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Nicholas Scarsdale

Publications and source records attributed to Nicholas Scarsdale.

At least 19 recordsLinked to original sources

JWST COMPASS: NIRSpec/G395H Transmission Observations of the Sub-Neptune HD 15337 c

We present the 3-5 $\mu$m transmission spectrum of HD 15337 c (TOI-402.02), a sub-Neptune (2.526 R$_{\oplus}$, 6.792 M$_{\oplus}$, T$_{\rm eq}$$\sim$656 K) around a K1V star observed as part of the JWST COMPASS program. We reduce these observations with two pipelines and find consistent transmission spectra. The resulting median precisions in 30 pixel spectroscopic bins for visit 1 are $\sim$40 ppm and $\sim$70 ppm and for visit 2 are $\sim$30 ppm and $\sim$54 ppm for NRS1 and NRS2, respectively. We attribute the differing precisions to the lack of adequate pre-transit baseline in visit 1 from an early transit arrival caused by previously undetected transit timing variations (TTVs), hinting at a potential exterior companion. Our median JWST timing precision is 10 seconds, revealing TTVs $>$20 minutes when combined with previous TESS and CHEOPS data, highlighting JWST's TTV measurement capabilities. The transmission spectrum of HD 15337 c is featureless and can best be described by a step function with an offset between the NRS1 and NRS2 detectors, likely caused by instrumental systematics. From thermochemical equilibrium retrievals we find that, to $>$3$\sigma$, the data can rule out atmospheres with metallicities $<$600 or $<$310 $\times$ solar, depending on the reduction, for opaque pressures greater than a few millibars. HD 15337 c joins other sub-Neptunes with similar masses, radii, and temperatures in possessing a featureless transmission spectrum indicative of high metallicity and/or high-altitude aerosols and adds support to recent studies showing that aerosol opacity reaches a maximum for planets with equilibrium temperatures of 500-700 K.

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JWST COMPASS: Insights into the Systematic Noise Properties of NIRSpec/G395H From a Uniform Reanalysis of Seven Transmission Spectra

JWST has already observed near-infrared transmission spectra of over a dozen super-Earths and sub-Neptunes. While some observations have allowed astronomers to characterize sub-Neptunes in unprecedented detail, small feature amplitudes and poorly-understood systematics have led to ambiguous results for others. Using the first seven targets from the COMPASS program, which is currently surveying 12 small planet atmospheres using NIRSpec/G395H, we investigate these timeseries systematics. We implement a model that uses the principle components of the normalized pixel fluxes to account for variations in the shape and position of the spectral trace. We find that observations with a smaller number of groups-per-integration benefit most profoundly from the use of this model, and that systematics are particularly strong between 2.8 and 3.5 $\mu$m. Despite these systematics, \texttt{pandexo} is a relatively accurate predictor of the precision of the spectra, with real error bars on average 5\% larger in NRS1 and 12\% larger in NRS2 than predicted. We compute new limits on metallicity and opaque pressure level for each target and compare these to previous results from the COMPASS program. Next, we co-add spectra from multiple targets to reduce the effective noise in the combined spectra in hopes of detecting transmission features in common between the targets, but this exercise does not yield compelling evidence any signals. We find that a handful of additional transits are sufficient to break the degeneracy between metallicity and aerosols for the majority of our targets, pointing towards the possibility of unraveling the mysteries of these worlds with future allocations of JWST time.

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THYME XIII: Two young Neptunes orbiting a 75-Myr star in the Alpha Persei Cluster

Young planets with mass measurements are particularly valuable in studying atmospheric mass-loss processes, but these planets are rare and their masses difficult to measure due to stellar activity. We report the discovery of a planetary system around TOI-6109, a young, 75 Myr-old Sun-like star in the Alpha Persei cluster. It hosts at least two transiting Neptune-like planets. Using three TESS sectors, 30 CHEOPS orbits, and photometric follow-up observations from the ground, we confirm the signals of the two planets. TOI-6109 b has an orbital period of P=$5.6904^{+0.0004}_{-0.0004}$ days and a radius of R=$4.87^{+0.16}_{-0.12}$ R$_\oplus$. The outer planet, TOI-6109 c has an orbital period of P=$8.5388^{+0.0006}_{-0.0005}$ days and a radius of R=$4.83^{+0.07}_{-0.06}$ R$_\oplus$. These planets orbit just outside a 3:2 mean motion resonance. The near-resonant configuration presents the opportunity to measure the planet's mass via TTV measurements and to bypass difficult RV measurements. Measuring the masses of the planets in this system will allow us to test theoretical models of atmospheric mass loss.

