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At least 469 records · Page 26

Magnetic Microcalorimeter (MMC) Gamma-Ray Detectors with Ultra-High Energy Resolution. Comprehensive Technology Readiness Assessment

Magnetic Microcalorimeter (MMC) gamma ray detectors have demonstrated very high energy resolution of 38 eV FWHM for gamma ray energies below 100 keV. This is an order or magnitude better than conventional HPGe detector and can remove most line-overlap problems in NDA by gamma spectroscopy below ~130 keV. Unlike superconducting transition edge sensors (TESs), MMCs have a reproducible and almost perfectly linear response, which greatly simplifies adding spectra from different detector pixels and reduces systematic errors in quantitative assays. The instrument is currently at TRL-5 but could advance to TRL-6 by improving the signal processing software and using the system for the quantitative analysis of a safeguards sample provided by e.g. the IAEA. Making MMC detectors commercially viable and used more widely then depends on making the technology more reliable, specifically by increasing the device uniformity and yield, and by developing commercial software. This situation is often only half-jokingly referred to as the “valley of death” and could be addressed though the SBIR program. Our collaborators at STAR Cryoelectronics LLC are well qualified to further advance MMC development, and XIA LLC is well-positioned to develop the data acquisition system and write the software for MMC readout. In addition, the advance to TRL-6 would be desirable to increase the visibility and showcase the value of MMC spectrometers, e.g. by placing one of them into the Safeguards Analytical Laboratory (SAL) at the IAEA, whose NDA experts have recently started to show interest in cryogenic detector technology. As a result of this LCP, we also now have an instrument at LLNL that we will use for various applications of MMCs in nuclear safeguards and science. We are confident that as the number of high-profile results increases, so will the interest in and commercial viability of this technology.

42 ENGINEERING↗

Magnetic Microcalorimeter (MMC) Gamma-Ray Detectors with Ultra-High Energy Resolution. Comprehensive Technology Readiness Assessment

Magnetic Microcalorimeter (MMC) gamma ray detectors have demonstrated very high energy resolution of 38 eV FWHM for gamma ray energies below 100 keV. This is an order or magnitude better than conventional HPGe detector and can remove most line-overlap problems in NDA by gamma spectroscopy below ~130 keV. Unlike superconducting transition edge sensors (TESs), MMCs have a reproducible and almost perfectly linear response, which greatly simplifies adding spectra from different detector pixels and reduces systematic errors in quantitative assays. The instrument is currently at TRL-5 but could advance to TRL-6 by improving the signal processing software and using the system for the quantitative analysis of a safeguards sample provided by e.g. the IAEA. Making MMC detectors commercially viable and used more widely then depends on making the technology more reliable, specifically by increasing the device uniformity and yield, and by developing commercial software. This situation is often only half-jokingly referred to as the “valley of death” and could be addressed though the SBIR program. Our collaborators at STAR Cryoelectronics LLC are well qualified to further advance MMC development, and XIA LLC is well-positioned to develop the data acquisition system and write the software for MMC readout. In addition, the advance to TRL-6 would be desirable to increase the visibility and showcase the value of MMC spectrometers, e.g. by placing one of them into the Safeguards Analytical Laboratory (SAL) at the IAEA, whose NDA experts have recently started to show interest in cryogenic detector technology. As a result of this LCP, we also now have an instrument at LLNL that we will use for various applications of MMCs in nuclear safeguards and science. We are confident that as the number of high-profile results increases, so will the interest in and commercial viability of this technology.

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Eject, crash, or survive: Using machine learning to predict orbital instability of exoplanetary systems

Astronomers throughout history, including titans like Kepler and Newton, have tackled planetary dynamics and orbital instability. Despite strides taken in research, understanding the evolution of planetary orbits remains an intricate, computationally expensive, and analytically unsolved problem. I apply machine learning classification methods to numerical simulations of planetary systems in order to predict the long-term fate of the planet - whether the planet remains in a stable orbit or not. My method uses the first 41.1 years (≤ 500 orbits) of data from a planet’s simulation to calculate 17 dynamically-motivated metrics; I trained my classifier on these features to predict a planet’s stability after 107 years. At 84.33%, my classifier was comparable in accuracy to pre-existing literature, despite using significantly less computational power than most other methods. In my research, I found that the standard deviation of eccentricity, mass ratios for neighboring planets, and semi-major axis ratio with the outer planet neighbor to be the most predictive features of instability. I propose reasons for the importance of these features, their role in planetary dynamics, as well as possible explanations for why some planets were misclassified. By understanding the important metrics of instability and reasons for misclassification, we can begin to understand more about system architectures, orbital motion and dynamics, and the formation and evolution of the exoplanetary systems. This is applicable in our own Solar System, and with exoplanet discovery missions such as TESS, this research becomes especially relevant in understanding the new exoplanetary systems we discover.

