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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Finding ExoEarths: The Problem of Exozodical Dust

Dust coming from asteroids and comets will strongly affect direct imaging and characterization of terrestrial planets in the Habitable Zones of nearby stars. Such dust in the Solar System is called the zodiacal dust. Higher levels of similar dust are seen around many nearby stars, confined in disks called debris disks. Future high-contrast images of an Earth-like exoplanet (or "exoEarth") will very likely be background-limited by light scattered of both local Solar System zodiacal dust and circumstellar dust in the extrasolar system (exozodiacal dust). Clumps in the exozodiacal dust, which are expected in planet-hosting systems,, may also be a source of confusion. Here we discuss the problems associated with direct observations of an Earth-like planet in the presence of unknown levels of exozodiacal dust. Basic formulae showing the effect of zodiacal and exozodiacal dust on exoEarth direct imaging will be presented, and performance estimates for some future mission concepts summarized. Current detection limits for debris dust and future prospects for sensitive exozodiacal dust observations will also be discussed. Finally, we highlight a few additional problems relating to exozodiacal dust that have yet to be solved.

Roberge, Aki↗
NASA NTRS2017

Lessons Learned from Radiative Transfer Simulations of the Venus Atmosphere

The Venus atmosphere is extremely complex, and because of this the spectrum of Earths sister planet is likewise intricate and a challenge to model accurately. However, accurate modeling of Venus spectrum opens up multiple opportunities to better understand the planet next door, and even for understanding Venus-like planets beyond our solar system. Near-infrared (1-2.5 um, NIR) spectral windows observable on the Venus nigthside present the opportunity to probe beneath the Venusian cloud deck and measure thermal emission from the surface and lower atmosphere remotely from Earth or from orbit. These nigthside spectral windows were discovered by Allen and Crawford (1984) and have since been used measure trace gas abundances in the Venus lower atmosphere (less than 45 km), map surface emissivity varisions, and measure properties of the lower cloud deck. These windows sample radiation from below the cloud base at roughly 45 km, and pressures in this region range from roughly Earthlike (approx. 1 bar) up to 90 bars at the surface. Temperatures in this region are high: they range from about 400 K at the base of the cloud deck up to about 740 K at the surface. This high temperature and pressure presents several challenges to modelers attempting radiative transfer simulations of this region of the atmosphere, which we will review. Venus is also important to spectrally model to predict the remote observables of Venus-like exoplanets in anticipation of data from future observatories. Venus-like planets are likely one of the most common types of terrestrial planets and so simulations of them are valuable for planning observatory and detector properties of future telescopes being designed, as well as predicting the types of observations required to characterize them.

Arney, G.↗
NASA NTRS2012

Transiting Exoplanet Survey Satellite (TESS)

The Transiting Exoplanet Survey Satellite (TESS) will discover thousands of exoplanets in orbit around the brightest stars in the sky. In a two-year survey, TESS will monitor more than 500,000 stars for temporary drops in brightness caused by planetary transits. This first-ever spaceborne all-sky transit survey will identify planets ranging from Earth-sized to gas giants, around a wide range of stellar types and orbital distances. No ground-based survey can achieve this feat. A large fraction of TESS target stars will be 30-100 times brighter than those observed by Kepler satellite, and therefore TESS . planets will be far easier to characterize with follow-up observations. TESS will make it possible to study the masses, sizes, densities, orbits, and atmospheres of a large cohort of small planets, including a sample of rocky worlds in the habitable zones of their host stars. TESS will provide prime targets for observation with the James Webb Space Telescope (JWST), as well as other large ground-based and space-based telescopes of the future. TESS data will be released with minimal delay (no proprietary period), inviting immediate community-wide efforts to study the new planets. The TESS legacy will be a catalog of the very nearest and brightest main-sequence stars hosting transiting exoplanets, thus providing future observers with the most favorable targets for detailed investigations.

