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Joshua D. Lothringer

Publications and source records attributed to Joshua D. Lothringer.

At least 37 records · Page 2Linked to original sources

Additional JWST/NIRSpec Transits of the Rocky M Dwarf Exoplanet GJ 1132 b Reveal a Featureless Spectrum

As an archetypal M-dwarf rocky exoplanet, GJ 1132 b has a varied history of atmospheric measurements. At 1.13 $\rm R_{\oplus}$, 1.66 $\rm M_{\oplus}$, and 580 K, it orbits a bright, slowly rotating M dwarf in a 1.6-day period, making it a prime target for characterization. In this study, we combine two JWST NIRSpec/G395H transits previously reported by May and MacDonald et al. 2023 with two new NIRSpec/G395M transits to constrain the presence of an atmosphere. This marks the first time the G395H and G395M modes have been combined for a single target, and we report no difference in the quality of data between the two modes. For rocky M-dwarf studies, G395H may still be preferred if stacking transits to utilize the high-resolution flux-calibrated stellar spectra and assess evolving stellar heterogeneity. GJ 1132 b's co-added transmission spectrum is best-fit with a flat line. A thin steam atmosphere is also consistent with the data, but this interpretation is driven almost entirely by the first transit, which suggests an increase in cool spot coverage-fraction derived from the flux-calibrated stellar spectra. This demonstrates the importance of always considering stellar heterogeneity evolution in multi-visit transits, and also the importance of a "leave-one-transit-out" approach in modeling efforts of co-added transits. We combine these results with MIRI/LRS emission data (Xue et al. 2024) to show that together, transmission and emission are consistent with only the thinnest of atmospheres. Given GJ 1132 b's age and distance from the star, a thin atmosphere is not likely stable. Therefore, the simplest explanation is that GJ 1132 b is indeed a bare rock.

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Overcast mornings and clear evenings in hot Jupiter exoplanet atmospheres

Aerosols is an old topic in the young field of exoplanet atmospheres. Understanding what they are, how they form, and where they go has long provided a fertile playground for theorists. For observers, however, aerosols have been a multi-decade migraine, as their chronic presence hides atmospheric features. For hot Jupiters, the large day-night temperature contrast drives inhomogeneous thermal structures and aerosol distribution, leading to different limb properties probed by transit spectra. We present JWST NIRISS/SOSS spectra of morning and evening limbs for nine gas giants with equilibrium temperatures of ~800-1700 K. By measuring feature size of the 1.4 $μ$m water band for both limbs, we found three planets (WASP-39 b, WASP-94 Ab, and WASP-17 b) show prominent ($>$5$σ$) limb-limb atmospheric opacity difference with muted morning and clear evening limbs. The heavily muted water features on morning limbs indicate high-altitude (0.1 to 0.01 mbar) aerosols. To simultaneously have clear evening limbs requires processes with timescales ($\sim$day) comparable to advection to remove these lofted grains, and we found that both downwelling flow and dayside cloud evaporation could be plausible mechanisms. We hypothesize an empirical boundary--termed the "asymmetry horizon"--in temperature-gravity space that marks the transition where inhomogeneous aerosol coverage begins to emerge. Heterogeneous aerosol coverage is common among hot Jupiters. If unrecognized, limb averaging suppresses spectral features, mimicking high-mean-molecular-weight atmospheres, inflating inferred metallicity by up to 2 dex, and underestimating limb temperatures by as much as half. Finally, we introduce the Limb Spectroscopy Metric (LSM) to predict limb spectral feature size based on planet parameters.

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SiO and a super-stellar C/O ratio in the atmosphere of the giant exoplanet WASP-121b

Refractory elements such as iron, magnesium, and silicon can be detected in the atmospheres of ultrahot giant planets. This provides an opportunity to quantify the amount of refractory material accreted during formation, along with volatile gases and ices. However, simultaneous detections of refractories and volatiles have proved challenging, as the most prominent spectral features of associated atoms and molecules span a broad wavelength range. Here, using a single JWST observation of the ultrahot giant planet WASP-121b, we report detections of H$_2$O (5.5-13.5$σ$), CO (10.8-12.8$σ$), and SiO (5.7-6.2$σ$) in the planet's dayside atmosphere, and CH$_4$ (3.1-5.1$σ$) in the nightside atmosphere. We measure super-stellar values for the atmospheric C/H, O/H, Si/H, and C/O ratios, which point to the joint importance of pebbles and planetesimals in giant planet formation. The CH$_4$-rich nightside composition is also indicative of dynamical processes, such as strong vertical mixing, having a profound influence on the chemistry of ultrahot giant planets.