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Eject, crash, or survive: Using machine learning to predict orbital instability of exoplanetary systems

Astronomers throughout history, including titans like Kepler and Newton, have tackled planetary dynamics and orbital instability. Despite strides taken in research, understanding the evolution of planetary orbits remains an intricate, computationally expensive, and analytically unsolved problem. I apply machine learning classification methods to numerical simulations of planetary systems in order to predict the long-term fate of the planet - whether the planet remains in a stable orbit or not. My method uses the first 41.1 years (≤ 500 orbits) of data from a planet’s simulation to calculate 17 dynamically-motivated metrics; I trained my classifier on these features to predict a planet’s stability after 107 years. At 84.33%, my classifier was comparable in accuracy to pre-existing literature, despite using significantly less computational power than most other methods. In my research, I found that the standard deviation of eccentricity, mass ratios for neighboring planets, and semi-major axis ratio with the outer planet neighbor to be the most predictive features of instability. I propose reasons for the importance of these features, their role in planetary dynamics, as well as possible explanations for why some planets were misclassified. By understanding the important metrics of instability and reasons for misclassification, we can begin to understand more about system architectures, orbital motion and dynamics, and the formation and evolution of the exoplanetary systems. This is applicable in our own Solar System, and with exoplanet discovery missions such as TESS, this research becomes especially relevant in understanding the new exoplanetary systems we discover.

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Pandora Telescope Isolation Systems Engineering Project

The collective imagination of humanity has always been captured by the possibility of other habitable planets. Only with recent advances in spacecraft and our understanding of astrophysics, has it become possible to study the atmospheres of planets orbiting stars other than our sun, also known as extrasolar planets or exoplanets. We know from the Keplar Space telescope, launched in the early 1990s, that there are more planets than stars in the Milky Way. The Transiting Exoplanet Survey Satellite, TESS, will continue the search for exoplanets outside our solar system. Two other well know telescopes with the capability to study exoplanets are the James Webb Space Telescope (JWST) and Hubble Space Telescope (HST). Together they provide full spectral coverage to do short deep dives into planets of interest, but tasking these satellites is both expensive and hard to obtain. A new mission dedicated to the characterization of exoplanets and the stars they orbit is needed to fill the gap.

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Discovery of 15 A-F Main Sequence Pulsating Star Candidates

Delta Scuti stars, spanning spectral types A to F with masses between 1.5 and 2.5 solar masses, exhibit a complex mix of radial and non-radial pressure modes. This study focuses on 15 Delta Scuti, Gamma Doradus, and Hybrid candidate stars using TESS satellite photometry data with a time series of exposures ranging from 20 to 600 seconds across different sky regions. Employing the prewhitening technique via fast Fourier transforms, significant frequencies are extracted from light curves. Three approximation methods are used to estimate critical stellar parameters such as density, radius, and mass. This research also verifies the variability of these stars, which are currently not classified as variable in databases like SIMBAD.

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FY26 Mid-Year Report

The goal of this project is to develop specific aspects of ultra-high-resolution microcalorimeter technologies that support IAEA Nuclear Material Laboratory needs and the goals of SP-1 19/NML-003 "Microcalorimetry Analysis Technique for NML" but are outside the scope of the SP-1. The focus is on commissioning, assembly, and testing of the microcalorimeter decay energy spectrometer with superconducting transition-edge sensors (TESs) and magnetic microcalorimeters (MMCs) in preparation for transfer to the IAEA Nuclear Material Laboratory.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Star-exoplanet interactions: A growing interdisciplinary field in heliophysics