Ricker, G. R.↗
DOE OSTI2021

TOI-2076 and TOI-1807: Two Young, Comoving Planetary Systems within 50 pc Identified by TESS that are Ideal Candidates for Further Follow Up

We report the discovery of two planetary systems around comoving stars: TOI-2076 (TIC 27491137) and TOI-1807 (TIC 180695581). TOI-2076 is a nearby (41.9 pc) multiplanetary system orbiting a young (204 ± 50 Myr), bright (K = 7.115 in TIC v8.1) start. TOI-1807 hosts a single transiting planet and is similarly nearby (42.58 pc), similarly young (180 ± 40 Myr ), and bright. Both targets exhibit significant, periodic variability due to starspots, characteristic of their young ages. Using photometric data collected by TESS we identify three transiting planets around TOI-2076 with radii of R {sub b} = 3.3 ± 0.04 R {sub ⊕}, R {sub c} = 4.4 ± 0.05 R {sub ⊕}, and R {sub d} = 4.1 ± 0.07 R {sub ⊕}. Planet TOI-2076b has a period of P {sub b} = 10.356 days. For both TOI-2076c and d, TESS observed only two transits, separated by a 2 yr interval in which no data were collected, preventing a unique period determination. A range of long periods (<17 days) are consistent with the data. We identify a short-period planet around TOI-1807 with a radius of R {sub b} = 1.8 ± 0.04 R {sub ⊕} and a period of P {sub b} = 0.549 days. Their close proximity, and bright, cool host stars, and young ages make these planets excellent candidates for follow up. TOI-1807b is one of the best-known small (R < 2 R{sub ⊕}) planets for characterization via eclipse spectroscopy and phase curves with JWST. TOI-1807b is the youngest ultra-short-period planet discovered to date, providing valuable constraints on formation timescales of short-period planets. Given the rarity of young planets, particularly in multiple-planet systems, these planets present an unprecedented opportunity to study and compare exoplanet formation, and young planet atmospheres, at a crucial transition age for formation theory.

47 OTHER INSTRUMENTATION↗
NASA NTRS2021

TOI-2076 and TOI-1807: Two Young, Comoving Planetary Systems within 50 pc Identified by TESS that are Ideal Candidates for Further Follow Up

We report the discovery of two planetary systems around comoving stars: TOI-2076 (TIC 27491137) and TOI-1807 (TIC 180695581). TOI-2076 is a nearby (41.9 pc) multiplanetary system orbiting a young (204 ± 50 Myr), bright (K = 7.115 in TIC v8.1) start. TOI-1807 hosts a single transiting planet and is similarly nearby (42.58 pc), similarly young (180 ± 40 Myr ), and bright. Both targets exhibit significant, periodic variability due to starspots, characteristic of their young ages. Using photometric data collected by TESS we identify three transiting planets around TOI-2076 with radii of Rb = 3.3 ± 0.04 R⊕, Rc = 4.4 ± 0.05 R⊕, and Rd = 4.1 ± 0.07 R⊕. Planet TOI-2076b has a period of Pb = 10.356 days. For both TOI-2076c and d, TESS observed only two transits, separated by a 2 yr interval in which no data were collected, preventing a unique period determination. A range of long periods (<17 days) are consistent with the data. We identify a short-period planet around TOI-1807 with a radius of Rb = 1.8 ± 0.04 R⊕ and a period of Pb = 0.549 days. Their close proximity, and bright, cool host stars, and young ages make these planets excellent candidates for follow up. TOI-1807b is one of the best-known small (R < 2 ${R}_{\oplus }$) planets for characterization via eclipse spectroscopy and phase curves with JWST. TOI-1807b is the youngest ultra-short-period planet discovered to date, providing valuable constraints on formation timescales of short-period planets. Given the rarity of young planets, particularly in multiple-planet systems, these planets present an unprecedented opportunity to study and compare exoplanet formation, and young planet atmospheres, at a crucial transition age for formation theory.

Christina Hedges↗
NASA NTRS2020

The Habitable Exoplanet Observatory (HabE) Mission Concept

The Habitable Exoplanet Observatory (HabEx), was one of four candidate flagship missions studied in detail by NASA, which were submitted for consideration to the 2020 Decadal Survey in Astronomy and Astrophysics for possible launch in the 2030s. For the first time in human history, technologies have matured sufficiently to enable an affordable spacebased telescope mission capable of discovering and characterizing Earthlike planets orbiting nearby bright sunlike stars to search for signs of habitability and biosignatures. Such a mission can also be equipped with instrumentation that will enable broad and exciting general astrophysics and planetary science not possible from current or planned facilities. HabEx was designed to be the Great Observatory of the 2030s and beyond, with unique imaging and multi-object spectroscopic capabilities at wavelengths ranging from ultraviolet (UV) to near-IR.

