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Steve B. Howell

Publications and source records attributed to Steve B. Howell.

At least 109 records · Page 6Linked to original sources

A Transiting Super-Earth in the Radius Valley and An Outer Planet Candidate Around HD 307842

We report the confirmation of a TESS-discovered transiting super-Earth planet orbiting a mid-G star, HD 307842 (TOI-784). The planet has a period of 2.8 days, and the radial velocity (RV) measurements constrain the mass to be 9.67+0.83/-0.82 [Earth Masses]. We also report the discovery of an additional planet candidate on an outer orbit that is most likely non-transiting. The possible periods of the planet candidate are approximately 20 to 63 days, with the corresponding RV semi-amplitudes expected to range from 3.2 to 5.4 m/s and minimum masses from 12.6 to 31.1 [Earth Masses]. The radius of the transiting planet (planet b) is 1.93+0.11/-0.09 [Earth Radii], which results in a mean density of 7.4+1.4/-1.2 g/cm^3 suggesting that TOI-784b is likely to be a rocky planet though it has a comparable radius to a sub-Neptune. We found TOI-784b is located at the lower edge of the so-called ``radius valley'' in the radius vs. insolation plane, which is consistent with the photoevaporation or core-powered mass loss prediction. The TESS data did not reveal any significant transit signal of the planet candidate, and our analysis shows that the orbital inclinations of planet b and the planet candidate are 88.60+0.84/-0.86 degrees and <= 88.3-89.2 degrees, respectively. More RV observations are needed to determine the period and mass of the second object, and search for additional planets in this system.

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A Mini-Neptune Orbiting the Metal-poor K Dwarf BD+29 2654

We report the discovery and Doppler mass measurement of a 7.4-day 2.3-$R_\oplus$ mini-Neptune around a metal-poor K dwarf BD+29 2654 (TOI-2018). Based on a high-resolution Keck/HIRES spectrum, the Gaia parallax, and multi-wavelength photometry from the ultraviolet to the mid-infrared, we found that the host star has $T_{\text{eff}}=4174^{+34}_{-42}$ K, $\log{g}=4.62^{+0.02}_{-0.03}$, $[\text{Fe/H}]=-0.58\pm0.18$, $M_{\ast}=0.57\pm0.02~M_{\odot}$, and $R_{\ast}=0.62\pm0.01~R_{\odot}$. Precise Doppler measurements with Keck/HIRES revealed a planetary mass of $M_{\text{p}}=9.2\pm2.1~M_{\oplus}$ for TOI-2018 b. TOI-2018 b has a mass and radius that are consistent with an Earth-like core with a $\sim1\%$-by-mass hydrogen/helium envelope, or an ice-rock mixture. The mass of TOI-2018 b is close to the threshold for run-away accretion and hence giant planet formation. Such a threshold is predicted to be around 10$M_\oplus$ or lower for a low-metallicity (low-opacity) environment. If TOI-2018 b is a planetary core that failed to undergo run-away accretion, it may underline the reason why giant planets are rare around low-metallicity host stars (one possibility is their shorter disk lifetimes). With a K-band magnitude of 7.1, TOI-2018 b may be a suitable target for transmission spectroscopy with the James Webb Space Telescope. The system is also amenable to metastable Helium observation; the detection of a Helium exosphere would help distinguish between a H/He enveloped planet and a water world.

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TESS and CHEOPS Discover Two Warm Sub-Neptunes Transiting the Bright K-dwarf HD 15906

We report the discovery of two warm sub-Neptunes transiting the bright (G = 9.5 mag) K-dwarf HD 15906 (TOI 461, TIC 4646810). This star was observed by the Transiting Exoplanet Survey Satellite (TESS) in sectors 4 and 31, revealing two small transiting planets. The inner planet, HD 15906 b, was detected with an unambiguous period but the outer planet, HD 15906 c, showed only two transits separated by $\sim$ 734 days, leading to 36 possible values of its period. We performed follow-up observations with the CHaracterising ExOPlanet Satellite (CHEOPS) to confirm the true period of HD 15906 c and improve the radius precision of the two planets. From TESS, CHEOPS and additional ground-based photometry, we find that HD 15906 b has a radius of 2.24 $\pm$ 0.08 R$_\oplus$ and a period of 10.924709 $\pm$ 0.000032 days, whilst HD 15906 c has a radius of 2.93$^{+0.07}_{-0.06}$ R$_\oplus$ and a period of 21.583298$^{+0.000052}_{-0.000055}$ days. Assuming zero bond albedo and full day-night heat redistribution, the inner and outer planet have equilibrium temperatures of 668 $\pm$ 13 K and 532 $\pm$ 10 K, respectively. The HD 15906 system has become one of only six multiplanet systems with two warm ($\lesssim$ 700 K) sub-Neptune sized planets transiting a bright star (G $\leq$ 10 mag). It is an excellent target for detailed characterisation studies to constrain the composition of sub-Neptune planets and test theories of planet formation and evolution.

