.98 ~M_{\rm{Jup}}$ and radius $R_p=1.295 \pm 0.066 ~R_{\rm{Jup}}$. We compare our \textit{Spitzer} observations with multiple atmospheric models to constrain the radiative and advective properties of XO-3b. While the decorrelated 4.5 $μ$m observations are pristine, the 3.6 $μ$m phase curve remains polluted with detector systematics due to larger amplitude intrapixel sensitivity variations in this channel. We focus our analysis on the more reliable 4.5 $μ$m phase curve and fit an energy balance model with solid body rotation to estimate the zonal wind speed and the pressure of the bottom of the mixed layer. Our energy balance model fit suggests an eastward equatorial wind speed of $3.13 ^{+0.26} _{-0.83}$ km/s, an atmospheric mixed layer down to $2.40 ^{+0.92} _{-0.16}$ bar, and Bond albedo of $0.106 ^{+0.008} _{-0.106}$. We assume that the wind speed and mixed layer depth are constant throughout the orbit. We compare our observations with a 1D planet-averaged model predictions at apoapse and periapse and 3D general circulation model (GCM) predictions for XO-3b. We also investigate the inflated radius of XO-3b and find that it would require an unusually large amount of internal heating to explain the observed planetary radius.

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A transiting warm giant planet around the young active star TOI-201

We present the confirmation of the eccentric warm giant planet TOI-201 b, first identified as a candidate in \textit{TESS} photometry (Sectors 1-8, 10-13, and 27-28) and confirmed using ground-based photometry from NGTS and radial velocities from FEROS, HARPS, CORALIE, and \textsc{Minerva}-Australis. TOI-201 b orbits a young ($\mathrm{0.87^{+0.46}_{-0.49} \, Gyr}$) and bright(V=9.07 mag) F-type star with a $\mathrm{52.9781 \, d}$ period. The planet has a mass of $\mathrm{0.42^{+0.05}_{-0.03}\, M_J}$, a radius of $\mathrm{1.008^{+0.012}_{-0.015}\, R_J}$, and an orbital eccentricity of $0.28^{+0.06}_{-0.09}$; it appears to still be undergoing fairly rapid cooling, as expected given the youth of the host star. The star also shows long-term variability in both the radial velocities and several activity indicators, which we attribute to stellar activity. The discovery and characterization of warm giant planets such as TOI-201 b is important for constraining formation and evolution theories for giant planets.

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WASP-107b's density is even lower: a case study for the physics of planetary gas envelope accretion and orbital migration

With a mass in the Neptune regime and a radius of Jupiter, WASP-107b presents a challenge to planet formation theories. Meanwhile, the planet's low surface gravity and the star's brightness also make it one of the most favorable targets for atmospheric characterization. Here, we present the results of an extensive 4-year Keck/HIRES radial-velocity (RV) follow-up program of the WASP-107 system and provide a detailed study of the physics governing the accretion of its gas envelope. We reveal that WASP-107b's mass is only 1.8 Neptune masses ($M_b = 30.5 \pm 1.7$ $M_\oplus$). The resulting extraordinarily low density suggests that WASP-107b has a H/He envelope mass fraction of $> 85$% unless it is substantially inflated. The corresponding core mass of $<4.6$ $M_\oplus$ at 3$σ$ is significantly lower than what is traditionally assumed to be necessary to trigger massive gas envelope accretion. We demonstrate that this large gas-to-core mass ratio most plausibly results from the onset of accretion at $\gtrsim 1$ AU onto a low-opacity, dust-free atmosphere and subsequent migration to the present-day $a_b = 0.0566 \pm 0.0017$ AU. Beyond WASP-107b, we also detect a second more massive planet ($M_c \sin i = 0.36 \pm 0.04$ $M_{J}$) on a wide eccentric orbit ($e_c = 0.28 \pm 0.07$) which may have influenced the orbital migration and spin-orbit misalignment of WASP-107b. Overall, our new RV observations and envelope accretion modeling provide crucial insights into the intriguing nature of WASP-107b and the system's formation history. Looking ahead, WASP-107b will be a keystone planet to understand the physics of gas envelope accretion.

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Transmission spectroscopy for the warm sub-Neptune HD3167c: evidence for molecular absorption and a possible high metallicity atmosphere

We present a transmission spectrum for the warm (500-600K) sub-Neptune HD3167c obtained using the Hubble Space Telescope Wide Field Camera 3 infrared spectrograph. We combine these data, which span the 1.125-1.643 micron wavelength range, with broadband transit measurements made using Kepler/K2 (0.6-0.9 micron) and Spitzer/IRAC (4-5 micron). We find evidence for absorption by at least one of H2O, HCN, CO2, and CH4 (Bayes factor 7.4; 2.5-sigma significance), although the data precision does not allow us to unambiguously discriminate between these molecules. The transmission spectrum rules out cloud-free hydrogen-dominated atmospheres with metallicities <100x solar at >5.8-sigma confidence. In contrast, good agreement with the data is obtained for cloud-free models assuming metallicities >700x solar. However, for retrieval analyses that include the effect of clouds, a much broader range of metallicities (including subsolar) is consistent with the data, due to the degeneracy with cloud-top pressure. Self-consistent chemistry models that account for photochemistry and vertical mixing are presented for the atmosphere of HD3167c. The predictions of these models are broadly consistent with our abundance constraints, although this is primarily due to the large uncertainties on the latter. Interior structure models suggest the core mass fraction is >40%, independent of a rock or water core composition, and independent of atmospheric envelope metallicity up to 1000x solar. We also report abundance measurements for fifteen elements in the host star, showing that it has a very nearly solar composition.