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WASP-121b's transmission spectrum observed with JWST/NIRSpec G395H reveals thermal dissociation and SiO in the atmosphere

WASP-121b has been established as a benchmark ultrahot Jupiter, serving as a laboratory for the atmospheric chemistry and dynamics of strongly irradiated extrasolar gas giants. Here, we present and analyze WASP-121b's transmission spectrum observed with NIRSpec G395H on board the James Webb Space Telescope and find evidence for the thermal dissociation of H$_2$O and H$_2$ on the planet's permanent dayside. Additionally, we detect SiO at a statistical significance of $5.2σ$ which is compatible with chemical equilibrium in the atmosphere. Constraining the abundance of SiO and abundance ratios between silicon and volatile atoms in WASP-121b's atmosphere could help discriminate between possible migration histories of the planet. The three-dimensional nature of thermal dissociation on WASP-121b's dayside and of recombination on its nightside, however, poses a challenge to constraining molecular abundances and elemental abundance ratios from the transmission spectrum. To account for this, we implemented an atmospheric model in the NEMESIS framework that splits the planet's atmosphere into dayside and nightside. A retrieval applying our atmospheric model to WASP-121b's transmission spectrum favors a higher H$_2$O abundance on the nightside than on the dayside, demonstrating the impact of hemispheric heterogeneity when attempting to constrain WASP-121b's bulk H$_2$O inventory.

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On Linking Planet Formation Models, Protoplanetary Disk Properties, and Mature Gas Giant Exoplanet Atmospheres

Measuring a single elemental ratio (e.g., carbon-to-oxygen) provides insufficient information for understanding the formation mechanisms and evolution that affect our observations of gas giant planet atmospheres. Although the fields of planet formation, protoplanetary disks, and exoplanets are well established and interconnected, our understanding of how to self-consistently and accurately link the theoretical and observational aspects of these fields together is lacking. To foster interdisciplinary conversations, the Max-Planck Institut für Astronomie (MPIA) hosted a week-long workshop called, "Challenge Accepted: Linking Planet Formation with Present-Day Atmospheres." Here, we summarize the latest theories and results in planet formation modeling, protoplanetary disk observations, and atmospheric observations of gas giant atmospheres to address one of the challenges of hosting interdisciplinary conferences: ensuring everyone is aware of the state-of-the-art results and technical language from each discipline represented. Additionally, we highlight key discussions held at the workshop. Our main conclusion is that it is unclear what the ideal observable is to make this link between formation scenarios and exoplanet atmospheres, whether it be multiple elemental abundance ratios, measuring refractory budgets, or something else. Based on discussions held throughout the workshop, we provide several key takeaways of what the workshop attendees feel need the most improvement and exploration within each discipline.

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JWST-TST High Contrast: Living on the Wedge, or, NIRCam Bar Coronagraphy Reveals CO$_2$ in the HR 8799 and 51 Eri Exoplanets' Atmospheres

High-contrast observations with JWST can reveal key composition and vertical mixing dependent absorption features in the spectra of directly imaged planets across the 3-5 $μ$m wavelength range. We present novel coronagraphic images of the HR 8799 and 51 Eri planetary systems using the NIRCam Long Wavelength Bar in an offset "narrow" position. These observations have revealed the four known gas giant planets encircling HR 8799, even at spatial separations challenging for a 6.5 m telescope in the mid-infrared, including the first ever detection of HR 8799 e at 4.6 $μ$m. The chosen filters constrain the strength of CO, CH4, and CO2 absorption in each planet's photosphere. The planets display a diversity of 3-5 $μ$m colors that could be due to differences in composition and ultimately be used to trace their formation history. They also show stronger CO2 absorption than expected from solar metallicity models, indicating that they are metal enriched. We detected 51 Eri b at 4.1 $μ$m and not at longer wavelengths, which, given the planet's temperature, is indicative of out-of-equilibrium carbon chemistry and an enhanced metallicity. Updated orbits fit to the new measurement of 51 Eri b validate previous studies that find a preference for high eccentricities ($e{=}0.57_{-0.09}^{+0.03}$), which likely indicates some dynamical processing in the system's past. These results present an exciting opportunity to model the atmospheres and formation histories of these planets in more detail in the near future, and are complementary to future higher-resolution, continuum-subtracted JWST spectroscopy.

