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Eric L. N. Jensen

Publications and source records attributed to Eric L. N. Jensen.

At least 73 records · Page 4Linked to original sources

The TESS-Keck Survey II: An Ultra-Short Period Rocky Planet and its Siblings Transiting the Galactic Thick-Disk Star TOI-561

We report the discovery of TOI-561, a multi-planet system in the galactic thick disk that contains a rocky, ultra-short period planet (USP). This bright ($V=10.2$) star hosts three small transiting planets identified in photometry from the NASA TESS mission: TOI-561 b (TOI-561.02, P=0.44 days, $R_b = 1.45\pm0.11\,R_\oplus$), c (TOI-561.01, P=10.8 days, $R_c=2.90\pm0.13\,R_\oplus$), and d (TOI-561.03, P=16.3 days, $R_d=2.32\pm0.16\,R_\oplus$). The star is chemically ([Fe/H]$=-0.41\pm0.05$, [$α$/H]$=+0.23\pm0.05$) and kinematically consistent with the galactic thick disk population, making TOI-561 one of the oldest ($10\pm3\,$Gyr) and most metal-poor planetary systems discovered yet. We dynamically confirm planets b and c with radial velocities from the W. M. Keck Observatory High Resolution Echelle Spectrometer. Planet b has a mass and density of $3.2\pm0.8\,M_\oplus$ and $5.5^{+2.0}_{-1.6}\,$g$\,$cm$^{-3}$, consistent with a rocky composition. Its lower-than-average density is consistent with an iron-poor composition, although an Earth-like iron-to-silicates ratio is not ruled out. Planet c is $7.0\pm2.3\,M_\oplus$ and $1.6\pm0.6\,$g$\,$cm$^{-3}$, consistent with an interior rocky core overlaid with a low-mass volatile envelope. Several attributes of the photometry for planet d (which we did not detect dynamically) complicate the analysis, but we vet the planet with high-contrast imaging, ground-based photometric follow-up and radial velocities. TOI-561 b is the first rocky world around a galactic thick-disk star confirmed with radial velocities and one of the best rocky planets for thermal emission studies.

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Two young planetary systems around field stars with ages between 20-320 Myr from TESS

Planets around young stars trace the early evolution of planetary systems. We report the discovery and validation of two planetary systems with ages $\lesssim 300$ Myr from observations by the Transiting Exoplanet Survey Satellite. TOI-251 is a 40-320 Myr old G star hosting a 2.74 +0.18/-0.18 REarth mini-Neptune with a 4.94 day period. TOI-942 is a 20-160 Myr old K star hosting a system of inflated Neptune-sized planets, with TOI-942b orbiting with a period of 4.32 days, with a radius of 4.81 +0.20/-0.20 REarth, and TOI-942c orbiting in a period of 10.16 days with a radius of 5.79 +0.19/-0.18 REarth. Though we cannot place either host star into a known stellar association or cluster, we can estimate their ages via their photometric and spectroscopic properties. Both stars exhibit significant photometric variability due to spot modulation, with measured rotation periods of $\sim 3.5$ days. These stars also exhibit significant chromospheric activity, with age estimates from the chromospheric calcium emission lines and X-ray fluxes matching that estimated from gyrochronology. Both stars also exhibit significant lithium absorption, similar in equivalent width to well-characterized young cluster members. TESS has the potential to deliver a population of young planet-bearing field stars, contributing significantly to tracing the properties of planets as a function of their age.

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Vetting of 384 TESS Objects of Interest with TRICERATOPS and Statistical Validation of 12 Planet Candidates

We present TRICERATOPS, a new Bayesian tool that can be used to vet and validate TESS Objects of Interest (TOIs). We test the tool on 68 TOIs that have been previously confirmed as planets or rejected as astrophysical false positives. By looking in the false positive probability (FPP) -- nearby false positive probability (NFPP) plane, we define criteria that TOIs must meet to be classified as validated planets (FPP < 0.015 and NFPP < 10^-3), likely planets (FPP < 0.5 and NFPP < 10^-3), and likely nearby false positives (NFPP > 10^-1). We apply this procedure on 384 unclassified TOIs and statistically validate 12, classify 125 as likely planets, and classify 52 as likely nearby false positives. Of the 12 statistically validated planets, 9 are newly validated. TRICERATOPS is currently the only TESS vetting and validation tool that models transits from nearby contaminant stars in addition to the target star. We therefore encourage use of this tool to prioritize follow-up observations that confirm bona fide planets and identify false positives originating from nearby stars.