Traditionally, heliophysics is characterized as the study of the near-Earth space environment, where plasmas and neutral gases originating from the Earth, the Sun, and other solar system bodies interact in ways that are detectable only through in-situ or close-range (usually within ~10 AU) remote sensing. As a result, heliophysics has data from the space environment around a handful of solar system objects, in particular the Sun and Earth. Comparatively, astrophysics has data from an extensive array of objects, but is more limited in temporal, spatial, and wavelength information from any individual object. Thus, our understanding of planetary space environments as a complex, multi-dimensional network of specific interacting systems may in the past have seemed to have little to do with the highly diverse space environments detected through astrophysical methods. Recent technological advances have begun to bridge this divide. Exoplanetary studies are opening up avenues to study planetary environments beyond our solar system, with missions like Kepler, TESS, and JWST, along with increasing capabilities of ground-based observations. At the same time, heliophysics studies are pushing beyond the boundaries of our heliosphere with Voyager, IBEX, and the future IMAP mission. The interdisciplinary field of star-exoplanet interactions is a critical, growing area of study that enriches heliophysics. A multidisciplinary approach to heliophysics enables us to better understand universal processes that operate in diverse environments, as well as the evolution of our solar system and extreme space weather. The expertise, data, theory, and modeling tools developed by heliophysicists are crucial in understanding the space environments of exoplanets, their host stars, and their potential habitability. The mutual benefit that heliophysics and exoplanetary studies offer each other depends on strong, continuing solar system-focused and Earth-focused heliophysics studies. The heliophysics discipline requires new targeted funding to support inter-divisional opportunities, including small multi-disciplinary research projects, large collaborative research teams, and observations targeting the heliophysics of planetary and exoplanet systems. Here we discuss areas of heliophysics-relevant exoplanetary research, observational opportunities and challenges, and ways to promote the inclusion of heliophysics within the wider exoplanetary community.

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KEPLER-21b: A ROCKY PLANET AROUND A V = 8.25 mag STAR

HD 179070, aka Kepler-21, is a V = 8.25 F6IV star and the brightest exoplanet host discovered by Kepler. An early detailed analysis by Howell et al. of the first 13 months (Q0–Q5) of Kepler light curves revealed transits of a planetary companion, Kepler-21b, with a radius of about 1.60 ± 0.04 R{sub ⊕} and an orbital period of about 2.7857 days. However, they could not determine the mass of the planet from the initial radial velocity (RV) observations with Keck-HIRES, and were only able to impose a 2σ upper limit of 10 M{sub ⊕}. Here, we present results from the analysis of 82 new RV observations of this system obtained with HARPS-N, together with the existing 14 HIRES data points. We detect the Doppler signal of Kepler-21b with a RV semiamplitude K = 2.00 ± 0.65 m s{sup −1}, which corresponds to a planetary mass of 5.1 ± 1.7 M{sub ⊕}. We also measure an improved radius for the planet of 1.639 +0.019/−0.015 R{sub ⊕}, in agreement with the radius reported by Howell et al. We conclude that Kepler-21b, with a density of 6.4 ± 2.1 g cm{sup −3}, belongs to the population of small, ≲6 M{sub ⊕} planets with iron and magnesium silicate interiors, which have lost the majority of their envelope volatiles via stellar winds or gravitational escape. The RV analysis presented in this paper serves as an example of the type of analysis that will be necessary to confirm the masses of TESS small planet candidates.

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Demonstrating high-precision, multiband transit photometry with MuSCAT: A case for HAT-P-14B

The Multicolor Simultaneous Camera for studying Atmospheres of Transiting exoplanets (MuSCAT) is an optical three-band (g{sub 2}{sup ′}-, r{sub 2}{sup ′}- and z{sub s,2}-band) imager that was recently developed for the 188 cm telescope at Okayama Astrophysical Observatory with the aim of validating and characterizing transiting planets. In a pilot observation with MuSCAT we observed a primary transit of HAT-P-14b, a high-surface gravity (g{sub p} = 38 ms{sup −2}) hot Jupiter around a bright (V = 10) F-type star. From a 2.9 hr observation we achieved the five-minute binned photometric precisions of 0.028%, 0.022%, and 0.024% in the g{sub 2}{sup ′}, r{sub 2}{sup ′}, and z{sub s,2} bands, respectively, which provided the highest-quality photometric data for this planet. Combining these results with those of previous observations, we search for variations of transit timing and duration over five years as well as variations of planet-star radius ratio (R{sub p}/R{sub s}) with wavelengths, but can find no considerable variation in any parameters. On the other hand, using the transit-subtracted light curves we simulate the achievable measurement error of R{sub p}/R{sub s} with MuSCAT for various planetary sizes, assuming three types of host stars: HAT-P-14, the nearby K-dwarf HAT-P-11, and the nearby M-dwarf GJ1214. Comparing our results with the expected atmospheric scale heights, we find that MuSCAT is capable of probing the atmospheres of planets as small as a sub-Jupiter (R{sub p}∼6R{sub ⊕}) around HAT-P-14 in all bands, a Neptune (∼4R{sub ⊕}) around HAT-P-11 in all bands, and a super-Earth (∼2.5R{sub ⊕}) around GJ1214 in r{sub 2}{sup ′} and z{sub s,2} bands. These results promise that MuSCAT will produce fruitful scientific outcomes in the K2 and TESS era.