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Refractory and Volatile Species in the UV-to-IR Transmission Spectrum of Ultra-hot Jupiter WASP-178b with HST and JWST

The atmospheres of ultra-hot Jupiters are unique compared to other planets because of the presence of both refractory and volatile gaseous species, enabling a new lens to constrain a planet's composition, chemistry, and formation. WASP-178b is one such ultra-hot Jupiter that was recently found to exhibit enormous NUV absorption between 0.2 and 0.4 $μ$m from some combination of Fe+, Mg, and SiO. Here, we present new infrared observations of WASP-178b with HST/WFC3 and JWST/NIRSpec/G395H, providing novel measurements of the volatile species H$_2$O and CO in WASP-178b's atmosphere. Atmospheric retrievals find a range of compositional interpretations depending on which dataset is retrieved, the type of chemistry assumed, and the temperature structure parametrization used due to the combined effects of thermal dissociation, the lack of volatile spectral features besides H$_2$O and CO, and the relative weakness of H$_2$O and CO themselves. Taken together with a new state-of-the-art characterization of the host star, our retrieval analyses suggests a solar to super-solar [O/H] and [Si/H], but sub-solar [C/H], perhaps suggesting rock-laden atmospheric enrichment near the H$_2$O iceline. To obtain meaningful abundance constraints for this planet, it was essential to combine the JWST IR data with short-wavelength HST observations, highlighting the ongoing synergy between the two facilities.

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Phase-resolved Hubble Space Telescope WFC3 Spectroscopy of Weakly-Irradiated Brown Dwarf GD 1400 and Energy Redistribution-Irradiation Trends in Six WD$-$BD Binaries

Irradiated brown dwarfs offer a unique opportunity to bridge the gap between stellar and planetary atmospheres. We present high-quality $\mathit{HST}$/WFC3/G141 phase-resolved spectra of the white dwarf + brown dwarf binary GD 1400, covering more than one full rotation of the brown dwarf. Accounting for brightness variations caused by ZZ Ceti pulsations, we revealed weak ($\sim$1\%) phase curve amplitude modulations originating from the brown dwarf. Sub-band light curve exploration in various bands showed no significant wavelength dependence on amplitude or phase shift. Extracted day- and night-side spectra indicated chemically similar hemispheres, with slightly higher day-side temperatures, suggesting efficient heat redistribution or dominance of radiative escape over atmospheric circulation. A simple radiative and energy redistribution model reproduced observed temperatures well. Cloud-inclusive models fit the day and night spectra better than cloudless models, indicating global cloud coverage. We also begin qualitatively exploring atmospheric trends across six irradiated brown dwarfs, from the now complete "Dancing with Dwarfs" WD$-$BD sample. The trend we find in the day-side/night-side temperature and irradiation levels is consistent with efficient heat redistribution for irradiation levels less than $\sim$10$^9$ ergs/s/cm$^2$ and decreasing efficiency above that level.

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An absolute mass, precise age, and hints of planetary winds for WASP-121 A and b from a JWST NIRSpec phase curve

We have conducted a planetary radial velocity measurement of the ultra-hot Jupiter WASP-121b using JWST NIRSpec phase curve data. Our analysis reveals the Doppler shift of the planetary spectral lines across the full orbit, which shifts considerably across the detector ($\sim$ 10 pixels). Using cross-correlation techniques, we have determined an overall planetary velocity amplitude of $K_{\rm p}=215.7\pm1.1$ km/s, which is in good agreement with the expected value. We have also calculated the dynamical mass for both components of the system by treating it as an eclipsing double-line spectroscopic binary, with WASP-121A having a mass of M$_{\star}$=1.330 $\pm$ 0.019 M$_{\odot}$, while WASP-121b has a mass of M$_{\rm p}$= 1.170 $\pm$ 0.043 M$_{\rm Jup}$. These dynamical measurements are $\sim3\times$ more precise than previous estimates and do not rely on any stellar modeling assumptions which have a $\sim$5\% systematic floor mass uncertainty. Additionally, we used stellar evolution modeling constrained with a stellar density and parallax measurement to determine a precise age for the system, found to be 1.11 $\pm$ 0.14 Gyr. Finally, we observed potential velocity differences between the two NIRSpec detectors, with NRS1 lower by 5.5$\pm$2.2 km/s. We suggest that differences can arise from day/night asymmetries in the thermal emission, which can lead to a sensitivity bias favoring the illuminated side of the planet, with planetary rotation and winds both acting to lower a measured $K_{\rm P}$. The planet's rotation can account for 1 km/s of the observed velocity difference, with 4.5$\pm$2.2 km/s potentially attributable to vertical differences in wind speeds.

