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Damien Ségransan

Publications and source records attributed to Damien Ségransan.

At least 37 records · Page 2Linked to original sources

Upgrading SPHERE with the second stage AO system SAXO+: frequency-based data-driven controller for adaptive optics

This study introduces a novel frequency-based data-driven controller for adaptive optics, using power spectral density for optimization while ensuring stability criteria. It addresses disturbance rejection, command amplitude constraints and system transfer functions through convex optimization to obtain an optimal control in an infinite input response filter form. Evaluated within the SAXO+ project, it demonstrates efficacy under diverse atmospheric conditions and operational scenarios. The proposed controller is tested in both standard and disentangled adaptive optics schemes, showcasing its adaptability and performance. Experimental validation is conducted using the COMPASS simulation tool, affirming the controller's promise for enhancing adaptive optics systems in real-world applications.

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Characterizing the performance of two C-RED ONE cameras for implementation in RISTRETTO and SAXO+ projects

In the near-infrared wavelength regime, atmospheric turbulence fluctuates at a scale of a few milliseconds, and its precise control requires the use of extreme adaptive optics (XAO) systems equipped with fast and sensitive detectors operating at kHz speeds. The C-RED One cameras developed by First Light Imaging (FLI), based on SAPHIRA detectors made of HgCdTe e-APD array sensitive to 0.8-2.5 $μ$m light, featuring a 320x256 pixels with 24 $μ$m pitch, offering sub-electron readout noise and the ability to read subarrays, at frame-rates of up to few 10-kHz, are state-of-the-art for XAO wavefront sensing. The Observatory of Geneva purchased two C-RED One cameras identified as necessary for RISTRETTO (a proposed high-contrast high-resolution spectrograph for the VLT) and SAXO+ (an upgrade of the VLT/SPHERE XAO system) projects. We present a comprehensive characterization and comparative analysis of both the cameras. We present test results examining key noise contributors, including readout noise, detector bias, etc. And we also study their temporal variability. Additionally, we assess the conversion gain and the avalanche gain calibration of the detector. We also study the evolution some of these parameters over time.

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Resonant sub-Neptunes are puffier

A systematic, population-level discrepancy exists between the densities of exoplanets whose masses have been measured with transit timing variations (TTVs) versus those measured with radial velocities (RVs). Since the TTV planets are predominantly nearly resonant, it is still unclear whether the discrepancy is attributed to detection biases or to astrophysical differences between the nearly resonant and non resonant planet populations. We defined a controlled, unbiased sample of 36 sub-Neptunes characterised by Kepler, TESS, HARPS, and ESPRESSO. We found that their density depends mostly on the resonant state of the system, with a low probability (of $0.002_{-0.001}^{+0.010}$) that the mass of (nearly) resonant planets is drawn from the same underlying population as the bulk of sub-Neptunes. Increasing the sample to 133 sub-Neptunes reveals finer details: the densities of resonant planets are similar and lower than non-resonant planets, and both the mean and spread in density increase for planets that are away from resonance. This trend is also present in RV-characterised planets alone. In addition, TTVs and RVs have consistent density distributions for a given distance to resonance. We also show that systems closer to resonances tend to be more co-planar than their spread-out counterparts. These observational trends are also found in synthetic populations, where planets that survived in their original resonant configuration retain a lower density; whereas less compact systems have undergone post-disc giant collisions that increased the planet's density, while expanding their orbits. Our findings reinforce the claim that resonant systems are archetypes of planetary systems at their birth.

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NIRPS first light and early science: breaking the 1 m/s RV precision barrier at infrared wavelengths

The Near-InfraRed Planet Searcher or NIRPS is a precision radial velocity spectrograph developed through collaborative efforts among laboratories in Switzerland, Canada, Brazil, France, Portugal and Spain. NIRPS extends to the 0.98-1.8 $μ$m domain of the pioneering HARPS instrument at the La Silla 3.6-m telescope in Chile and it has achieved unparalleled precision, measuring stellar radial velocities in the infrared with accuracy better than 1 m/s. NIRPS can be used either stand-alone or simultaneously with HARPS. Commissioned in late 2022 and early 2023, NIRPS embarked on a 5-year Guaranteed Time Observation (GTO) program in April 2023, spanning 720 observing nights. This program focuses on planetary systems around M dwarfs, encompassing both the immediate solar vicinity and transit follow-ups, alongside transit and emission spectroscopy observations. We highlight NIRPS's current performances and the insights gained during its deployment at the telescope. The lessons learned and successes achieved contribute to the ongoing advancement of precision radial velocity measurements and high spectral fidelity, further solidifying NIRPS' role in the forefront of the field of exoplanets.