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TOI 122b and TOI 237b, two small warm planets orbiting inactive M dwarfs, found by \textit{TESS}

We report the discovery and validation of TOI 122b and TOI 237b, two warm planets transiting inactive M dwarfs observed by \textit{TESS}. Our analysis shows TOI 122b has a radius of 2.72$\pm$0.18 R$_\rm{e}$ and receives 8.8$\pm$1.0$\times$ Earth's bolometric insolation, and TOI 237b has a radius of 1.44$\pm$0.12 R$_\rm{e}$ and receives 3.7$\pm$0.5$\times$ Earth insolation, straddling the 6.7$\times$ Earth insolation that Mercury receives from the sun. This makes these two of the cooler planets yet discovered by \textit{TESS}, even on their 5.08-day and 5.43-day orbits. Together, they span the small-planet radius valley, providing useful laboratories for exploring volatile evolution around M dwarfs. Their relatively nearby distances (62.23$\pm$0.21 pc and 38.11$\pm$0.23 pc, respectively) make them potentially feasible targets for future radial velocity follow-up and atmospheric characterization, although such observations may require substantial investments of time on large telescopes.

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TOI-824 b: A New Planet on the Lower Edge of the Hot Neptune Desert

We report the detection of a transiting hot Neptune exoplanet orbiting TOI-824 (SCR J1448-5735), a nearby (d = 64 pc) K4V star, using data from the \textit{Transiting Exoplanet Survey Satellite} (TESS). The newly discovered planet has a radius, $R_{\rm{p}}$ = 2.93 $\pm$ 0.20 R$_{\oplus}$, and an orbital period of 1.393 days. Radial velocity measurements using the Planet Finder Spectrograph (PFS) and the High Accuracy Radial velocity Planet Searcher (HARPS) spectrograph confirm the existence of the planet and we estimate its mass to be $M_{\rm{p}}$ = 18.47 $\pm$ 1.84 M$_{\oplus}$. The planet's mean density is $ρ_{\rm{p}}$ = 4.03$^{+0.98}_{-0.78}$ g cm$^{-3}$ making it more than twice as dense as Neptune. TOI-824 b's high equilibrium temperature makes the planet likely to have a cloud free atmosphere, and thus an excellent candidate for follow up atmospheric studies. The detectability of TOI-824 b's atmosphere from both ground and space is promising and could lead to the detailed characterization of the most irradiated, small planet at the edge of the hot Neptune desert that has retained its atmosphere to date.

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TESS Reveals a Short-period Sub-Neptune Sibling (HD 86226c) to a Known Long-period Giant Planet

The Transiting Exoplanet Survey Satellite mission was designed to find transiting planets around bright, nearby stars. Here we present the detection and mass measurement of a small, short-period ($\approx\,4$\,days) transiting planet around the bright ($V=7.9$), solar-type star HD 86226 (TOI-652, TIC 22221375), previously known to host a long-period ($\sim$1600 days) giant planet. HD 86226c (TOI-652.01) has a radius of $2.16\pm0.08$ $R_{\oplus}$ and a mass of 7.25$^{+1.19}_{-1.12}$ $M_{\oplus}$ based on archival and new radial velocity data. We also update the parameters of the longer-period, not-known-to-transit planet, and find it to be less eccentric and less massive than previously reported. The density of the transiting planet is $3.97$ g cm$^{-3}$, which is low enough to suggest that the planet has at least a small volatile envelope, but the mass fractions of rock, iron, and water are not well-constrained. Given the host star brightness, planet period, and location of the planet near both the ``radius gap'' and the ``hot Neptune desert'', HD 86226c is an interesting candidate for transmission spectroscopy to further refine its composition.