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TESS spots a mini-neptune interior to a hot saturn in the TOI-2000 system

Hot jupiters (P < 10 d, M > 60 $\mathrm{M}_\oplus$) are almost always found alone around their stars, but four out of hundreds known have inner companion planets. These rare companions allow us to constrain the hot jupiter's formation history by ruling out high-eccentricity tidal migration. Less is known about inner companions to hot Saturn-mass planets. We report here the discovery of the TOI-2000 system, which features a hot Saturn-mass planet with a smaller inner companion. The mini-neptune TOI-2000 b ($2.70 \pm 0.15 \,\mathrm{R}_\oplus$, $11.0 \pm 2.4 \,\mathrm{M}_\oplus$) is in a 3.10-day orbit, and the hot saturn TOI-2000 c ($8.14^{+0.31}_{-0.30} \,\mathrm{R}_\oplus$, $81.7^{+4.7}_{-4.6} \,\mathrm{M}_\oplus$) is in a 9.13-day orbit. Both planets transit their host star TOI-2000 (TIC 371188886, V = 10.98, TESS magnitude = 10.36), a metal-rich ([Fe/H] = $0.439^{+0.041}_{-0.043}$) G dwarf 174 pc away. TESS observed the two planets in sectors 9-11 and 36-38, and we followed up with ground-based photometry, spectroscopy, and speckle imaging. Radial velocities from CHIRON, FEROS, and HARPS allowed us to confirm both planets by direct mass measurement. In addition, we demonstrate constraining planetary and stellar parameters with MIST stellar evolutionary tracks through Hamiltonian Monte Carlo under the PyMC framework, achieving higher sampling efficiency and shorter run time compared to traditional Markov chain Monte Carlo. Having the brightest host star in the V band among similar systems, TOI-2000 b and c are superb candidates for atmospheric characterization by the JWST, which can potentially distinguish whether they formed together or TOI-2000 c swept along material during migration to form TOI-2000 b.

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Kepler's Last Planet Discoveries: Two New Planets and One Single-Transit Candidate from K2 Campaign 19

The Kepler space telescope was responsible for the discovery of over 2,700 confirmed exoplanets, more than half of the total number of exoplanets known today. These discoveries took place during both Kepler's primary mission, when it spent 4 years staring at the same part of the sky, and its extended K2 mission, when a mechanical failure forced it to observe different parts of the sky along the ecliptic. At the very end of the mission, when Kepler was exhausting the last of its fuel reserves, it collected a short set of observations known as K2 Campaign 19. So far, no planets have been discovered in this dataset because it only yielded about a week of high-quality data. Here, we report some of the last planet discoveries made by Kepler in the Campaign 19 dataset. We conducted a visual search of the week of high-quality Campaign 19 data and identified three possible planet transits. Each planet candidate was originally identified with only one recorded transit, from which we were able to estimate the planets' radii and estimate the semimajor axes and orbital periods. Analysis of lower-quality data collected after low fuel pressure caused the telescope's pointing precision to suffer revealed additional transits for two of these candidates, allowing us to statistically validate them as genuine exoplanets. We also tentatively confirm the transits of one planet with TESS. These discoveries demonstrate Kepler's exoplanet detection power, even when it was literally running on fumes.