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JWST COMPASS: A NIRSpec G395H Transmission Spectrum of the Super-Earth GJ 357 b

We present JWST NIRSpec/G395H transmission spectroscopy observations of GJ 357 b, a warm ($T_{\mathrm{eq}} \approx 525$ K) super-Earth ($1.2\ \mathrm{R_{\oplus}} $, $1.84\ \mathrm{M_{\oplus}} $) orbiting a nearby M3-type star, with a median precision of 18 ppm and 27 ppm in NRS1 and NRS2, respectively. These precisions are obtained by binning the spectrum into 53 spectroscopic channels with a resolution of 60 pixels (around 0.02 $\mu$m) each. Our analysis of the transmission spectrum reveals no detectable atmospheric spectral features. By comparing the observed spectrum with 1D forward models, we rule out atmospheres with mean molecular weights (MMW) lower than 8 g/mol to $3 \sigma$, as well as atmospheres with metallicities less than 300x solar. The lack of a low MMW primary atmosphere is consistent with a primordial H$_2$ rich atmosphere having escaped, given the planet's $\gtrsim5$ Gyr age, relatively low surface gravity (log g = 3.09), and its likely history of substantial incident extreme ultraviolet radiation. We conclude that GJ 357 b most likely possesses either a high-MMW secondary atmosphere, perhaps rich in oxidized gases like CO$_2$, or is a bare rock with no atmosphere. Upcoming scheduled JWST thermal emission observations could help distinguish between these scenarios by detecting signatures indicative of atmospheric heat redistribution or molecular absorption.

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JWST COMPASS: NIRSpec/G395H Transmission Observations of TOI-776 c, a 2 Rearth M Dwarf Planet

The atmospheres of planets between the size of Earth and Neptune at short orbital periods have been under intense scrutiny. Of the ~dozen planets in this regime with atmospheres studied so far, a few appear to have prominent molecular features while others appear relatively void of detectable atmospheres. Further work is therefore needed to understand the atmospheres of these planets, starting with observing a larger sample. To this end, we present the 3-5 micron transmission spectrum of TOI-776 c, a warm (Teq ~420 K), ~2 Rearth, ~7 Mearth planet orbiting an M1V star, measured with JWST NIRSpec/G395H. By combining two visits, we measure a median transit precision of ~18 ppm and ~32 ppm in the NRS1 and NRS2 detectors, respectively. We compare the transmission spectrum to both non-physical and physical models, and find no strong evidence for molecular features. For cloud-top pressures larger than 10^-3 bar, we rule out atmospheric metallicities less than 180-240x solar (depending on the reduction and modeling technique), which corresponds to a mean molecular weight of ~6-8 g/mol. However, we find simple atmosphere mixture models (H2O+H2/He or CO2+H2/He) give more pessimistic constraints, and caution that mean molecular weight inferences are model dependent. We compare TOI-776 c to the similar planet TOI-270 d, and discuss possible options for further constraining TOI-776 c's atmospheric composition. Overall, we suggest these TOI-776 c observations may represent a combination of planetary and stellar parameters that fall just below the threshold of detectable features in small planet spectra; finding this boundary is one of the main goals of the COMPASS program.

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The TESS-Keck Survey XXIV: Outer Giants may be More Prevalent in the Presence of Inner Small Planets

We present the results of the Distant Giants Survey, a three-year radial velocity (RV) campaign to search for wide-separation giant planets orbiting Sun-like stars known to host an inner transiting planet. We defined a distant giant to have $a$ = 1--10 AU and $M_{p} \sin i = 70-4000$ \mearth~ = 0.2-12.5 \mj, and required transiting planets to have $a<1$ AU and $R_{p} = 1-4$ \rearth. We assembled our sample of 47 stars using a single selection function, and observed each star at monthly intervals to obtain $\approx$30 RV observations per target. The final catalog includes a total of twelve distant companions: four giant planets detected during our survey, two previously known giant planets, and six objects of uncertain disposition identified through RV/astrometric accelerations. Statistically, half of the uncertain objects are planets and the remainder are stars/brown dwarfs. We calculated target-by-target completeness maps to account for missed planets. We found evidence for a moderate enhancement of distant giants (DG) in the presence of close-in small planets (CS), P(DG|CS) = $30^{+14}_{-12}\%$, over the field rate of P(DG) = $16^{+2}_{-2}\%$. No enhancement is disfavored ($p \sim$ 8%). In contrast to a previous study, we found no evidence that stellar metallicity enhances P(DG|CS). We found evidence that distant giant companions are preferentially found in systems with multiple transiting planets and have lower eccentricities than randomly selected giant planets. This points toward dynamically cool formation pathways for the giants that do not disturb the inner systems.