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The discovery of two new benchmark brown dwarfs with precise dynamical masses at the stellar-substellar boundary

Aims. Measuring dynamical masses of substellar companions is a powerful tool to test models of mass-luminosity-age relations, as well as determining observational features that constrain the boundary between stellar and substellar companions. In order to dynamically constrain the mass of such companions, we use multiple exoplanet measurement techniques to remove degeneracies in the orbital fits of these objects and place tight constraints on their model-independent masses. Methods. We combine long-period radial-velocity data from the CORALIE survey with relative astrometry from direct imaging with VLT/SPHERE, along with astrometric accelerations from Hipparcos-Gaia eDR3 to perform a combined orbital fit and measure precise dynamical masses of two newly discovered benchmark brown dwarfs. Results. We report the discovery of HD112863B and HD206505B, which are two new benchmark likely brown dwarfs that sit at the substellar-stellar boundary, with precise dynamical masses. We perform an orbital fit which yields dynamical masses for HD112863B and HD206505B to be $77.1^{+2.9}_{-2.8}~M_{\rm{Jup}}$ and $79.8\pm1.8~M_{\rm{Jup}}$ respectively. The orbital period for HD112863B is determined to be $21.59\pm0.05$ years and the orbital period of HD206505B is determined to be ${50.9}_{-1.5}^{+1.7}$ years. From the $H$ and $K$ band photometry from IRDIS data taken with VLT/SPHERE, we estimate the spectral types of both HD112863B and HD206505B to be early-mid L-types.

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The EBLM project X. Benchmark masses, radii and temperatures for two fully convective M-dwarfs using K2

M-dwarfs are the most abundant stars in the galaxy and popular targets for exoplanet searches. However, their intrinsic faintness and complex spectra inhibit precise characterisation. We only know of dozens of M-dwarfs with fundamental parameters of mass, radius and effective temperature characterised to better than a few per cent. Eclipsing binaries remain the most robust means of stellar characterisation. Here we present two targets from the Eclipsing Binary Low Mass (EBLM) survey that were observed with K2: EBLM J0055-00 and EBLM J2217-04. Combined with HARPS and CORALIE spectroscopy, we measure M-dwarf masses with precisions better than 5%, radii better than 3% and effective temperatures on order 1%. However, our fits require invoking a model to derive parameters for the primary star. By investigating three popular models, we determine that the model uncertainty is of similar magnitude to the statistical uncertainty in the model fits. Therefore, whilst these can be considered benchmark M-dwarfs, we caution the community to consider model uncertainty when pushing the limits of precise stellar characterisation.

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Masses, Revised Radii, and a Third Planet Candidate in the "Inverted" Planetary System Around TOI-1266