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TOI-1859b: A 64-Day Warm Jupiter on an Eccentric and Misaligned Orbit

Warm Jupiters are close-in giant planets with relatively large planet-star separations (i.e., $10< a/R_\star <100$). Given their weak tidal interactions with their host stars, measurements of stellar obliquity may be used to probe the initial obliquity distribution and dynamical history for close-in gas giants. Using spectroscopic observations, we confirm the planetary nature of TOI-1859b and determine the stellar obliquity of TOI-1859 to be $λ= 38.9^{+2.8}_{-2.7}°$ relative to its planetary companion using the Rossiter-McLaughlin effect. TOI-1859b is a 64-day warm Jupiter orbiting around a late-F dwarf and has an orbital eccentricity of $0.57^{+0.12}_{-0.16}$, inferred purely from transit light curves. The eccentric and misaligned orbit of TOI-1859b is likely an outcome of dynamical interactions, such as planet-planet scattering and planet-disk resonance crossing.

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Revised Properties and Dynamical History for the HD 17156 System

From the thousands of known exoplanets, those that transit bright host stars provide the greatest accessibility toward detailed system characterization. The first known such planets were generally discovered using the radial velocity technique, then later found to transit. HD 17156b is particularly notable among these initial discoveries because it diverged from the typical hot Jupiter population, occupying a 21.2 day eccentric ($e = 0.68$) orbit, offering preliminary insights into the evolution of planets in extreme orbits. Here we present new data for this system, including ground and space-based photometry, radial velocities, and speckle imaging, that further constrain the system properties and stellar/planetary multiplicity. These data include photometry from the Transiting Exoplanet Survey Satellite (TESS) that cover five transits of the known planet. We show that the system does not harbor any additional giant planets interior to 10 AU. The lack of stellar companions and the age of the system indicate that the eccentricity of the known planet may have resulted from a previous planet-planet scattering event. We provide the results from dynamical simulations that suggest possible properties of an additional planet that culminated in ejection from the system, leaving a legacy of the observed high eccentricity for HD 17156b.

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VaTEST II: Statistical Validation of 11 TESS-Detected Exoplanets Orbiting K-type Stars

NASA's Transiting Exoplanet Survey Satellite (TESS) is an all-sky survey mission designed to find transiting exoplanets orbiting nearby bright stars. It has identified more than 329 transiting exoplanets, and almost 6,000 candidates remain unvalidated. In this manuscript, we discuss the findings from the ongoing VaTEST (Validation of Transiting Exoplanets using Statistical Tools) project, which aims to validate new exoplanets for further characterization. We validated 11 new exoplanets by examining the light curves of 24 candidates using the LATTE and TESS-Plot tools and computing the False Positive Probabilities using the statistical validation tool TRICERATOPS. These include planets suitable for atmospheric characterization using transmission spectroscopy (TOI-2194b), emission spectroscopy (TOI-3082b and TOI-5704b) and for both transmission and emission spectroscopy (TOI-672b, TOI- 1694b, and TOI-2443b); One super-Earth (TOI-2194b) orbiting a bright (V = 8.42 mag), metal-poor ([Fe/H] = -0.3720 $\pm$ 0.1) star; one short-period Neptune-like planet (TOI-5704) in the Hot Neptune Desert. In total, we validated 1 super-Earth, 7 sub-Neptunes, 1 Neptune-like, and 2 sub-Saturn or super-Neptune-like exoplanets. Additionally, we identify five likely planet candidates (TOI-323, TOI- 1180, TOI-2200, TOI-2408 and TOI-3913) which can be further studied to establish their planetary nature.

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A 1.55 R$_{\oplus}$ habitable-zone planet hosted by TOI-715, an M4 star near the ecliptic South Pole

A new generation of observatories is enabling detailed study of exoplanetary atmospheres and the diversity of alien climates, allowing us to seek evidence for extraterrestrial biological and geological processes. Now is therefore the time to identify the most unique planets to be characterised with these instruments. In this context, we report on the discovery and validation of TOI-715 b, a $R_{\rm b}=1.55\pm 0.06\rm R_{\oplus}$ planet orbiting its nearby ($42$ pc) M4 host (TOI-715/TIC 271971130) with a period $P_{\rm b} = 19.288004_{-0.000024}^{+0.000027}$ days. TOI-715 b was first identified by TESS and validated using ground-based photometry, high-resolution imaging and statistical validation. The planet's orbital period combined with the stellar effective temperature $T_{\rm eff}=3075\pm75~\rm K$ give this planet an instellation $S_{\rm b} = 0.67_{-0.20}^{+0.15}~\rm S_\oplus$, placing it within the most conservative definitions of the habitable zone for rocky planets. TOI-715 b's radius falls exactly between two measured locations of the M-dwarf radius valley; characterising its mass and composition will help understand the true nature of the radius valley for low-mass stars. We demonstrate TOI-715 b is amenable for characterisation using precise radial velocities and transmission spectroscopy. Additionally, we reveal a second candidate planet in the system, TIC 271971130.02, with a potential orbital period of $P_{02} = 25.60712_{-0.00036}^{+0.00031}$ days and a radius of $R_{02} = 1.066\pm0.092\,\rm R_{\oplus}$, just inside the outer boundary of the habitable zone, and near a 4:3 orbital period commensurability. Should this second planet be confirmed, it would represent the smallest habitable zone planet discovered by TESS to date.