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The Spin Zone: Synchronously and Asynchronously Rotating Exoplanets Have Spectral Differences in Transmission

New observational facilities are beginning to enable insights into the three-dimensional (3D) nature of exoplanets. Transmission spectroscopy is the most widely used method for characterizing transiting temperate exoplanet's atmospheres, but because it only provides a glimpse of the planet's limb and nightside for a typical orbit, its ability to probe 3D characteristics is still an active area of research. Here, we use the ROCKE-3D general circulation model to test the impact of synchronization state, a ``low-order'' 3D characteristic previously shown to drive differences in planetary phase curves, on the transmission spectrum of a representative super-Earth land planet across temperate-to-warm instellations (S$_p$=0.8, 1, 1.25, 1.66, 2, 2.5, 3, 4, 4.56~S$_\oplus$). We find that different synchronization states do display differences in their transmission spectra, primarily driven by clouds and humidity, and that the differences shrink or disappear in hotter regimes where water clouds are unable to condense (though our simulations do not consider haze formation). The small size of the feature differences and potential for degeneracy with other properties, like differing water content or atmospheric structure, mean that we do not specifically claim to have identified a single transmission diagnostic for synchronization state, but our results can be used for holistic spectrum interpretation and sample creation, and suggest the need for more modelling in this area.

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JWST COMPASS: The 3-5 Micron Transmission Spectrum of the Super-Earth L 98-59 c

We present a JWST NIRSpec transmission spectrum of the super-Earth exoplanet L 98-59 c. This small (R$_p=1.385\pm0.085$R$_\oplus$, M$_p=2.22\pm0.26$R$_\oplus$), warm (T$_\textrm{eq}=553$K) planet resides in a multi-planet system around a nearby, bright (J = 7.933) M3V star. We find that the transmission spectrum of L 98-59 c is featureless at the precision of our data. We achieve precisions of 22ppm in NIRSpec G395H's NRS1 detector and 36ppm in the NRS2 detector at a resolution R$\sim$200 (30 pixel wide bins). At this level of precision, we are able rule out primordial H$_2$-He atmospheres across a range of cloud pressure levels up to at least $\sim$0.1mbar. By comparison to atmospheric forward models, we also rule out atmospheric metallicities below $\sim$300$\times$ solar at 3$σ$ (or equivalently, atmospheric mean molecular weights below $\sim$10~g/mol). We also rule out pure methane atmospheres. The remaining scenarios that are compatible with our data include a planet with no atmosphere at all, or higher mean-molecular weight atmospheres, such as CO$_2$- or H$_2$O-rich atmospheres. This study adds to a growing body of evidence suggesting that planets $\lesssim1.5$R$_\oplus$ lack extended atmospheres.

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The TESS-Keck Survey. XXII. A sub-Neptune Orbiting TOI-1437

Exoplanet discoveries have revealed a dramatic diversity of planet sizes across a vast array of orbital architectures. Sub-Neptunes are of particular interest; due to their absence in our own solar system, we rely on demographics of exoplanets to better understand their bulk composition and formation scenarios. Here, we present the discovery and characterization of TOI-1437 b, a sub-Neptune with a 18.84 day orbit around a near-Solar analog (Mstar = 1.10 +/- 0.10 Msun, Rstar = 1.17 +/- 0.12 Rsun). The planet was detected using photometric data from the Transiting Exoplanet Survey Satellite (TESS) mission and radial velocity follow-up observations were carried out as a part of the TESS-Keck Survey (TKS) using both the HIRES instrument at Keck Observatory and the Levy Spectrograph on the Automated Planet Finder (APF) telescope. A combined analysis of these data reveal a planet radius of Rp = 2.24 +/- 0.23 Rearth and a mass measurement of Mp = 9.6 +/- 3.9 Mearth). TOI-1437 b is one of few (~50) known transiting sub-Neptunes orbiting a solar-mass star that has a radial velocity mass measurement. As the formation pathway of these worlds remains an unanswered question, the precise mass characterization of TOI-1437 b may provide further insight into this class of planet.