Is the population of close-in planets orbiting M dwarfs sculpted by thermally driven escape or is it a direct outcome of the planet formation process? A number of recent empirical results strongly suggest the latter. However, the unique architecture of the TOI-1266 system presents a challenge to models of planet formation and atmospheric escape given its seemingly "inverted" architecture of a large sub-Neptune ($P_b=10.9$ days, $R_{p,b}=2.62\pm 0.11\, \mathrm{R}_{\oplus}$) orbiting interior to that of the system's smaller planet ($P_c=18.8$ days, $R_{p,c}=2.13\pm 0.12\, \mathrm{R}_{\oplus}$). Here we present revised planetary radii based on new TESS and diffuser-assisted ground-based transit observations, and characterize both planetary masses using a set of 145 radial velocity measurements from HARPS-N ($M_{p,b}=4.23\pm 0.69\, \mathrm{M}_{\oplus}, M_{p,c}=2.88\pm 0.80\, \mathrm{M}_{\oplus}$). Our analysis also reveals a third planet candidate ($P_d=32.3$ days, $M_{p,d}\sin{i} = 4.59^{+0.96}_{-0.94}\, \mathrm{M}_{\oplus}$), which if real, would form a chain of near 5:3 period ratios, although the system is likely not in a mean motion resonance. Our results indicate that TOI-1266 b and c are among the lowest density sub-Neptunes around M dwarfs and likely exhibit distinct bulk compositions of a gas-enveloped terrestrial ($X_{\mathrm{env},b}=5.5\pm 0.7$%) and a water-rich world (WMF$_c=59\pm 14$%), which is supported by hydrodynamic escape models. If distinct bulk compositions are confirmed through atmospheric characterization, the system's unique architecture would represent an interesting test case of inside-out sub-Neptune formation at pebble traps.

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TOI-1695 b: A Water World Orbiting an Early M Dwarf in the Planet Radius Valley

Characterizing the bulk compositions of transiting exoplanets within the M dwarf radius valley offers a unique means to establish whether the radius valley emerges from an atmospheric mass loss process or is imprinted by planet formation itself. We present the confirmation of such a planet orbiting an early M dwarf ($T_{\rm mag} = 11.0294 \pm 0.0074, M_s = 0.513 \pm 0.012\ M_\odot, R_s = 0.515 \pm 0.015\ R_\odot, T_{\rm eff} =3690\pm 50 K$): TOI-1695 b ($P = 3.13$ days, $R_p = 1.90^{+0.16}_{-0.14}\ R_\oplus$). TOI-1695 b's radius and orbital period situate the planet between model predictions from thermally-driven mass loss versus gas depleted formation, offering an important test case for radius valley emergence models around early M dwarfs. We confirm the planetary nature of TOI-1695 b based on five sectors of TESS data and a suite of follow-up observations including 49 precise radial velocity measurements taken with the HARPS-N spectrograph. We measure a planetary mass of $6.36 \pm 1.00\ M_\oplus$, which reveals that TOI-1695 b is inconsistent with a purely terrestrial composition of iron and magnesium silicate, and instead is likely a water-rich planet. Our finding that TOI-1695 b is not terrestrial is inconsistent with the planetary system being sculpted by thermally driven mass loss. We present a statistical analysis of seven well-characterized planets within the M dwarf radius valley demonstrating that a thermally-driven mass loss scenario is unlikely to explain this population.

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ISPY-NACO Imaging Survey for Planets around Young stars. The demographics of forming planets embedded in protoplanetary disks

We present the statistical analysis of a subsample of 45 young stars surrounded by protoplanetary disks (PPDs). This is the largest imaging survey uniquely focused on PPDs to date. Our goal is to search for young forming companions embedded in the disk material and to constrain their occurrence rate in relation to the formation mechanism. We used principal component analysis based point spread function subtraction techniques to reveal young companions forming in the disks. We calculated detection limits for our datasets and adopted a black-body model to derive temperature upper limits of potential forming planets. We then used Monte Carlo simulations to constrain the population of forming gas giant companions and compare our results to different types of formation scenarios. Our data revealed a new binary system (HD38120) and a recently identified triple system with a brown dwarf companion orbiting a binary system (HD101412), in addition to 12 known companions. Furthermore, we detected signals from 17 disks, two of which (HD72106 and TCrA) were imaged for the first time. We reached median detection limits of L =15.4 mag at 2.0 arcsec, which were used to investigate the temperature of potentially embedded forming companions. We can constrain the occurrence of forming planets with semi-major axis a in [20 - 500] au and Teff in [600 - 3000] K, in line with the statistical results obtained for more evolved systems from other direct imaging surveys. The NaCo-ISPY data confirm that massive bright planets accreting at high rates are rare. More powerful instruments with better sensitivity in the near- to mid-infrared are likely required to unveil the wealth of forming planets sculpting the observed disk substructures.