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A speckle search for the outer companion of KIC 9832227

We present Gemini-N/'Alopeke speckle observations of KIC 9832227, a system originally predicted to become a red nova. The diffraction limited observations do not find an outer companion between 11 and 678 AU that could be responsible for the period changes of the system.

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Validation of TOI-1221 b: A warm sub-Neptune exhibiting TTVs around a Sun-like star

We present a validation of the long-period ($91.68278^{+0.00032}_{-0.00041}$ days) transiting sub-Neptune planet TOI-1221 b (TIC 349095149.01) around a Sun-like (m$_{\rm V}$=10.5) star. This is one of the few known exoplanets with period >50 days, and belongs to the even smaller subset of which have bright enough hosts for detailed spectroscopic follow-up. We combine TESS light curves and ground-based time-series photometry from PEST (0.3~m) and LCOGT (1.0~m) to analyze the transit signals and rule out nearby stars as potential false positive sources. High-contrast imaging from SOAR and Gemini/Zorro rule out nearby stellar contaminants. Reconnaissance spectroscopy from CHIRON sets a planetary scale upper mass limit on the transiting object (1.1 and 3.5 M$_{\rm Jup}$ at 1$σ$ and 3$σ$, respectively) and shows no sign of a spectroscopic binary companion. We determine a planetary radius of $R_{\rm p} = 2.91^{+0.13}_{-0.12} R_{\oplus}$, placing it in the sub-Neptune regime. With a stellar insolation of $S = 6.06^{+0.85}_{-0.77}\ S_{\oplus}$, we calculate a moderate equilibrium temperature of $T_{\rm eq} =$ 440 K, assuming no albedo and perfect heat redistribution. We find a false positive probability from TRICERATOPS of FPP $ = 0.0014 \pm 0.0003$ as well as other qualitative and quantitative evidence to support the statistical validation of TOI-1221 b. We find significant evidence (>$5σ$) of oscillatory transit timing variations, likely indicative of an additional non-transiting planet.

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Doppler Constraints on Planetary Companions to Nearby Sun-like Stars: An Archival Radial Velocity Survey of Southern Targets for Proposed NASA Direct Imaging Missions

Directly imaging temperate rocky planets orbiting nearby, Sun-like stars with a 6-m-class IR/O/UV space telescope, recently dubbed the Habitable Worlds Observatory, is a high priority goal of the Astro2020 Decadal Survey. To prepare for future direct imaging surveys, the list of potential targets should be thoroughly vetted to maximize efficiency and scientific yield. We present an analysis of archival radial velocity data for southern stars from the NASA/NSF Extreme Precision Radial Velocity Working Group's list of high priority target stars for future direct imaging missions (drawn from the HabEx, LUVOIR, and Starshade studies). For each star, we constrain the region of companion mass and period parameter space we are already sensitive to based on the observational baseline, sampling, and precision of the archival RV data. Additionally, for some of the targets we report new estimates of magnetic activity cycle periods, rotation periods, improved orbital parameters for previously known exoplanets, and new candidate planet signals that require further vetting or observations to confirm. Our results show that for many of these stars we are not yet sensitive to even Saturn-mass planets in the habitable zone, let alone smaller planets, highlighting the need for future EPRV vetting efforts before the launch of a direct imaging mission. We present evidence that the candidate temperate super-Earth exoplanet HD 85512 b is most likely due to the star's rotation, and report an RV acceleration for delta Pav which supports the existence of a distant giant planet previously inferred from astrometry.