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A remnant planetary core in the hot-Neptune desert

The interiors of giant planets remain poorly understood. Even for the planets in the Solar System, difficulties in observation lead to large uncertainties in the properties of planetary cores. Exoplanets that have undergone rare evolutionary processes provide a route to understanding planetary interiors. Planets found in and near the typically barren hot-Neptune 'desert' (a region in mass-radius space that contains few planets) have proved to be particularly valuable in this regard. These planets include HD149026b, which is thought to have an unusually massive core, and recent discoveries such as LTT9779b and NGTS-4b, on which photoevaporation has removed a substantial part of their outer atmospheres. Here we report observations of the planet TOI-849b, which has a radius smaller than Neptune's but an anomalously large mass of $39.1^{+2.7}_{-2.6}$ Earth masses and a density of $5.2^{+0.7}_{-0.8}$ grams per cubic centimetre, similar to Earth's. Interior structure models suggest that any gaseous envelope of pure hydrogen and helium consists of no more than $3.9^{+0.8}_{-0.9}$ per cent of the total planetary mass. The planet could have been a gas giant before undergoing extreme mass loss via thermal self-disruption or giant planet collisions, or it could have avoided substantial gas accretion, perhaps through gap opening or late formation. Although photoevaporation rates cannot account for the mass loss required to reduce a Jupiter-like gas giant, they can remove a small (a few Earth masses) hydrogen and helium envelope on timescales of several billion years, implying that any remaining atmosphere on TOI-849b is likely to be enriched by water or other volatiles from the planetary interior. We conclude that TOI-849b is the remnant core of a giant planet.

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The First Habitable Zone Earth-sized Planet from TESS. I: Validation of the TOI-700 System

We present the discovery and validation of a three-planet system orbiting the nearby (31.1 pc) M2 dwarf star TOI-700 (TIC 150428135). TOI-700 lies in the TESS continuous viewing zone in the Southern Ecliptic Hemisphere; observations spanning 11 sectors reveal three planets with radii ranging from 1 R$_\oplus$ to 2.6 R$_\oplus$ and orbital periods ranging from 9.98 to 37.43 days. Ground-based follow-up combined with diagnostic vetting and validation tests enable us to rule out common astrophysical false-positive scenarios and validate the system of planets. The outermost planet, TOI-700 d, has a radius of $1.19\pm0.11$ R$_\oplus$ and resides in the conservative habitable zone of its host star, where it receives a flux from its star that is approximately 86% of the Earth's insolation. In contrast to some other low-mass stars that host Earth-sized planets in their habitable zones, TOI-700 exhibits low levels of stellar activity, presenting a valuable opportunity to study potentially-rocky planets over a wide range of conditions affecting atmospheric escape. While atmospheric characterization of TOI-700 d with the James Webb Space Telescope (JWST) will be challenging, the larger sub-Neptune, TOI-700 c (R = 2.63 R$_\oplus$), will be an excellent target for JWST and beyond. TESS is scheduled to return to the Southern Hemisphere and observe TOI-700 for an additional 11 sectors in its extended mission, which should provide further constraints on the known planet parameters and searches for additional planets and transit timing variations in the system.

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TOI-1235 b: a keystone super-Earth for testing radius valley emergence models around early M dwarfs

Small planets on close-in orbits tend to exhibit envelope mass fractions of either effectively zero or up to a few percent depending on their size and orbital period. Models of thermally-driven atmospheric mass loss and of terrestrial planet formation in a gas-poor environment make distinct predictions regarding the location of this rocky/non-rocky transition in period-radius space. Here we present the confirmation of TOI-1235 b ($P=3.44$ days, $r_p=1.738^{+0.087}_{-0.076}$ R$_{\oplus}$), a planet whose size and period are intermediate between the competing model predictions thus making the system an important test case for emergence models of the rocky/non-rocky transition around early M dwarfs ($R_s=0.630\pm 0.015$ R$_{\odot}$, $M_s=0.640\pm 0.016$ M$_{\odot}$). We confirm the TESS planet discovery using reconnaissance spectroscopy, ground-based photometry, high-resolution imaging, and a set of 38 precise radial-velocities from HARPS-N and HIRES. We measure a planet mass of $6.91^{+0.75}_{-0.85}$ M$_{\oplus}$, which implies an iron core mass fraction of $20^{+15}_{-12}$% in the absence of a gaseous envelope. The bulk composition of TOI-1235 b is therefore consistent with being Earth-like and we constrain a H/He envelope mass fraction to be $<0.5$% at 90% confidence. Our results are consistent with model predictions from thermally-driven atmospheric mass loss but not with gas-poor formation, suggesting that the former class of processes remain efficient at sculpting close-in planets around early M dwarfs. Our RV analysis also reveals a strong periodicity close to the first harmonic of the photometrically-determined stellar rotation period that we treat as stellar activity, despite other lines of evidence favoring a planetary origin ($P=21.8^{+0.9}_{-0.8}$ days, $m_p\sin{i}=13.0^{+3.8}_{-5.3}$ M$_{\oplus}$) that cannot be firmly ruled out by our data.