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An HST Transmission Spectrum of the Closest M-Dwarf Transiting Rocky Planet LTT 1445Ab

Which rocky exoplanets have atmospheres? This presumably simply question is the first that must be answered to understand the prevalence of nearby habitable planets. A mere 6.9 pc from Earth, LTT 1445A is the closest transiting M-dwarf system, and its largest known planet, at $\rm 1.31\; R_{\oplus}$ and 424 K, is one of the most promising targets in which to search for an atmosphere. We use HST/WFC3 transmission spectroscopy with the G280 and G141 grisms to study the spectrum of LTT 1445Ab between $\rm 0.2-1.65\;μm$. In doing so, we uncover a UV flare on the neighboring star LTT 1445C that is completely invisible at optical wavelengths; we report one of the first simultaneous near-UV/optical spectra of an M~dwarf flare. The planet spectrum is consistent with a flat line (with median transit depth uncertainties of 128 and 52 ppm for the G280 and G141 observations, respectively), though the infrared portion displays potential features that could be explained by known opacity sources such as HCN. Some atmospheric retrievals weakly favor ($\sim2σ$) an atmosphere, but it remains challenging to discern between stellar contamination, an atmosphere, and a featureless spectrum at this time. We do, however, confidently rule out $\leq100\times$ solar metallicity atmospheres. Although stellar contamination retrievals cannot fit the infrared features well, the overall spectrum is consistent with stellar contamination from hot or cold spots. Based on the UV/optical data, we place limits on the extent of stellar variability expected in the near-infrared ($30-40$ ppm), which will be critical for future JWST observations.

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CRIRES+ and ESPRESSO reveal an atmosphere enriched in volatiles relative to refractories on the ultra-hot Jupiter WASP-121b

One of the outstanding goals of the planetary science community is to measure the present-day atmospheric composition of planets and link this back to formation. As giant planets are formed by accreting gas, ices, and rocks, constraining the relative amounts of these components is critical to understand their formation and evolution. For most known planets, including the Solar System giants, this is difficult as they reside in a temperature regime where only volatile elements (e.g., C, O) can be measured, while refractories (e.g., Fe, Ni) are condensed to deep layers of the atmosphere where they cannot be remotely probed. With temperatures allowing for even rock-forming elements to be in the gas phase, ultra-hot Jupiter atmospheres provide a unique opportunity to simultaneously probe the volatile and refractory content of giant planets. Here we directly measure and obtain bounded constraints on the abundances of volatile C and O as well as refractory Fe and Ni on the ultra-hot giant exoplanet WASP-121b. We find that ice-forming elements are comparatively enriched relative to rock-forming elements, potentially indicating that WASP-121b formed in a volatile-rich environment much farther away from the star than where it is currently located. The simultaneous constraint of ice and rock elements in the atmosphere of WASP-121b provides insights into the composition of giant planets otherwise unattainable from Solar System observations.

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Novel Constraints on Companions to the Helix Nebula Central Star

The Helix is a visually striking and the nearest planetary nebula, yet any companions responsible for its asymmetric morphology have yet to be identified. In 2020, low-amplitude photometric variations with a periodicity of 2.8 d were reported based on Cycle 1 TESS observations. In this work, with the inclusion of two additional sectors, these periodic light curves are compared with lcurve simulations of irradiated companions in such an orbit. Based on the light curve modelling, there are two representative solutions: i) a Jupiter-sized body with 0.102 Rsol and an arbitrarily small orbital inclination i=1 deg, and ii) a 0.021 Rsol exoplanet with i approx. 25 deg, essentially aligned with the Helix Nebular inclination. Irradiated substellar companion models with equilibrium temperature 4970 K are constructed and compared with existing optical spectra and infrared photometry, where Jupiter-sized bodies can be ruled out, but companions modestly larger than Neptune are still allowed. Additionally, any spatially-unresolved companions are constrained based on the multi-wavelength, photometric spectral energy distribution of the central star. No ultracool dwarf companion earlier than around L5 is permitted within roughly 1200 au, leaving only faint white dwarfs and cold brown dwarfs as possible surviving architects of the nebular asymmetries. While a planetary survivor is a tantalizing possibility, it cannot be ruled out that the light curve modulation is stellar in nature, where any substellar companion requires confirmation and may be possible with JWST observations.