Warfield, Keith↗
NASA NTRS2020

KELT-25 b and KELT-26 b: A Hot Jupiter and a Substellar Companion Transiting Young A Stars Observed by TESS

We present the discoveries of KELT-25 b (TIC 65412605, TOI-626.01) and KELT-26 b (TIC 160708862, TOI-1337.01), two transiting companions orbiting relatively bright, early A stars. The transit signals were initially detected by the KELT survey and subsequently confirmed by Transiting Exoplanet Survey Satellite (TESS) photometry. KELT-25 b is on a 4.40 day orbit around the V=9.66 star CD-24 5016(=-+T8280eff180440K,Må=-+2.180.110.12Me), while KELT-26 b is on a 3.34 day orbit around the V=9.95 star HD 134004 (Teff=-+8640240500K,Må=-+1.930.160.14Me), which is likely an Am star. We have confirmed the substellar nature of both companions through detailed characterization of each system using ground-based and TESS photometry, radial velocity measurements, Doppler tomography, and high-resolution imaging. For KELT-25, we determine a companion radius of RP=-+1.640.0430.039RJ and a 3σupper limit on the companion’s mass of64MJ. For KELT-26 b, we infer a planetary mass and radius of MP=-+1.410.510.43MJ and RP=-+1.940.0580.060RJ. From Doppler tomographic observations, we find KELT-26 b to reside in a highly misaligned orbit. This conclusion is weakly corroborated by a subtle asymmetry in the transit light curve from the TESS data. KELT-25 b appears to be in a well-aligned, prograde orbit, and the system is likely a member of the cluster Theia 449.

Exoplanet astronomy↗
NASA NTRS2023

Atmospheric Science Questions for a Uranian Probe

The Ice Giants represent a unique and relatively poorly characterized class of planets that have been largely unexplored since the brief Voyager 2 flyby in the late 1980’s. Uranus is particularly enigmatic, due to its extreme axial tilt, offset magnetic field, apparent low heat budget, mysteriously cool stratosphere and warm thermosphere, as well as a lack of well-defined, long-lived storm systems and distinct atmospheric features. All these characteristics make Uranus a scientifically intriguing target, particularly for missions able to complete in situ measurements. The 2023-2032 Decadal Strategy for Planetary Science and Astrobiology prioritized a flagship orbiter and probe to explore Uranus with the intent to “...transform our knowledge of Ice Giants in general and the Uranian system in particular” (National Academies of Sciences and Medicine, 2022). In support of this recommendation, we present community-supported science questions, key measurements, and a suggested instrument suite that focuses on the exploration and characterization of the Uranian atmosphere by an in situ probe. The scope of these science questions encompasses the origin, evolution, and current processes that shape the Uranian atmosphere, and in turn the Uranian system overall. Addressing these questions will inform vital new insights about Uranus, Ice Giants and Gas Giants in general, the large population of Neptune-sized exoplanets, and the Solar System as a whole.

Uranus↗
DOE OSTI2021

Detection and Bulk Properties of the HR 8799 Planets with High-resolution Spectroscopy

Using the Keck Planet Imager and Characterizer, we obtained high-resolution (R ~ 35,000) K-band spectra of the four planets orbiting HR 8799. We clearly detected H{sub 2}O and CO in the atmospheres of HR 8799 c, d, and e, and tentatively detected a combination of CO and H{sub 2}O in b. These are the most challenging directly imaged exoplanets that have been observed at high spectral resolution to date when considering both their angular separations and flux ratios. We developed a forward-modeling framework that allows us to jointly fit the spectra of the planets and the diffracted starlight simultaneously in a likelihood-based approach and obtained posterior probabilities on their effective temperatures, surface gravities, radial velocities, and spins. We measured vsin (i) values of 10.1{sub -2.7}{sup +2.8} km s{sup -1} for HR 8799 d and 15.0{sub -2.6}{sup +2.3} km s{sup -1} for HR 8799 e, and placed an upper limit of <14 km s{sup -1} of HR 8799 c. Under two different assumptions of their obliquities, we found tentative evidence that rotation velocity is anticorrelated with companion mass, which could indicate that magnetic braking with a circumplanetary disk at early times is less efficient at spinning down lower-mass planets.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Constraints on Metastable Helium in the Atmospheres of WASP-69b and WASP-52b with Ultranarrowband Photometry