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The Magellan/PFS Exoplanet Search: A 55-day period dense Neptune transiting the bright ($V=8.6$) star HD 95338

We report the detection of a transiting, dense Neptune planet candidate orbiting the bright ($V=8.6$) K0.5V star HD 95338. Detection of the 55-day periodic signal comes from the analysis of precision radial velocities from the Planet Finder Spectrograph on the Magellan II Telescope. Follow-up observations with HARPS also confirm the presence of the periodic signal in the combined data. HD 95338 was also observed by the Transiting Exoplanet Survey Satellite ({\it TESS}) where we identify a clear single transit in the photometry. A Markov Chain Monte Carlo period search on the velocities allows strong constraints on the expected transit time, matching well the epoch calculated from \tess{} data, confirming both signals describe the same companion. A joint fit model yields an absolute mass of 42.44$^{+2.22}_{-2.08} M_{\oplus}$ and a radius of 3.89$^{+0.19}_{-0.20}$ $R_{\oplus}$ which translates to a density of 3.98$^{+0.62}_{-0.64}$ \gcm\, for the planet. Given the planet mass and radius, structure models suggest it is composed of a mixture of ammonia, water, and methane. HD 95338\,b is one of the most dense Neptune planets yet detected, indicating a heavy element enrichment of $\sim$90\% ($\sim38\, M_{\oplus}$). This system presents a unique opportunity for future follow-up observations that can further constrain structure models of cool gas giant planets.

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Diffuser-Assisted Infrared Transit Photometry for Four Dynamically Interacting \textit{Kepler} Systems

We present ground-based infrared transit observations for four dynamically interacting \textit{Kepler} planets, including Kepler-29b, Kepler-36c, KOI-1783.01, and Kepler-177c, obtained using the Wide-field Infrared Camera on the Hale 200" telescope at Palomar Observatory. By utilizing an engineered diffuser and custom guiding software, we mitigate time-correlated telluric and instrumental noise sources in these observations. We achieve an infrared photometric precision comparable to or better than that of space-based observatories such as the \textit{Spitzer Space Telescope}, and detect transits with greater than 3$σ$ significance for all planets. For Kepler-177c ($J=13.9$) our measurement uncertainties are only $1.2\times$ the photon noise limit and 1.9 times better than the predicted photometric precision for \textit{Spitzer} IRAC photometry of this same target. We find that a single transit observation obtained $4-5$ years after the end of the original \textit{Kepler} mission can reduce dynamical mass uncertainties by as much as a factor of three for these systems. Additionally, we combine our new observations of KOI-1783.01 with information from the literature to confirm the planetary nature of this system. We discuss the implications of our new mass and radius constraints in the context of known exoplanets with low incident fluxes, and we note that Kepler-177c may be a more massive analog to the currently known super-puffs given its core mass (3.8$\pm0.9M_\Earth$) and large gas-to-core ratio (2.8$\pm0.7$). Our demonstrated infrared photometric performance opens up new avenues for ground-based observations of transiting exoplanets previously thought to be restricted to space-based investigation.

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Saturn's Probable Interior: An Exploration of Saturn's Potential Interior Density Structures

The gravity field of a giant planet is typically our best window into its interior structure and composition. Through comparison of a model planet's calculated gravitational potential with the observed potential, inferences can be made about interior quantities, including possible composition and the existence of a core. Necessarily, a host of assumptions go into such calculations, making every inference about a giant planet's structure strongly model dependent. In this work we present a more general picture by setting Saturn's gravity field, as measured during the \emph{Cassini} Grand Finale, as a likelihood function driving a Markov-Chain Monte Carlo exploration of the possible interior density profiles. The result is a posterior distribution of the interior structure that is not tied to assumed composition, thermal state, or material equations of state. Constraints on interior structure derived in this Bayesian framework are necessarily less informative, but are also less biased and more general. These empirical and probabilistic constraints on the density structure are our main data product which we archive for continued analysis. We find that the outer half of Saturn's radius is relatively well constrained, and we interpret our findings as suggesting a significant metal enrichment, in line with atmospheric abundances from remote sensing. As expected, the inner half of Saturn's radius is less well-constrained by gravity, but we generally find solutions that include a significant density enhancement, which can be interpreted as a core, although this core is often lower in density and larger in radial extent than typically found by standard models. This is consistent with a dilute core and/or composition gradients.