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The only inflated brown dwarf in an eclipsing white dwarf-brown dwarf binary: WD1032+011B

Due to their short orbital periods and relatively high flux ratios, irradiated brown dwarfs in binaries with white dwarfs offer better opportunities to study irradiated atmospheres than hot Jupiters, which have lower planet-to-star flux ratios. WD1032+011 is an eclipsing, tidally locked white dwarf-brown dwarf binary with a 9950 K white dwarf orbited by a 69.7 M$_{Jup}$ brown dwarf in a 0.09 day orbit. We present time-resolved Hubble Space Telescope Wide Field Camera 3 spectrophotometric data of WD1032+011. We isolate the phase-dependent spectra of WD1032+011B, finding a 210 K difference in brightness temperature between the dayside and nightside. The spectral type of the brown dwarf is identified as L1 peculiar, with atmospheric retrievals and comparison to field brown dwarfs showing evidence for a cloud-free atmosphere. The retrieved temperature of the dayside is $1748^{+66}_{-67}$ K, with a nightside temperature of $1555^{+76}_{-62}$ K, showing an irradiation-driven temperature contrast coupled with inefficient heat redistribution from the dayside to the nightside. The brown dwarf radius is inflated, likely due to the constant irradiation from the white dwarf, making it the only known inflated brown dwarf in an eclipsing white dwarf-brown dwarf binary.

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The Unrealised Interdisciplinary Advantage of Observing High Mass Transiting Exoplanets and Brown Dwarfs -- Strategic Exoplanet Initiatives with HST and JWST White Paper

We advocate for further prioritisation of atmospheric characterisation observations of high mass transiting exoplanets and brown dwarfs. This population acts as a unique comparative sample to the directly imaged exoplanet and brown dwarf populations, of which a range of JWST characterisation observations are planned. In contrast, only two observations of transiting exoplanets in this mass regime were performed in Cycle 1, and none are planned for Cycle 2. Such observations will: improve our understanding of how irradiation influences high gravity atmospheres, provide insights towards planetary formation and evolution across this mass regime, and exploit JWST's unique potential to characterise exoplanets across the known population.

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Sulphur dioxide in the mid-infrared transmission spectrum of WASP-39b

The recent inference of sulphur dioxide (SO$_2$) in the atmosphere of the hot ($\sim$1100 K), Saturn-mass exoplanet WASP-39b from near-infrared JWST observations suggests that photochemistry is a key process in high temperature exoplanet atmospheres. This is due to the low ($<$1 ppb) abundance of SO$_2$ under thermochemical equilibrium, compared to that produced from the photochemistry of H$_2$O and H$_2$S (1-10 ppm). However, the SO$_2$ inference was made from a single, small molecular feature in the transmission spectrum of WASP-39b at 4.05 $μ$m, and therefore the detection of other SO$_2$ absorption bands at different wavelengths is needed to better constrain the SO$_2$ abundance. Here we report the detection of SO$_2$ spectral features at 7.7 and 8.5 $μ$m in the 5-12 $μ$m transmission spectrum of WASP-39b measured by the JWST Mid-Infrared Instrument (MIRI) Low Resolution Spectrometer (LRS). Our observations suggest an abundance of SO$_2$ of 0.5-25 ppm (1$σ$ range), consistent with previous findings. In addition to SO$_2$, we find broad water vapour absorption features, as well as an unexplained decrease in the transit depth at wavelengths longer than 10 $μ$m. Fitting the spectrum with a grid of atmospheric forward models, we derive an atmospheric heavy element content (metallicity) for WASP-39b of $\sim$7.1-8.0 $\times$ solar and demonstrate that photochemistry shapes the spectra of WASP-39b across a broad wavelength range.