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A pair of TESS planets spanning the radius valley around the nearby mid-M dwarf LTT 3780

We present the confirmation of two new planets transiting the nearby mid-M dwarf LTT 3780 (TIC 36724087, TOI-732, $V=13.07$, $K_s=8.204$, $R_s$=0.374 R$_{\odot}$, $M_s$=0.401 M$_{\odot}$, d=22 pc). The two planet candidates are identified in a single TESS sector and are validated with reconnaissance spectroscopy, ground-based photometric follow-up, and high-resolution imaging. With measured orbital periods of $P_b=0.77$ days, $P_c=12.25$ days and sizes $r_{p,b}=1.33\pm 0.07$ R$_{\oplus}$, $r_{p,c}=2.30\pm 0.16$ R$_{\oplus}$, the two planets span the radius valley in period-radius space around low mass stars thus making the system a laboratory to test competing theories of the emergence of the radius valley in that stellar mass regime. By combining 63 precise radial-velocity measurements from HARPS and HARPS-N, we measure planet masses of $m_{p,b}=2.62^{+0.48}_{-0.46}$ M$_{\oplus}$ and $m_{p,c}=8.6^{+1.6}_{-1.3}$ M$_{\oplus}$, which indicates that LTT 3780b has a bulk composition consistent with being Earth-like, while LTT 3780c likely hosts an extended H/He envelope. We show that the recovered planetary masses are consistent with predictions from both photoevaporation and from core-powered mass loss models. The brightness and small size of LTT 3780, along with the measured planetary parameters, render LTT 3780b and c as accessible targets for atmospheric characterization of planets within the same planetary system and spanning the radius valley.

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TESS spots a hot Jupiter with an inner transiting Neptune

Hot Jupiters are rarely accompanied by other planets within a factor of a few in orbital distance. Previously, only two such systems have been found. Here, we report the discovery of a third system using data from the Transiting Exoplanet Survey Satellite (TESS). The host star, TOI-1130, is an 11th magnitude K-dwarf in the Gaia G band. It has two transiting planets: a Neptune-sized planet ($3.65\pm 0.10$ $R_E$) with a 4.1-day period, and a hot Jupiter ($1.50^{+0.27}_{-0.22}$ $R_J$) with an 8.4-day period. Precise radial-velocity observations show that the mass of the hot Jupiter is $0.974^{+0.043}_{-0.044}$ $M_J$. For the inner Neptune, the data provide only an upper limit on the mass of 0.17 $M_J$ (3$σ$). Nevertheless, we are confident the inner planet is real, based on follow-up ground-based photometry and adaptive optics imaging that rule out other plausible sources of the TESS transit signal. The unusual planetary architecture of and the brightness of the host star make TOI-1130 a good test case for planet formation theories, and an attractive target for future spectroscopic observations.

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LHS 1815b: The First Thick-Disk Planet Detected By TESS

We report the first discovery of a thick-disk planet, LHS 1815b (TOI-704b, TIC 260004324), detected in the TESS survey. LHS 1815b transits a bright (V = 12.19 mag, K = 7.99 mag) and quiet M dwarf located $ 29.87\pm0.02 pc$ away with a mass of $0.502\pm0.015 M_{\odot}$ and a radius of $0.501\pm0.030 R_{\odot}$. We validate the planet by combining space and ground-based photometry, spectroscopy, and imaging. The planet has a radius of $1.088\pm 0.064 R_{\oplus}$ with a $3 σ$ mass upper-limit of $8.7 M_{\oplus}$. We analyze the galactic kinematics and orbit of the host star LHS1815 and find that it has a large probability ($P_{thick}/P_{thin} = 6482$) to be in the thick disk with a much higher expected maximal height ($Z_{max} = 1.8 kpc$) above the Galactic plane compared with other TESS planet host stars. Future studies of the interior structure and atmospheric properties of planets in such systems using for example the upcoming James Webb Space Telescope (JWST), can investigate the differences in formation efficiency and evolution for planetary systems between different Galactic components (thick and thin disks, and halo).