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197 candidates and 104 validated planets in K2's first five fields

We present 197 planet candidates discovered using data from the first year of the NASA K2 mission (Campaigns 0–4), along with the results of an intensive program of photometric analyses, stellar spectroscopy, high-resolution imaging, and statistical validation. We distill these candidates into sets of 104 validated planets (57 in multi-planet systems), 30 false positives, and 63 remaining candidates. Our validated systems span a range of properties, with median values of R {sub P} = 2.3 R{sub ⊕}, P = 8.6 days, T{sub eff} = 5300 K, and Kp = 12.7 mag. Stellar spectroscopy provides precise stellar and planetary parameters for most of these systems. We show that K2 has increased by 30% the number of small planets known to orbit moderately bright stars (1–4 R {sub ⊕}, Kp = 9–13 mag). Of particular interest are 76 planets smaller than 2 R {sub ⊕}, 15 orbiting stars brighter than Kp = 11.5 mag, 5 receiving Earth-like irradiation levels, and several multi-planet systems—including 4 planets orbiting the M dwarf K2–72 near mean-motion resonances. By quantifying the likelihood that each candidate is a planet we demonstrate that our candidate sample has an overall false positive rate of 15%–30%, with rates substantially lower for small candidates (<2R{sub ⊕}) and larger for candidates with radii >8R{sub ⊕} and/or with P<3 days. Extrapolation of the current planetary yield suggests that K2 will discover between 500 and 1000 planets in its planned four-year mission, assuming sufficient follow-up resources are available. Efficient observing and analysis, together with an organized and coherent follow-up strategy, are essential for maximizing the efficacy of planet-validation efforts for K2, TESS, and future large-scale surveys.

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THE KEPLER FOLLOW-UP OBSERVATION PROGRAM. I. A CATALOG OF COMPANIONS TO KEPLER STARS FROM HIGH-RESOLUTION IMAGING

We present results from high-resolution, optical to near-IR imaging of host stars of Kepler Objects of Interest (KOIs), identified in the original Kepler field. Part of the data were obtained under the Kepler imaging follow-up observation program over six years (2009–2015). Almost 90% of stars that are hosts to planet candidates or confirmed planets were observed. We combine measurements of companions to KOI host stars from different bands to create a comprehensive catalog of projected separations, position angles, and magnitude differences for all detected companion stars (some of which may not be bound). Our compilation includes 2297 companions around 1903 primary stars. From high-resolution imaging, we find that ∼10% (∼30%) of the observed stars have at least one companion detected within 1″ (4″). The true fraction of systems with close (≲4″) companions is larger than the observed one due to the limited sensitivities of the imaging data. We derive correction factors for planet radii caused by the dilution of the transit depth: assuming that planets orbit the primary stars or the brightest companion stars, the average correction factors are 1.06 and 3.09, respectively. The true effect of transit dilution lies in between these two cases and varies with each system. Applying these factors to planet radii decreases the number of KOI planets with radii smaller than 2 R{sub ⊕} by ∼2%–23% and thus affects planet occurrence rates. This effect will also be important for the yield of small planets from future transit missions such as TESS.