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Hot Exoplanet Atmospheres Resolved with Transit Spectroscopy (HEARTS) VII. Detection of sodium on the long-transiting inflated sub-Saturn KELT-11 b

KELT-11b is an inflated sub-Saturn with a hot atmosphere and that orbits a bright evolved subgiant star, making it a prime choice for atmospheric characterization, but that transits its host star for more than seven hours. We observed this system in series of three consecutive nights with the HARPS spectrograph and report on the analysis of the transmission spectrum obtained from this dataset. Our results highlight the potential for independent observations of a long-transiting planet over consecutive nights. Our study reveals a sodium excess absorption of $0.28 \pm 0.05 %$ and $0.50 \pm 0.06 %$ in the Na D1 and D2 lines, respectively. This corresponds to 1.44 and 1.69 times the white-light planet radius in the line cores. Wind pattern modeling tends to prefer day-to-night side winds with no vertical winds, which is surprising considering the planet bloatedness. The modeling of the Rossiter-Mclaughlin effect yields a significantly misaligned orbit, with a projected spin-orbit angle of $λ = -77.86^{+2.36}_{-2.26}{}^\circ$. The characteristics of KELT-11 b, notably its extreme scale height and long transit, make it an ideal and unique target for next-generation telescopes. Our results as well as recent findings from HST, TESS, and CHEOPS observations could make KELT-11 b a benchmark exoplanet in atmospheric characterization.

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Uncovering the true periods of the young sub-Neptunes orbiting TOI-2076

Context: TOI-2076 is a transiting three-planet system of sub-Neptunes orbiting a bright (G = 8.9 mag), young ($340\pm80$ Myr) K-type star. Although a validated planetary system, the orbits of the two outer planets were unconstrained as only two non-consecutive transits were seen in TESS photometry. This left 11 and 7 possible period aliases for each. Aims: To reveal the true orbits of these two long-period planets, precise photometry targeted on the highest-probability period aliases is required. Long-term monitoring of transits in multi-planet systems can also help constrain planetary masses through TTV measurements. Methods: We used the MonoTools package to determine which aliases to follow, and then performed space-based and ground-based photometric follow-up of TOI-2076 c and d with CHEOPS, SAINT-EX, and LCO telescopes. Results: CHEOPS observations revealed a clear detection for TOI-2076 c at $P=21.01538^{+0.00084}_{-0.00074}$ d, and allowed us to rule out three of the most likely period aliases for TOI-2076 d. Ground-based photometry further enabled us to rule out remaining aliases and confirm the $P=35.12537\pm0.00067$ d alias. These observations also improved the radius precision of all three sub-Neptunes to $2.518\pm0.036$, $3.497\pm0.043$, and $3.232\pm0.063$ $R_\oplus$. Our observations also revealed a clear anti-correlated TTV signal between planets b and c likely caused by their proximity to the 2:1 resonance, while planets c and d appear close to a 5:3 period commensurability, although model degeneracy meant we were unable to retrieve robust TTV masses. Their inflated radii, likely due to extended H-He atmospheres, combined with low insolation makes all three planets excellent candidates for future comparative transmission spectroscopy with JWST.

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GJ 367b: A dense ultra-short period sub-Earth planet transiting a nearby red dwarf star

Ultra-short-period (USP) exoplanets have orbital periods shorter than one day. Precise masses and radii of USPs could provide constraints on their unknown formation and evolution processes. We report the detection and characterization of the USP planet GJ 367b using high precision photometry and radial velocity observations. GJ 367b orbits a bright (V-band magnitude = 10.2), nearby, red (M-type) dwarf star every 7.7 hours. GJ 367b has a radius of $0.718 \pm 0.054$ Earth-radii, a mass of $0.546 \pm 0.078$ Earth-masses, making it a sub-Earth. The corresponding bulk density is $8.106 \pm 2.165$ g cm$^-3$, close to that of iron. An interior structure model predicts the planet has an iron core radius fraction of $86 \pm 5\%$, similar to Mercury's interior.