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TOI-4562 b: A highly eccentric temperate Jupiter analog orbiting a young field star

We report the discovery of TOI-4562 b (TIC-349576261), a Jovian planet orbiting a young F7V-type star, younger than the Praesepe/Hyades clusters (< $700$ Myr). This planet stands out because of its unusually long orbital period for transiting planets with known masses ($P_{\mathrm{orb}}$ = $225.11781^{+0.00025}_{-0.00022}$ days), and because it has a substantial eccentricity ($e$ = $0.76^{+0.02}_{-0.02}$). The location of TOI-4562 near the southern continuous viewing zone of TESS allowed observations throughout 25 sectors, enabling an unambiguous period measurement from TESS alone. Alongside the four available TESS transits, we performed follow-up photometry using the South African Astronomical Observatory node of the Las Cumbres Observatory, and spectroscopy with the CHIRON spectrograph on the 1.5 m SMARTS telescope. We measure a radius of $1.118_{+0.013}^{-0.014}$ $R_{\mathrm{J}}$ and a mass of $2.30^{+0.48}_{-0.47}$ $M_{\mathrm{J}}$ for TOI-4562 b. The radius of the planet is consistent with contraction models describing the early evolution of the size of giant planets. We detect tentative transit timing variations at the $\sim$ 20 min level from five transit events, favouring the presence of a companion that could explain the dynamical history of this system if confirmed by future follow-up observations. With its current orbital configuration, tidal timescales are too long for TOI-4562 b to become a hot-Jupiter via high eccentricity migration, though it is not excluded that interactions with the possible companion could modify TOI-4562 b eccentricity and trigger circularization. The characterisation of more such young systems is essential to set constraints on models describing giant planet evolution.

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HIP 33609 b: An Eccentric Brown Dwarf Transiting a V=7.3 Rapidly Rotating B-Star

We present the discovery and characterization of HIP 33609 b, a transiting warm brown dwarf orbiting a late B star, discovered by NASA's Transiting Exoplanet Survey Satellite TESS as TOI-588 b. HIP 33609 b is a large (R$_{b}$ = 1.580$_{-0.070}^{+0.074}$ R$_{J}$) brown dwarf on a highly eccentric (e = 0.560$_{-0.031}^{+0.029}$) orbit with a 39-day period. The host star is a bright (V = 7.3 mag), T$_{eff}$ = 10,400$_{-660}^{+800}$ K star with a mass of M$_{*}$ = 2.383$_{-0.095}^{+0.10}$ M$_{\odot}$ and radius of R$_{*}$ = 1.863$_{-0.082}^{+0.087}$ R$_{\odot}$, making it the hottest transiting brown dwarf host star discovered to date. We obtained radial velocity measurements from the CHIRON spectrograph confirming the companion's mass of M$_{b}$ = 68.0$_{-7.1}^{+7.4}$ M$_{J}$ as well as the host star's rotation rate ($vsini_{*} = 55.6 \pm 1.8$ km/s). We also present the discovery of a new comoving group of stars, designated as MELANGE-6, and determine that HIP 33609 is a member. We use a combination of rotation periods and isochrone models fit to the cluster members to estimate an age of 150 $\pm$ 25 Myr. With a measured mass, radius, and age, HIP 33609 b becomes a benchmark for substellar evolutionary models.

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A Spectroscopic Analysis of a Sample of K2 Planet-Host Stars: Stellar Parameters, Metallicities and Planetary Radii

The physical properties of transiting exoplanets are connected with the physical properties of their host stars. We present a homogeneous spectroscopic analysis based on spectra of FGK-type stars observed with the Hydra spectrograph on the WIYN telescope. We derived effective temperatures, surface gravities, and metallicities, for 81 stars observed by K2 and 33 from Kepler 1. We constructed an Fe I and II line list that is adequate for the analysis of R$\sim$18,000 spectra covering 6050-6350 Å and adopted the spectroscopic technique based on equivalent width measurements. The calculations were done in LTE using Kurucz model atmospheres and the qoyllur-quipu (q$^2$) package. We validated our methodology via analysis of a benchmark solar twin and solar proxies, which are used as the solar reference. We estimated the effects that including Zeeman sensitive Fe I lines have on the derived stellar parameters for young and possibly active stars in our sample and found it not to be significant. Stellar masses and radii were derived by combining the stellar parameters with Gaia EDR3 and V magnitudes and isochrones. The measured stellar radii have 4.2\% median internal precision, leading to a median internal uncertainty of 4.4\% in the derived planetary radii. With our sample of 83 confirmed planets orbiting K2 host stars, the radius gap near R$_{planet}1.9R{_\plus}$ is detected, in agreement with previous findings. Relations between the planetary radius, orbital period and metallicity are explored and these also confirm previous findings for Kepler 1 systems.