Infrared observations of metastable 2{sup 3}S helium absorption with ground- and space-based spectroscopy are rapidly maturing, as this species is a unique probe of exoplanet atmospheres. Specifically, the transit depth in the triplet feature (with vacuum wavelengths near 1083.3 nm) can be used to constrain the temperature and mass-loss rate of an exoplanet’s upper atmosphere. Here, we present a new photometric technique to measure metastable 2{sup 3}S helium absorption using an ultranarrowband filter (FWHM 0.635 nm) coupled to a beam-shaping diffuser installed in the Wide-field Infrared Camera on the 200 inch Hale Telescope at Palomar Observatory. We use telluric OH lines and a helium arc lamp to characterize refractive effects through the filter and to confirm our understanding of the filter transmission profile. We benchmark our new technique by observing a transit of WASP-69b and detect an excess absorption of 0.498% ± 0.045% (11.1σ), consistent with previous measurements after considering our bandpass. We then use this method to study the inflated gas giant WASP-52b and place a 95th percentile upper limit on excess absorption in our helium bandpass of 0.47%. Using an atmospheric escape model, we constrain the mass-loss rate for WASP-69b to be 5.25{sub −0.46}{sup +0.65}×10{sup −4} M{sub J} Gyr{sup −1} (3.32{sub −0.56}{sup +0.67}×10{sup −3} M{sub J} Gyr{sup −1}) at 7000 K (12,000 K). Additionally, we set an upper limit on the mass-loss rate of WASP-52b at these temperatures of 2.1×10{sup −4} M{sub J} Gyr{sup −1} (2.1×10{sup −3} M{sub J} Gyr{sup −1}). These results show that ultranarrowband photometry can reliably quantify absorption in the metastable helium feature.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2012

SPICES: Spectro-Polarimetric Imaging and Characterization of Exoplanetary Systems - From Planetary Disks To Nearby Super Earths

SPICES (Spectro-Polarimetric Imaging and Characterization of Exoplanetary Systems) is a five-year M-class mission proposed to ESA Cosmic Vision. Its purpose is to image and characterize long-period extrasolar planets and circumstellar disks in the visible (450-900 nm) at a spectral resolution of about 40 using both spectroscopy and polarimetry. By 2020/2022, present and near-term instruments will have found several tens of planets that SPICES will be able to observe and study in detail. Equipped with a 1.5 m telescope, SPICES can preferentially access exoplanets located at several AUs (0.5-10 AU) from nearby stars (less than 25 pc) with masses ranging from a few Jupiter masses to Super Earths (approximately 2 Earth radii, approximately 10 mass compared to Earth) as well as circumstellar disks as faint as a few times the zodiacal light in the Solar System.

Boccaletti, Anthony↗
NASA NTRS2021

TESS and HARPS reveal two sub-Neptunes around TOI 1062

The Transiting Exoplanet Survey Satellite (TESS) mission was designed to perform an all-sky search of planets around bright and nearby stars. Here we report the discovery of two sub-Neptunes orbiting around TOI 1062 (TIC 299799658), a V = 10.25 G9V star observed in the TESS Sectors 1, 13, 27, and 28. We use precise radial velocity observations from HARPS to confirm and characterize these two planets. TOI 1062b has a radius of 2.265(-0.091,+0.096) Rꚛ, a mass of 10.15 ± 0.8 Mꚛ, and an orbital period of 4.1130 ± 0.0015 days. The second planet is not transiting, has a minimum mass of 9.78(−1.18,+1.26) Mꚛ and is near the 2:1 mean motion resonance with the innermost planet with an orbital period of 7.972(−0.024,+0.018) days. We performed a dynamical analysis to explore the proximity of the system to this resonance, and to attempt further constraining the orbital parameters. The transiting planet has a mean density of 4.85(−0.74,+0.84) g/cu. cm and an analysis of its internal structure reveals that it is expected to have a small volatile envelope accounting for 0.35% of the mass at most. The star’s brightness and the proximity of the inner planet to what is know as the radius gap make it an interesting candidate for transmission spectroscopy, which could further constrain the composition and internal structure of TOI 1062b.