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Do Metal-Rich Stars Make Metal-Rich Planets? New Insights on Giant Planet Formation from Host Star Abundances

The relationship between the compositions of giant planets and their host stars is of fundamental interest in understanding planet formation. The solar system giant planets are enhanced above solar composition in metals, both in their visible atmospheres and bulk compositions. A key question is whether the metal enrichment of giant exoplanets is correlated with that of their host stars. Thorngren et al. (2016) showed that in cool (Teq < 1000 K) giant exoplanets, the total heavy-element mass increases with total Mp and the heavy element enrichment relative to the parent star decreases with total Mp. In their work, the host star metallicity was derived from literature [Fe/H] measurements. Here we conduct a more detailed and uniform study to determine whether different host star metals (C, O, Mg, Si, Fe, and Ni) correlate with the bulk metallicity of their planets, using correlation tests and Bayesian linear fits. We present new host star abundances of 19 cool giant planet systems, and combine these with existing host star data for a total of 22 cool giant planet systems (24 planets). Surprisingly, we find no clear correlation between stellar metallicity and planetary residual metallicity (the relative amount of metal versus that expected from the planet mass alone), which is in conflict with common predictions from formation models. We also find a potential correlation between residual planet metals and stellar volatile-to-refractory element ratios. These results provide intriguing new relationships between giant planet and host star compositions for future modeling studies of planet formation.

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A Piecewise Deterministic Markov Process via $(r,θ)$ swaps in hyperspherical coordinates

Recently, a class of stochastic processes known as piecewise deterministic Markov processes has been used to define continuous-time Markov chain Monte Carlo algorithms with a number of attractive properties, including compatibility with stochastic gradients like those typically found in optimization and variational inference, and high efficiency on certain big data problems. Not many processes in this class that are capable of targeting arbitrary invariant distributions are currently known, and within one subclass all previously known processes utilize linear transition functions. In this work, we derive a process whose transition function is nonlinear through solving its Fokker-Planck equation in hyperspherical coordinates. We explore its behavior on Gaussian targets, as well as a Bayesian logistic regression model with synthetic data. We discuss implications to both the theory of piecewise deterministic Markov processes, and to Bayesian statisticians as well as physicists seeking to use them for simulation-based computation.

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Water, High-Altitude Condensates, and Possible Methane Depletion in the Atmosphere of the Warm Super-Neptune WASP-107b

The super-Neptune exoplanet WASP-107b is an exciting target for atmosphere characterization. It has an unusually large atmospheric scale height and a small, bright host star, raising the possibility of precise constraints on its current nature and formation history. We report the first atmospheric study of WASP-107b, a Hubble Space Telescope measurement of its near-infrared transmission spectrum. We determined the planet's composition with two techniques: atmospheric retrieval based on the transmission spectrum and interior structure modeling based on the observed mass and radius. The interior structure models set a $3\,σ$ upper limit on the atmospheric metallicity of $30\times$ solar. The transmission spectrum shows strong evidence for water absorption ($6.5\,σ$ confidence), and the retrieved water abundance is consistent with expectations for a solar abundance pattern. The inferred carbon-to-oxygen ratio is subsolar at $2.7\,σ$ confidence, which we attribute to possible methane depletion in the atmosphere. The spectral features are smaller than predicted for a cloud-free composition, crossing less than one scale height. A thick condensate layer at high altitudes (0.1 - 3 mbar) is needed to match the observations. We find that physically motivated cloud models with moderate sedimentation efficiency ($f_\mathrm{sed} = 0.3$) or hazes with a particle size of 0.3 $μ$m reproduce the observed spectral feature amplitude. Taken together, these findings serve as an illustration of the diversity and complexity of exoplanet atmospheres. The community can look forward to more such results with the high precision and wide spectral coverage afforded by future observing facilities.

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Metal enrichment leads to low atmospheric C/O ratios in transiting giant exoplanets

We predict the carbon-to-oxygen (C/O) ratios in the hydrogen-helium envelope and atmospheres of a sample of nearly 50 relatively cool ($T_{\mathrm eq}<$ 1000 K) transiting gas giant planets. The method involves planetary envelope metallicity estimates that use the structure models of Thorngren et al. (2016) and the disk and planetary accretion model of Öberg et al. (2011). We find that nearly all of these planets are strongly metal-enriched which, coupled with the fact that solid material is the main deliverer of metals in the protoplanetary disk, implies that the substellar C/O ratios of their accreted solid material dominate compared to the enhanced C/O ratio of their accreted gaseous component. We predict that these planets will have atmospheres that are typically reduced in their C/O compared to parent star values independent of the assessed formation locations, with C/O $<1$ a nearly universal outcome within the framework of the model. We expect water vapor absorption features to be ubiquitous in the atmospheres of these planets, and by extension, other gas giants.

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