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TESS Discovery of Twin Planets near 2:1 Resonance around Early M-Dwarf TOI 4342

With data from the Transiting Exoplanet Survey Satellite (TESS), we showcase improvements to the MIT Quick-Look Pipeline (QLP) through the discovery and validation of a multi-planet system around M-dwarf TOI 4342 ($T_{mag}=11.032$, $M_* = 0.63 M_\odot$, $R_* = 0.60 R_\odot$, $T_{eff} = 3900$ K, $d = 61.54$ pc). With updates to QLP, including a new multi-planet search, as well as faster cadence data from TESS' First Extended Mission, we discovered two sub-Neptunes ($R_b = 2.266_{-0.038}^{+0.038} R_\oplus$ and $R_c = 2.415_{-0.040}^{+0.043} R_\oplus$; $P_b$ = 5.538 days and $P_c$ = 10.689 days) and validated them with ground-based photometry, spectra, and speckle imaging. Both planets notably have high transmission spectroscopy metrics (TSMs) of 36 and 32, making TOI 4342 one of the best systems for comparative atmospheric studies. This system demonstrates how improvements to QLP, along with faster cadence Full-Frame Images (FFIs), can lead to the discovery of new multi-planet systems.

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TESS Hunt for Young and Maturing Exoplanets (THYME) IX: a 27 Myr extended population of Lower-Centaurus Crux with a transiting two-planet system

We report the discovery and characterization of a nearby (~ 85 pc), older (27 +/- 3 Myr), distributed stellar population near Lower-Centaurus-Crux (LCC), initially identified by searching for stars co-moving with a candidate transiting planet from TESS (HD 109833; TOI 1097). We determine the association membership using Gaia kinematics, color-magnitude information, and rotation periods of candidate members. We measure it's age using isochrones, gyrochronology, and Li depletion. While the association is near known populations of LCC, we find that it is older than any previously found LCC sub-group (10-16 Myr), and distinct in both position and velocity. In addition to the candidate planets around HD 109833 the association contains four directly-imaged planetary-mass companions around 3 stars, YSES-1, YSES-2, and HD 95086, all of which were previously assigned membership in the younger LCC. Using the Notch pipeline, we identify a second candidate transiting planet around HD 109833. We use a suite of ground-based follow-up observations to validate the two transit signals as planetary in nature. HD 109833 b and c join the small but growing population of <100 Myr transiting planets from TESS. HD 109833 has a rotation period and Li abundance indicative of a young age (< 100 Myr), but a position and velocity on the outskirts of the new population, lower Li levels than similar members, and a CMD position below model predictions for 27 Myr. So, we cannot reject the possibility that HD 109833 is a young field star coincidentally nearby the population.

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TESS-Keck Survey XIV: Two giant exoplanets from the Distant Giants Survey

We present the Distant Giants Survey, a three-year radial velocity (RV) campaign to measure P(DG|CS), the conditional occurrence of distant giant planets (DG; M_p ~ 0.3 - 13 M_J, P > 1 year) in systems hosting a close-in small planet (CS; R_p < 10 R_E). For the past two years, we have monitored 47 Sun-like stars hosting small transiting planets detected by TESS. We present the selection criteria used to assemble our sample and report the discovery of two distant giant planets, TOI-1669 b and TOI-1694 c. For TOI-1669 b we find that Msin i = 0.573 +/- 0.074 M_J, P = 502 +/- 16 days, and e < 0.27, while for TOI-1694 c, Msin i = 1.05 +/- 0.05 M_J, P = 389.2 +/- 3.9 days, and e = 0.18 +/- 0.05. We also confirmed the 3.8-day transiting planet TOI-1694 b by measuring a true mass of M = 26.1 +/- 2.2 M_E. We also confirmed the 3.8-day transiting planet TOI-1694 b by measuring a true mass of M = 26.1 +/- 2.2 M_E. At the end of the Distant Giants Survey, we will incorporate TOI-1669 b and TOI-1694 c into our calculation of P(DG|CS), a crucial statistic for understanding the relationship between outer giants and small inner companions.

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