J. F. Otegi↗
NASA NTRS2019

TESS Discoveries

TESS discoveries have already become fruitful targets for HST follow up, and this will undoubtedly continue through the JWST era. In addition to providing targets for atmospheric characterization, TESS' Level One Science Requirement is to measure masses for 50 transiting planets smaller than 4 Earth radii. A full suite of ground based facilities will be working together to optimize the TESS science yield. Somewhat surprisingly though, no study has quantified the accuracy of mass constraints required to yield robust atmospheric properties of small planets. Previous work showed that the mass of a transiting exoplanet could be inferred from its transmission spectrum alone. The method leverages the effect of the planet's surface gravity on the atmospheric scale height, which in turn influences the transmission spectrum. However, significant degeneracies exist between transmission spectra of planets with different masses and compositions, making difficult to unambiguously determine the planet's mass and composition in many cases. I will present the first quantitative answer to this pressing question. Our analysis places definitive limits on how accurate mass constraints need to be in order to unambiguously determine atmospheric composition for a diverse array of planets ranging from terrestrial-size (TRAPPIST-1-like) to mini-Neptunes and hot Jupiters. These results broadly impact the community of scientists working on exoplanets -- from the full breadth of ground based observers conducting TESS follow-up, to those studying planet populations, and finally to those planning atmospheric investigations. This is particularly timely as the STScI Director charged the HST-TESS Advisory committee to report to the Space Telescope Users Committee on how HST can best support follow-up observations of TESS exoplanet discoveries. The community needs to determine optimal strategies for maximizing the rapid scientific return from TESS targets.

Batalha, Natasha E.↗
DOE OSTI2025

HD 143811 AB b: A Directly Imaged Planet Orbiting a Spectroscopic Binary in Sco-Cen

We present confirmation of HD 143811 AB b, a substellar companion to spectroscopic binary HD 143811 AB through direct imaging with the Gemini Planet Imager (GPI) and Keck NIRC2. HD 143811 AB was observed as a part of the GPI Exoplanet Survey in 2016 and 2019 and is a member of the Sco-Cen star formation region. The exoplanet is detected ∼430 mas from the host star by GPI. With two GPI epochs and one from Keck/NIRC2 in 2022, we confirm through common proper motion analysis that the object is bound to its host star. We derive an orbit with a semimajor axis of $64^{+32}_{-14}$ au and eccentricity $0.23^{+0.24}_{-0.16}$. Spectral analysis of the GPI H-band spectrum and NIRC2 L′ photometry provides additional proof that this object is a substellar companion. We compare the spectrum of HD 143811 AB b to PHOENIX stellar models and Exo-Radioactive-Convective Equilibrium Model (REM) exoplanet atmosphere models and find that Exo-REM models provide the best fits to the data. From the Exo-REM models, we derive an effective temperature of $1042^{+178}_{-132}$ K for the planet and translate the derived luminosity of the planet to a mass of 5.6 ± 1.1 M Jup assuming hot-start evolutionary models. HD 143811 AB b is the first directly imaged planet around a binary that is not on an ultrawide orbit. Future characterization of this object will shed light on the formation of planets around binary star systems.

Astronomy and AstroPhysics↗
DOE OSTI2020

EXPRES. I. HD 3651 as an Ideal RV Benchmark

The next generation of exoplanet-hunting spectrographs should deliver up to an order of magnitude improvement in radial velocity (RV) precision over the standard 1 m s{sup −1} state-of-the-art spectrographs. This advance is critical for enabling the detection of Earth-mass planets around Sun-like stars. New calibration techniques such as laser frequency combs and stabilized etalons ensure that the instrumental stability is well characterized. However, additional sources of error include stellar noise, undetected short-period planets, and telluric contamination. To understand and ultimately mitigate error sources, the contributing terms in the error budget must be isolated to the greatest extent possible. Here, we introduce a new high-cadence RV program, the Extreme Precision Spectrograph (EXPRES) 100 Earths Survey, which aims to identify rocky planets around bright, nearby G and K dwarfs. We also present a benchmark case: the 62 day orbit of a Saturn-mass planet orbiting the chromospherically quiet star, HD 3651. The combination of high eccentricity (0.6) and a moderately long orbital period ensures significant dynamical clearing of any inner planets. Our Keplerian model for this planetary orbit has a residual rms of 58 cm s{sup −1} over a ∼6 month time baseline. By eliminating significant contributors to the RV error budget, HD 3651 serves as a standard for evaluating the long-term precision of extreme precision RV programs.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2018