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GJ 1252 b: A 1.2 $R_{\oplus}$ planet transiting an M3-dwarf at 20.4 pc

We report the discovery of GJ 1252 b, a planet with a radius of 1.193 $\pm$ 0.074 $R_{\oplus}$ and an orbital period of 0.52 days around an M3-type star (0.381 $\pm$ 0.019 $M_{\odot}$, 0.391 $\pm$ 0.020 $R_{\odot}$) located 20.385 $\pm$ 0.019 pc away. We use TESS data, ground-based photometry and spectroscopy, Gaia astrometry, and high angular resolution imaging to show that the transit signal seen in the TESS data must originate from a transiting planet. We do so by ruling out all false positive scenarios that attempt to explain the transit signal as originating from an eclipsing stellar binary. Precise Doppler monitoring also leads to a tentative mass measurement of 2.09 $\pm$ 0.56 $M_{\oplus}$. The host star proximity, brightness ($V$ = 12.19 mag, $K$ = 7.92 mag), low stellar activity, and the system's short orbital period make this planet an attractive target for detailed characterization, including precise mass measurement, looking for other objects in the system, and planet atmosphere characterization.

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

We present the discoveries of KELT-25b (TIC 65412605, TOI-626.01) and KELT-26b (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 \textit{TESS} photometry. KELT-25b is on a 4.40-day orbit around the V = 9.66 star CD-24 5016 ($T_{\rm eff} = 8280^{+440}_{-180}$ K, $M_{\star}$ = $2.18^{+0.12}_{-0.11}$ $M_{\odot}$), while KELT-26b is on a 3.34-day orbit around the V = 9.95 star HD 134004 ($T_{\rm eff}$ =$8640^{+500}_{-240}$ K, $M_{\star}$ = $1.93^{+0.14}_{-0.16}$ $M_{\odot}$), which is likely an Am star. We have confirmed the sub-stellar nature of both companions through detailed characterization of each system using ground-based and \textit{TESS} photometry, radial velocity measurements, Doppler Tomography, and high-resolution imaging. For KELT-25, we determine a companion radius of $R_{\rm P}$ = $1.64^{+0.039}_{-0.043}$ $R_{\rm J}$, and a 3-sigma upper limit on the companion's mass of $\sim64~M_{\rm J}$. For KELT-26b, we infer a planetary mass and radius of $M_{\rm P}$ = $1.41^{+0.43}_{-0.51}$ $M_{\rm J}$ and $R_{\rm P}$ = $1.940^{+0.060}_{-0.058}$ $R_{\rm J}$. From Doppler Tomographic observations, we find KELT-26b to reside in a highly misaligned orbit. This conclusion is weakly corroborated by a subtle asymmetry in the transit light curve from the \textit{TESS} data. KELT-25b appears to be in a well-aligned, prograde orbit, and the system is likely a member of a cluster or moving group.

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HD 213885b: A transiting 1-day-period super-Earth with an Earth-like composition around a bright ($V=7.9$) star unveiled by TESS

We report the discovery of the 1.008-day, ultra-short period (USP) super-Earth HD 213885b (TOI-141b) orbiting the bright ($V=7.9$) star HD 213885 (TOI-141, TIC 403224672), detected using photometry from the recently launched TESS mission. Using FEROS, HARPS and CORALIE radial-velocities, we measure a precise mass of $8.8\pm0.6$ $M_\oplus$ for this $1.74 \pm 0.05$ $R_\oplus$ exoplanet, which provides enough information to constrain its bulk composition, which is similar to Earth's but enriched in iron. The radius, mass and stellar irradiation of HD 213885b are, given our data, very similar to 55 Cancri e, making this exoplanet a good target to perform comparative exoplanetology of short period, highly irradiated super-Earths. Our precise radial-velocities reveal an additional $4.78$-day signal which we interpret as arising from a second, non-transiting planet in the system, HD 213885c (TOI-141c), whose minimum mass of $19.95\pm 1.4$ $M_\oplus$ makes it consistent with being a Neptune-mass exoplanet. The HD 213885 system is very interesting from the perspective of future atmospheric characterization, being the second brightest star to host an ultra-short period transiting super-Earth (with the brightest star being, in fact, 55 Cancri). Prospects for characterization with present and future observatories are discussed.