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Atmospheric Retrievals of the Phase-resolved Spectra of Irradiated Brown Dwarfs WD-0137B and EPIC-2122B

We present an atmospheric retrieval analysis of HST/WFC3/G141 spectroscopic phase curve observations of two brown dwarfs, WD-0137B and EPIC-2122B, in ultra-short period orbits around white dwarf hosts. These systems are analogous to hot and ultra-hot Jupiter systems, enabling a unique and high-precision comparison to exoplanet systems. We use the PETRA retrieval suite to test various analysis setups, including joint-phase retrievals, multiple temperature structures, and non-uniform abundances. We find that WD-0137B has a dayside that closely resembles that of other ultra-hot Jupiters with inverted temperature structures and H$^-$ opacity, but quickly transitions to a mostly non-inverted temperature structure on the nightside. Meanwhile, EPIC-2122B's atmosphere remains inverted at all constrained longitudes, with dominant H$^-$ opacity. Retrievals with multiple temperature profiles and non-uniform vertical abundances were generally not statistically justified for this dataset, but retrievals with dayside-dilution factors were found to be justified. Retrieving all phases simultaneously with a linear combination of a dayside and nightside atmosphere was found to be an adequate representation of the entire phase-curve once a longitudinal temperature gradient free parameter was included in the retrieval. Comparing to global circulation models, we attribute behavior in the 1D retrievals to the inclined viewing geometry of the systems, which results in always-visible irradiated and inverted portions of the atmosphere "contaminating" spectra measured from the nightside hemisphere. This study sheds light on the similarities between these irradiated brown dwarf systems and hot and ultra-hot Jupiters, but also their unique differences, including the influence of the inclined viewing geometry.

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Time-resolved Hubble Space Telescope Wide Field Camera 3 Spectrophotometry Reveals Inefficient Day-to-Night Heat Redistribution in the Highly Irradiated Brown Dwarf SDSS 1557B

Brown dwarfs in ultra-short period orbits around white dwarfs offer a unique opportunity to study the properties of tidally-locked, fast rotating (1-3 hr), and highly-irradiated atmospheres. Here, we present phase-resolved spectrophotometry of the white dwarf-brown dwarf (WD-BD) binary SDSS 1557, which is the fifth WD-BD binary in our six-object sample. Using the Hubble Space Telescope Wide Field Camera 3 Near-infrared G141 instrument, the 1.1 to 1.7 $μ$m phase curves show rotational modulations with semi-amplitudes of 10.5$\pm$0.1%. We observe a wavelength dependent amplitude, with longer wavelengths producing larger amplitudes, while no wavelength dependent phase shifts were identified. The phase-resolved extracted BD spectra exhibit steep slopes and are nearly featureless. A simple radiative energy redistribution atmospheric model recreates the hemisphere integrated brightness temperatures at three distinct phases and finds evidence for weak redistribution efficiency. Our model also predicts a higher inclination than previously published. We find that SDSS 1557B, the second most irradiated BD in our sample, is likely dominated by clouds on the night side, whereas the featureless day side spectrum is likely dominated by H$^-$ opacity and a temperature inversion, much like the other highly-irradiated BD EPIC2122B.

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Nightside clouds and disequilibrium chemistry on the hot Jupiter WASP-43b

Hot Jupiters are among the best-studied exoplanets, but it is still poorly understood how their chemical composition and cloud properties vary with longitude. Theoretical models predict that clouds may condense on the nightside and that molecular abundances can be driven out of equilibrium by zonal winds. Here we report a phase-resolved emission spectrum of the hot Jupiter WASP-43b measured from 5-12 $μ$m with JWST's Mid-Infrared Instrument (MIRI). The spectra reveal a large day-night temperature contrast (with average brightness temperatures of 1524$\pm$35 and 863$\pm$23 Kelvin, respectively) and evidence for water absorption at all orbital phases. Comparisons with three-dimensional atmospheric models show that both the phase curve shape and emission spectra strongly suggest the presence of nightside clouds which become optically thick to thermal emission at pressures greater than ~100 mbar. The dayside is consistent with a cloudless atmosphere above the mid-infrared photosphere. Contrary to expectations from equilibrium chemistry but consistent with disequilibrium kinetics models, methane is not detected on the nightside (2$σ$ upper limit of 1-6 parts per million, depending on model assumptions).

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