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Dynamically Hot Super-Earths from Outer Giant Planet Scattering

The hundreds of multiple planetary systems discovered by the Kepler mission are typically observed to reside in close-in (≲0.5 AU), low-eccentricity, low-inclination orbits. We run N-body experiments to study the effect that unstable outer (≳1 AU) giant planets, whose end orbital configurations resemble those in the Radial Velocity population, have on these close-in multiple super-Earth systems. Our experiments show that the giant planets greatly reduce the multiplicity of the inner super-Earths, and the surviving population can have large eccentricities (e≳0.3) and inclinations (i≳20{sup ∘}) at levels that anti-correlate with multiplicity. Consequently, this model predicts the existence of a population of dynamically hot single-transiting planets with typical eccentricities and inclinations of ∼0.1–0.5 and ∼10°–40°. We show that these results can explain the following observations: (i) the recent eccentricity measurements of Kepler super-Earths from transit durations; (ii) the tentative observation that single-transiting systems have a wider distribution of stellar obliquity angles compared to the multiple-transiting systems; (iii) the architecture of some eccentric super-Earths discovered by Radial Velocity surveys such as HD 125612c. Future observations from TESS will reveal many more dynamically hot single transiting planets, for which follow up radial velocity studies will be able to test our models and see whether they have outer giant planets.

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Determining Empirical Stellar Masses and Radii from Transits and Gaia Parallaxes as Illustrated by Spitzer Observations of KELT-11b

Using the Spitzer Space Telescope, we observed a transit at 3.6 μm of KELT-11b. We also observed three partial planetary transits from the ground. We simultaneously fit these observations, ground-based photometry from Pepper et al., radial velocity data from Pepper et al., and a spectral energy distribution (SED) model using catalog magnitudes and the Hipparcos parallax to the system. The only significant difference between our results and those of Pepper et al. is that we find the orbital period to be shorter by 37 s, 4.73610 ± 0.00003 versus 4.73653 ± 0.00006 days, and we measure a transit center time of BJD{sub TDB} 2457483.4310 ± 0.0007, which is 42 minutes earlier than predicted. Using our new photometry, we precisely measure the density of the star KELT-11 to 4%. By combining the parallax and catalog magnitudes of the system, we are able to measure the radius of KELT-11b essentially empirically. Coupled with the stellar density, this gives a parallactic mass and radius of 1.8 M{sub ⊙} and 2.9 R{sub ⊙}, which are each approximately 1σ higher than the adopted model-estimated mass and radius. If we conduct the same fit using the expected parallax uncertainty from the final Gaia data release, this difference increases to 4σ. The differences between the model and parallactic masses and radii for KELT-11 demonstrate the role that precise Gaia parallaxes, coupled with simultaneous photometric, radial velocity, and SED fitting, can play in determining stellar and planetary parameters. With high-precision photometry of transiting planets and high-precision Gaia parallaxes, the parallactic mass and radius uncertainties of stars become 1% and 3%, respectively. TESS is expected to discover 60–80 systems where these measurements will be possible. These parallactic mass and radius measurements have uncertainties small enough that they may provide observational input into the stellar models themselves.

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Three’s Company: An Additional Non-transiting Super-Earth in the Bright HD 3167 System, and Masses for All Three Planets

HD 3167 is a bright (V = 8.9), nearby K0 star observed by the NASA K2 mission (EPIC 220383386), hosting two small, short-period transiting planets. Here we present the results of a multi-site, multi-instrument radial-velocity campaign to characterize the HD 3167 system. The masses of the transiting planets are 5.02 ± 0.38 M{sub ⊕} for HD 3167 b, a hot super-Earth with a likely rocky composition (ρ{sub b} = 5.60{sub −1.43}{sup +2.15} g cm{sup −3}), and 9.80{sub −1.24}{sup +1.30} M{sub ⊕} for HD 3167 c, a warm sub-Neptune with a likely substantial volatile complement (ρ{sub c} = 1.97{sub −0.59}{sup +0.94} g cm{sup −3}). We explore the possibility of atmospheric composition analysis and determine that planet c is amenable to transmission spectroscopy measurements, and planet b is a potential thermal emission target. We detect a third, non-transiting planet, HD 3167 d, with a period of 8.509 ± 0.045 d (between planets b and c) and a minimum mass of 6.90 ± 0.71 M{sub ⊕}. We are able to constrain the mutual inclination of planet d with planets b and c: we rule out mutual inclinations below 1.°3 because we do not observe transits of planet d. From 1.°3 to 40°, there are viewing geometries invoking special nodal configurations, which result in planet d not transiting some fraction of the time. From 40° to 60°, Kozai–Lidov oscillations increase the system’s instability, but it can remain stable for up to 100 Myr. Above 60°, the system is unstable. HD 3167 promises to be a fruitful system for further study and a preview of the many exciting systems expected from the upcoming NASA TESS mission.