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Unveiling wide-orbit companions to K-type stars in Sco-Cen with Gaia EDR3

Abbreviated. We aim to identify new low-mass companions to young stars using the astrometric measurements provided by the Gaia space mission and complementary VLT/SPHERE data. We identify companion candidates from a sample of K-type, pre-main sequence stars in the Scorpius Centaurus association using the early version of the third data release of the Gaia space mission. Based on the provided positions, proper motions, and magnitudes, we identify all objects within a predefined radius whose differential proper motions are consistent with a gravitationally bound system. We derive companion masses through comparison with evolutionary tracks. For seven identified companion candidates we use additional data collected with VLT/SPHERE and VLT/NACO to assess the accuracy of the properties of the companions based on Gaia photometry alone. We identify 110 comoving companions that have a companionship likelihood of more than $95\,\%$. We identify ten especially intriguing companions that have masses in the brown dwarf regime down to $20\,M_\mathrm{Jup}$. Our high-contrast imaging data confirm both astrometry and photometric masses derived from Gaia alone. We discover a new brown dwarf companion, TYC 8252-533-1 B, with a projected separation of approximately $570\,\mathrm{au}$ from its Sun-like primary. SED modeling provides a companion mass of $52^{+17}_{-11}\,M_\mathrm{Jup}$. We show that the Gaia database can identify low-mass companions at wide separations from their host stars. For K-type Sco-Cen members Gaia can detect sub-stellar objects at projected separations larger than $300\,\mathrm{au}$ and is sensitivity limited beyond $1,000\,\mathrm{au}$ with a lower mass limit down to $20\,M_\mathrm{Jup}$. A similar analysis of other star-forming regions could significantly enlarge the sample size of such objects and test formation and evolution theories of planetary systems.

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Populating the brown dwarf and stellar boundary: Five stars with transiting companions near the hydrogen-burning mass limit

We report the discovery of five transiting companions near the hydrogen-burning mass limit in close orbits around main sequence stars originally identified by the Transiting Exoplanet Survey Satellite (TESS) as TESS Objects of Interest (TOIs): TOI-148, TOI-587, TOI-681, TOI-746, and TOI-1213. Using TESS and ground-based photometry as well as radial velocities from the CORALIE, CHIRON, TRES, and FEROS spectrographs, we found the companions have orbital periods between 4.8 and 27.2 days, masses between 77 and 98 $\mathrm{M_{Jup}}$, and radii between 0.81 and 1.66 $\mathrm{R_{Jup}}$. These targets have masses near the uncertain lower limit of hydrogen core fusion ($\sim$73-96 $\mathrm{M_{Jup}}$), which separates brown dwarfs and low-mass stars. We constrained young ages for TOI-587 (0.2 $\pm$ 0.1 Gyr) and TOI-681 (0.17 $\pm$ 0.03 Gyr) and found them to have relatively larger radii compared to other transiting companions of a similar mass. Conversely we estimated older ages for TOI-148 and TOI-746 and found them to have relatively smaller companion radii. With an effective temperature of 9800 $\pm$ 200 K, TOI-587 is the hottest known main-sequence star to host a transiting brown dwarf or very low-mass star. We found evidence of spin-orbit synchronization for TOI-148 and TOI-746 as well as tidal circularization for TOI-148. These companions add to the population of brown dwarfs and very low-mass stars with well measured parameters ideal to test formation models of these rare objects, the origin of the brown dwarf desert, and the distinction between brown dwarfs and hydrogen-burning main sequence stars.

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Transit detection of the long-period volatile-rich super-Earth $ν^2$ Lupi d with $CHEOPS$