Kepler Data Validation I: Architecture, Diagnostic Tests, and Data Products for Vetting Transiting Planet Candidates

The Kepler Mission was designed to identify and characterize transiting planets in the Kepler Field of View and to determine their occurrence rates. Emphasis was placed on identification of Earth-size planets orbiting in the Habitable Zone of their host stars. Science data were acquired for a period of four years. Long-cadence data with 29.4 min sampling were obtained for approx. 200,000 individual stellar targets in at least one observing quarter in the primary Kepler Mission. Light curves for target stars are extracted in the Kepler Science Data Processing Pipeline, and are searched for transiting planet signatures. A Threshold Crossing Event is generated in the transit search for targets where the transit detection threshold is exceeded and transit consistency checks are satisfied. These targets are subjected to further scrutiny in the Data Validation (DV) component of the Pipeline. Transiting planet candidates are characterized in DV, and light curves are searched for additional planets after transit signatures are modeled and removed. A suite of diagnostic tests is performed on all candidates to aid in discrimination between genuine transiting planets and instrumental or astrophysical false positives. Data products are generated per target and planet candidate to document and display transiting planet model fit and diagnostic test results. These products are exported to the Exoplanet Archive at the NASA Exoplanet Science Institute, and are available to the community. We describe the DV architecture and diagnostic tests, and provide a brief overview of the data products. Transiting planet modeling and the search for multiple planets on individual targets are described in a companion paper. The final revision of the Kepler Pipeline code base is available to the general public through GitHub. The Kepler Pipeline has also been modified to support the Transiting Exoplanet Survey Satellite (TESS) Mission which is expected to commence in 2018.

data analysis↗
NASA NTRS2021

High Contrast Imaging With MEMS Deformable Mirrors in the Decadal Survey Testbed

Deformable mirrors (DMs) are an essential part of any coronagraphic, high contrast instrument. They mitigate optical aberrations in the system and can even be used to generate contrast for the coronagraph. MEMS DMs from Boston Micromachines have been selected as the baseline for two flagship space telescopes proposed to the 2020 Decadal Survey. Although MEMS DMs have over a decade of heritage on ground-based telescopes and in in-air testbeds around the globe, they have not been tested in vacuum down to the ∼10−10 contrast level needed to image terrestrial exoplanets. In this paper, we describe vacuum tests of MEMS DMs in the Decadal Survey Testbed at the Jet Propulsion Laboratory. The first challenge was a bright, temporally incoherent signal, which was identified as electronics noise and removed with a low-pass filter. After that, the contrast has been limited in broadband light by the strong print-through on the DM surfaces. We performed numerical simulations to confirm that conclusion and to characterize the improvements needed to the MEMS DM surfaces and the testbed layout to attain our goal of 10−10 contrast.

Seo, Byoung-Joon↗
NASA NTRS2010

Implications of the Secondary Eclipse of Exoplanet HAT-P-11b

We observed exoplanet HAT-P-11b and have successfully detected its secondary eclipse. We conducted observations using the Spitzer Space Telescope in the post-cryo mission at 3.6 microns for a period of 22 hours centered on the anticipated secondary eclipse time, to detect the eclipse and determine its phase. Having detected the secondary eclipse, we are at present making a more focused series of observations in both the 3.6 and 4.5 micron bands to fully characterize it. HAT-P-11b is one of only two known exo-Neptunes and has a period of 4.8878 days, radius of 0.422 RJ, mass of 0.081 MJ and semi-major axis 0.053 AU. Measurements of the secondary eclipse will serve to clarify two key issues; 1) the planetary brightness temperature and the nature of its atmosphere, and 2) the eccentricity of its orbit, with implications for its dynamical evolution. We discuss implications of these observations.

Barry, Richard K.↗