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KELT-24b: A 5M$_{\rm J}$ Planet on a 5.6 day Well-Aligned Orbit around the Young V=8.3 F-star HD 93148

We present the discovery of KELT-24 b, a massive hot Jupiter orbiting a bright (V=8.3 mag, K=7.2 mag) young F-star with a period of 5.6 days. The host star, KELT-24 (HD 93148), has a $T_{\rm eff}$ =$6509^{+50}_{-49}$ K, a mass of $M_{*}$ = $1.460^{+0.055}_{-0.059}$ $M_{\odot}$, radius of $R_{*}$ = $1.506\pm0.022$ $R_{\odot}$, and an age of $0.78^{+0.61}_{-0.42}$ Gyr. Its planetary companion (KELT-24 b) has a radius of $R_{\rm P}$ = $1.272\pm0.021$ $R_{\rm J}$, a mass of $M_{\rm P}$ = $5.18^{+0.21}_{-0.22}$ $M_{\rm J}$, and from Doppler tomographic observations, we find that the planet's orbit is well-aligned to its host star's projected spin axis ($λ$ = $2.6^{+5.1}_{-3.6}$). The young age estimated for KELT-24 suggests that it only recently started to evolve from the zero-age main sequence. KELT-24 is the brightest star known to host a transiting giant planet with a period between 5 and 10 days. Although the circularization timescale is much longer than the age of the system, we do not detect a large eccentricity or significant misalignment that is expected from dynamical migration. The brightness of its host star and its moderate surface gravity make KELT-24b an intriguing target for detailed atmospheric characterization through spectroscopic emission measurements since it would bridge the current literature results that have primarily focused on lower mass hot Jupiters and a few brown dwarfs.

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TOI-150b and TOI-163b: two transiting hot Jupiters, one eccentric and one inflated, revealed by TESS near and at the edge of the JWST CVZ

We present the discovery of TYC9191-519-1b (TOI-150b, TIC 271893367) and HD271181b (TOI-163b, TIC 179317684), two hot Jupiters initially detected using 30-minute cadence Transiting Exoplanet Survey Satellite TESS photometry from Sector 1 and thoroughly characterized through follow-up photometry (CHAT, Hazelwood, LCO/CTIO, El Sauce, TRAPPIST-S), high-resolution spectroscopy (FEROS, CORALIE) and speckle imaging (Gemini/DSSI), confirming the planetary nature of the two signals. A simultaneous joint fit of photometry and radial velocity using a new fitting package juliet reveals that TOI-150b is a $1.254\pm0.016\ R_J$, massive ($2.61^{+0.19}_{-0.12}\ M_J$) hot Jupiter in a $5.857$-day orbit, while TOI-163b is an inflated ($R_P$ = $1.478^{+0.022}_{-0.029} R_J$, $M_P$ = $1.219\pm0.11 M_J$) hot Jupiter on a $P$ = $4.231$-day orbit; both planets orbit F-type stars. A particularly interesting result is that TOI-150b shows an eccentric orbit ($e=0.262^{+0.045}_{-0.037}$), which is quite uncommon among hot Jupiters. We estimate that this is consistent, however, with the circularization timescale which is slightly larger than the age of the system. These two hot Jupiters are both prime candidates for further characterization --- in particular, both are excellent candidates for determining spin-orbit alignments via the Rossiter-McLaughlin (RM) effect and for characterizing atmospheric thermal structures using secondary eclipse observations considering they are both located closely to the James Webb Space Telescope (JWST) Continuous Viewing Zone (CVZ).

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The Degree of Alignment Between Circumbinary Disks and Their Binary Hosts

All four circumbinary (CB) protoplanetary disks orbiting short-period ($P < 20$ day) double-lined spectroscopic binaries (SB2s)---a group that includes UZ Tau E, for which we present new ALMA data---exhibit sky-plane inclinations $i_{\rm disk}$ which match, to within a few degrees, the sky-plane inclinations $i_\star$ of their stellar hosts. Although for these systems the true mutual inclinations $θ$ between disk and binary cannot be directly measured because relative nodal angles are unknown, the near-coincidence of $i_{\rm disk}$ and $i_\star$ suggests that $θ$ is small for these most compact of systems. We confirm this hypothesis using a hierarchical Bayesian analysis, showing that 68% of CB disks around short-period SB2s have $θ< 3.0^\circ$. Near co-planarity of CB disks implies near co-planarity of CB planets discovered by Kepler, which in turn implies that the occurrence rate of close-in CB planets is similar to that around single stars. By contrast, at longer periods ranging from $30-10^5$ days (where the nodal degeneracy can be broken via, e.g., binary astrometry), CB disks exhibit a wide range of mutual inclinations, from co-planar to polar. Many of these long-period binaries are eccentric, as their component stars are too far separated to be tidally circularized. We discuss how theories of binary formation and disk-binary gravitational interactions can accommodate all these observations.

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