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The TESS-Keck Survey XX: 15 New TESS Planets and a Uniform RV Analysis of all Survey Targets

The Transiting Exoplanet Survey Satellite (TESS) has discovered hundreds of new worlds, with TESS planet candidates now outnumbering the total number of confirmed planets from $\textit{Kepler}$. Owing to differences in survey design, TESS continues to provide planets that are better suited for subsequent follow-up studies, including mass measurement through radial velocity (RV) observations, compared to Kepler targets. In this work, we present the TESS-Keck Survey's (TKS) Mass Catalog: a uniform analysis of all TKS RV survey data which has resulted in mass constraints for 126 planets and candidate signals. This includes 58 mass measurements that have reached $\geq5σ$ precision. We confirm or validate 32 new planets from the TESS mission either by significant mass measurement (15) or statistical validation (17), and we find no evidence of likely false positives among our entire sample. This work also serves as a data release for all previously unpublished TKS survey data, including 9,204 RV measurements and associated activity indicators over our three year survey. We took the opportunity to assess the performance of our survey, and found that we achieved many of our goals including measuring the mass of 38 small ($<4R_{\oplus}$) planets, nearly achieving the TESS mission's basic science requirement. In addition, we evaluated the performance of the Automated Planet Finder (APF) as survey support and observed meaningful constraints on system parameters due to its more uniform phase coverage. Finally, we compared our measured masses to those predicted by commonly used mass-radius relations and investigated evidence of systematic bias.

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JWST COMPASS: A NIRSpec/G395H Transmission Spectrum of the Sub-Neptune TOI-836c

Planets between the sizes of Earth and Neptune are the most common in the Galaxy, bridging the gap between the terrestrial and giant planets in our Solar System. Now that we are firmly in the era of JWST, we can begin to measure, in more detail, the atmospheres of these ubiquitous planets to better understand their evolutionary trajectories. The two planets in the TOI-836 system are ideal candidates for such a study, as they fall on either side of the radius valley, allowing for direct comparisons of the present-day atmospheres of planets that formed in the same environment but had different ultimate end states. We present results from the JWST NIRSpec G395H transit observation of the larger and outer of the planets in this system, TOI-836c (2.587 R$_{\oplus}$, 9.6 M$_{\oplus}$, T$_{\rm eq}$$\sim$665 K). While we measure average 30-pixel binned precisions of $\sim$24ppm for NRS1 and $\sim$43ppm for NRS2 per spectral bin, we do find residual correlated noise in the data, which we attempt to correct using the JWST Engineering Database. We find a featureless transmission spectrum for this sub-Neptune planet, and are able to rule out atmospheric metallicities $<$175$\times$ Solar in the absence of aerosols at $\lesssim$1 millibar. We leverage microphysical models to determine that aerosols at such low pressures are physically plausible. The results presented herein represent the first observation from the COMPASS (Compositions of Mini-Planet Atmospheres for Statistical Study) JWST program, which also includes TOI-836b and will ultimately compare the presence and compositions of atmospheres for 12 super-Earths/sub-Neptunes.

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JWST COMPASS: NIRSpec/G395H Transmission Observations of the Super-Earth TOI-836b

We present two transit observations of the ~870K, 1.7R$_E$ super-Earth TOI-836b with JWST NIRSpec/G395H, resulting in a 2.8-5.2$μ$m transmission spectrum. Using two different reduction pipelines, we obtain a median transit depth precision of 34ppm for Visit 1 and 36ppm for Visit 2, leading to a combined precision of 25ppm in spectroscopic channels 30 pixels wide (~0.02$μ$m). We find that the transmission spectrum from both visits is well fit by a zero-sloped line by fitting zero-sloped and sloped lines, as well as step functions to our data. Combining both visits, we are able to rule out atmospheres with metallicities <250xSolar for an opaque pressure level of 0.1 bar, corresponding to mean molecular weights to <6gmol$^{-1}$. We therefore conclude that TOI-836b does not have an H$_2$-dominated atmosphere, in possible contrast with its larger, exterior sibling planet, TOI-836c. We recommend that future proposals to observe small planets exercise caution when requiring specific numbers of transits to rule out physical scenarios, particularly for high metallicities and planets around bright host stars, as PandExo predictions appear to be more optimistic than that suggested by the gains from additional transits implied by our data.