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Bright Opportunities for Atmospheric Characterization of Small Planets: Masses and Radii of K2-3 b, c, and d and GJ3470 b from Radial Velocity Measurements and Spitzer Transits

We report improved masses, radii, and densities for four planets in two bright M-dwarf systems, K2-3 and GJ3470, derived from a combination of new radial velocity and transit observations. Supplementing K2 photometry with follow-up Spitzer transit observations refined the transit ephemerides of K2-3 b, c, and d by over a factor of 10. We analyze ground-based photometry from the Evryscope and Fairborn Observatory to determine the characteristic stellar activity timescales for our Gaussian Process fit, including the stellar rotation period and activity region decay timescale. The stellar rotation signals for both stars are evident in the radial velocity data and is included in our fit using a Gaussian process trained on the photometry. We find the masses of K2-3 b, K2-3 c, and GJ3470 b to be 6.48{sub −0.93}{sup +0.99}, 2.14{sub −1.04}{sup +1.08}, and 12.58{sub −1.28}{sup +1.31} M {sub ⊕,} respectively. K2-3 d was not significantly detected and has a 3σ upper limit of 2.80 M {sub ⊕}. These two systems are training cases for future TESS systems; due to the low planet densities (ρ < 3.7 g cm{sup −3}) and bright host stars (K < 9 mag), they are among the best candidates for transmission spectroscopy in order to characterize the atmospheric compositions of small planets.

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Ultra-short-period Planets from Secular Chaos

Over 100 rocky planets orbiting Sun-like stars in very short orbital periods (≲1 day) have been discovered by the Kepler mission. The origin of these planets, known as ultra-short-period (USP) planets, remains elusive. Here, we propose that most of these planets, originally at periods of ∼5–10 days, reach their current orbits via high-eccentricity migration. In a scaled-down version of the dynamics that may have been experienced by their high-mass analogs, the hot Jupiters, these planets reach high eccentricities via chaotic secular interactions with their companion planets and then undergo orbital circularization due to dissipation from tides raised on the planet. This proposal is motivated by the following observations: planetary systems observed by Kepler often contain several super-Earths with non-negligible eccentricities and inclinations, possibly extending beyond ∼au distances; by contrast, only a small fraction of USP planets have known transiting companions, which are generally not closely spaced, and we argue that most of them should have companions with periods ≳10 days. The proposed scenario naturally explains the observation that most USP planets have significantly more distant transiting companions compared to their counterparts at slightly longer periods (1–3 days). Our model predicts that USP planets should have: (i) spin–orbit angles, and inclinations relative to outer planets, in the range of ∼10–50°; (ii) several outer planetary companions extending beyond ∼1 au distances. Both of these predictions may be tested by TESS and its follow-up observations.

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Revisiting the HIP 41378 System with K2 and Spitzer

We present new observations of the multiplanet system HIP 41378, a bright star (V = 8.9, K {sub s} = 7.7) with five known transiting planets. Previous K2 observations showed multiple transits of two Neptune-sized bodies and single transits of three larger planets (R {sub P} = 0.33R {sub J}, 0.47R {sub J}, 0.88R {sub J}). K2 recently observed the system again in Campaign 18 (C18). We observe one new transit each of two of the larger planets d/f, giving maximal orbital periods of 1114/1084 days, as well as integer divisions of these values down to a lower limit of about 50 days. We use all available photometry to determine the eccentricity distributions of HIP 41378 d and f, finding that periods ≲300 days require non-zero eccentricity. We check for overlapping orbits of planets d and f to constrain their mutual periods, finding that short periods (P < 300 days) for planet f are disfavored. We also observe transits of planets b and c with Spitzer/Infrared Array Camera (IRAC), which we combine with the K2 observations to search for transit timing variations (TTVs). We find a linear ephemeris for planet b, but see a significant TTV signal for planet c. The ability to recover the two smaller planets with Spitzer shows that this fascinating system will continue to be detectable with Spitzer, CHEOPS, TESS, and other observatories, allowing us to precisely determine the periods of d and f, characterize the TTVs of planet c, recover the transits of planet e, and further enhance our view of this remarkable dynamical laboratory.

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