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The TESS-Keck Survey. XII. A Dense 1.8 R$_\oplus$ Ultra-Short-Period Planet Possibly Clinging to a High-Mean-Molecular-Weight Atmosphere After the First Gyr

The extreme environments of ultra-short-period planets (USPs) make excellent laboratories to study how exoplanets obtain, lose, retain, and/or regain gaseous atmospheres. We present the confirmation and characterization of the USP TOI-1347 b, a $1.8 \pm 0.1$ R$_\oplus$ planet on a 0.85 day orbit that was detected with photometry from the TESS mission. We measured radial velocities of the TOI-1347 system using Keck/HIRES and HARPS-N and found the USP to be unusually massive at $11.1 \pm 1.2$ M$_\oplus$. The measured mass and radius of TOI-1347 b imply an Earth-like bulk composition. A thin H/He envelope (>0.01% by mass) can be ruled out at high confidence. The system is between 1 and 1.8 Gyr old; therefore, intensive photoevaporation should have concluded. We detected a tentative phase curve variation (3$σ$) and a secondary eclipse (2$σ$) in TESS photometry, which if confirmed could indicate the presence of a high-mean-molecular-weight atmosphere. We recommend additional optical and infrared observations to confirm the presence of an atmosphere and investigate its composition.

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The TESS-Keck Survey. XIX. A Warm Transiting Sub-Saturn Mass Planet and a non-Transiting Saturn Mass Planet Orbiting a Solar Analog

The Transiting Exoplanet Survey Satellite (TESS) continues to dramatically increase the number of known transiting exoplanets, and is optimal for monitoring bright stars amenable to radial velocity (RV) and atmospheric follow-up observations. TOI-1386 is a solar-type (G5V) star that was detected via TESS photometry to exhibit transit signatures in three sectors with a period of 25.84 days. We conducted follow-up RV observations using Keck/HIRES as part of the TESS-Keck Survey (TKS), collecting 64 RV measurements of TOI-1386 with the HIRES spectrograph over 2.5 years. Our combined fit of the TOI-1386 photometry and RV data confirm the planetary nature of the detected TESS signal, and provide a mass and radius for planet b of $0.148\pm0.019$ $M_J$ and $0.540\pm0.017$ $R_J$, respectively, marking TOI-1386 b as a warm sub-Saturn planet. Our RV data further reveal an additional outer companion, TOI-1386 c, with an estimated orbital period of 227.6 days and a minimum mass of $0.309\pm0.038$ $M_J$. The dynamical modeling of the system shows that the measured system architecture is long-term stable, although there may be substantial eccentricity oscillations of the inner planet due to the dynamical influence of the outer planet.

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The TESS-Keck Survey XVII: Precise Mass Measurements in a Young, High Multiplicity Transiting Planet System using Radial Velocities and Transit Timing Variations

We present a radial velocity (RV) analysis of TOI-1136, a bright TESS system with six confirmed transiting planets, and a seventh single-transiting planet candidate. All planets in the system are amenable to transmission spectroscopy, making TOI-1136 one of the best targets for intra-system comparison of exoplanet atmospheres. TOI-1136 is young ($\sim$ 700 Myr), and the system exhibits transit timing variations (TTVs). The youth of the system contributes to high stellar variability on the order of 50 m s$^{-1}$, much larger than the likely RV amplitude of any of the transiting exoplanets. Utilizing 359 HIRES and APF RVs collected as a part of the TESS-Keck Survey (TKS), and 51 HARPS-N RVs, we experiment with a joint TTV-RV fit. With seven possible transiting planets, TTVs, more than 400 RVs, and a stellar activity model, we posit that we may be presenting the most complex mass recovery of an exoplanet system in the literature to date. By combining TTVs and RVs, we minimized GP overfitting and retrieved new masses for this system: (m$_{b-g}$ = 3.50$^{+0.8}_{-0.7}$, 6.32$^{+1.1}_{-1.3}$, 8.35$^{+1.8}_{-1.6}$, 6.07$^{+1.09}_{-1.01}$, 9.7$^{+3.9}_{-3.7}$, 5.6$^{+4.1}_{-3.2}$ M$_{\oplus}$). We are unable to significantly detect the mass of the seventh planet candidate in the RVs, but we are able to loosely constrain a possible orbital period near 80 days. Future TESS observations might confirm the existence of a seventh planet in the system, better constrain the masses and orbital properties of the known exoplanets, and generally shine light on this scientifically interesting system.

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The TESS-Keck Survey. XVI. Mass Measurements for 12 Planets in Eight Systems

With JWST's successful deployment and unexpectedly high fuel reserves, measuring the masses of sub-Neptunes transiting bright, nearby stars will soon become the bottleneck for characterizing the atmospheres of small exoplanets via transmission spectroscopy. Using a carefully curated target list and more than two years' worth of APF-Levy and Keck-HIRES Doppler monitoring, the TESS-Keck Survey is working toward alleviating this pressure. Here we present mass measurements for 11 transiting planets in eight systems that are particularly suited to atmospheric follow-up with JWST. We also report the discovery and confirmation of a temperate super-Jovian-mass planet on a moderately eccentric orbit. The sample of eight host stars, which includes one subgiant, spans early-K to late-F spectral types ($T_\mathrm{eff} =$ 5200--6200 K). We homogeneously derive planet parameters using a joint photometry and radial velocity modeling framework, discuss the planets' possible bulk compositions, and comment on their prospects for atmospheric characterization.

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Awesome SOSS: Transmission Spectroscopy of WASP-96b with NIRISS/SOSS

The future is now - after its long-awaited launch in December 2021, JWST began science operations in July 2022 and is already revolutionizing exoplanet astronomy. The Early Release Observations (ERO) program was designed to provide the first images and spectra from JWST, covering a multitude of science cases and using multiple modes of each on-board instrument. Here, we present transmission spectroscopy observations of the hot-Saturn WASP-96b with the Single Object Slitless Spectroscopy (SOSS) mode of the Near Infrared Imager and Slitless Spectrograph, observed as part of the ERO program. As the SOSS mode presents some unique data reduction challenges, we provide an in-depth walk-through of the major steps necessary for the reduction of SOSS data: including background subtraction, correction of 1/f noise, and treatment of the trace order overlap. We furthermore offer potential routes to correct for field star contamination, which can occur due to the SOSS mode's slitless nature. By comparing our extracted transmission spectrum with grids of atmosphere models, we find an atmosphere metallicity between 1x and 5x solar, and a solar carbon-to-oxygen ratio. Moreover, our models indicate that no grey cloud deck is required to fit WASP-96b's transmission spectrum, but find evidence for a slope shortward of 0.9$μ$m, which could either be caused by enhanced Rayleigh scattering or the red wing of a pressure-broadened Na feature. Our work demonstrates the unique capabilities of the SOSS mode for exoplanet transmission spectroscopy and presents a step-by-step reduction guide for this new and exciting instrument.

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The TESS-Keck Survey. XV. Precise Properties of 108 TESS Planets and Their Host Stars

We present the stellar and planetary properties for 85 TESS Objects of Interest (TOIs) hosting 108 planet candidates which comprise the TESS-Keck Survey (TKS) sample. We combine photometry, high-resolution spectroscopy, and Gaia parallaxes to measure precise and accurate stellar properties. We then use these parameters as inputs to a lightcurve processing pipeline to recover planetary signals and homogeneously fit their transit properties. Among these transit fits, we detect significant transit-timing variations among at least three multi-planet systems (TOI-1136, TOI-1246, TOI-1339) and at least one single-planet system (TOI-1279). We also reduce the uncertainties on planet-to-star radius ratios $R_p/R_\star$ across our sample, from a median fractional uncertainty of 8.8$\%$ among the original TOI Catalog values to 3.0$\%$ among our updated results. With this improvement, we are able to recover the Radius Gap among small TKS planets and find that the topology of the Radius Gap among our sample is broadly consistent with that measured among Kepler planets. The stellar and planetary properties presented here will facilitate follow-up investigations of both individual TOIs and broader trends in planet properties, system dynamics, and the evolution of planetary systems.

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