Exoplanets transiting bright nearby stars are key objects for advancing our knowledge of planetary formation and evolution. The wealth of photons from the host star gives detailed access to the atmospheric, interior, and orbital properties of the planetary companions. $ν^2$ Lupi (HD 136352) is a naked-eye ($V = 5.78$) Sun-like star that was discovered to host three low-mass planets with orbital periods of 11.6, 27.6, and 107.6 days via radial velocity monitoring (Udry et al. 2019). The two inner planets (b and c) were recently found to transit (Kane et al. 2020), prompting a photometric follow-up by the brand-new $CHaracterising\:ExOPlanets\:Satellite\:(CHEOPS)$. Here, we report that the outer planet d is also transiting, and measure its radius and mass to be $2.56\pm0.09$ $R_{\oplus}$ and $8.82\pm0.94$ $M_{\oplus}$, respectively. With its bright Sun-like star, long period, and mild irradiation ($\sim$5.7 times the irradiation of Earth), $ν^2$ Lupi d unlocks a completely new region in the parameter space of exoplanets amenable to detailed characterization. We refine the properties of all three planets: planet b likely has a rocky mostly dry composition, while planets c and d seem to have retained small hydrogen-helium envelopes and a possibly large water fraction. This diversity of planetary compositions makes the $ν^2$ Lupi system an excellent laboratory for testing formation and evolution models of low-mass planets.

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Improving exoplanet detection capabilities with the false inclusion probability. Comparison with other detection criteria in the context of radial velocities

Context. In exoplanet searches with radial velocity data, the most common statistical significance metrics are the Bayes factor and the false alarm probability (FAP). Both have proved useful, but do not directly address whether an exoplanet detection should be claimed. Furthermore, it is unclear which detection threshold should be taken and how robust the detections are to model misspecification. Aims. The present work aims at defining a detection criterion which conveys as precisely as possible the information needed to claim an exoplanet detection. We compare this new criterion to existing ones in terms of sensitivity and robustness. Methods. We define a significance metric called the false inclusion probability (FIP) based on the posterior probability of presence of a planet. Posterior distributions are computed with the nested sampling package Polychord. We show that for FIP and Bayes factor calculations, defining priors on linear parameters as Gaussian mixture models allows to significantly speed up computations. The performances of the FAP, Bayes factor and FIP are studied with simulations as well as analytical arguments. We compare the methods assuming the model is correct, then evaluate their sensitivity to the prior and likelihood choices. Results. Among other properties, the FIP offers ways to test the reliability of the significance levels, it is particularly efficient to account for aliasing and allows to exclude the presence of planets with a certain confidence. We find that, in our simulations, the FIP outperforms existing detection metrics. We show that planet detections are sensitive to priors on period and semi-amplitude and that letting free the noise parameters offers better performances than fixing a noise model based on a fit to ancillary indicators.

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The CHEOPS mission

The CHaracterising ExOPlanet Satellite (CHEOPS) was selected in 2012, as the first small mission in the ESA Science Programme and successfully launched in December 2019. CHEOPS is a partnership between ESA and Switzerland with important contributions by ten additional ESA Member States. CHEOPS is the first mission dedicated to search for transits of exoplanets using ultrahigh precision photometry on bright stars already known to host planets. As a follow-up mission, CHEOPS is mainly dedicated to improving, whenever possible, existing radii measurements or provide first accurate measurements for a subset of those planets for which the mass has already been estimated from ground-based spectroscopic surveys and to following phase curves. CHEOPS will provide prime targets for future spectroscopic atmospheric characterisation. Requirements on the photometric precision and stability have been derived for stars with magnitudes ranging from 6 to 12 in the V band. In particular, CHEOPS shall be able to detect Earth-size planets transiting G5 dwarf stars in the magnitude range between 6 and 9 by achieving a photometric precision of 20 ppm in 6 hours of integration. For K stars in the magnitude range between 9 and 12, CHEOPS shall be able to detect transiting Neptune-size planets achieving a photometric precision of 85 ppm in 3 hours of integration. This is achieved by using a single, frame-transfer, back-illuminated CCD detector at the focal plane assembly of a 33.5 cm diameter telescope. The 280 kg spacecraft has a pointing accuracy of about 1 arcsec rms and orbits on a sun-synchronous dusk-dawn orbit at 700 km altitude. The nominal mission lifetime is 3.5 years. During this period, 20% of the observing time is available to the community through a yearly call and a discretionary time programme managed by ESA.

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Transits of Known Planets Orbiting a Naked-Eye Star

Some of the most scientifically valuable transiting planets are those that were already known from radial velocity (RV) surveys. This is primarily because their orbits are well characterized and they preferentially orbit bright stars that are the targets of RV surveys. The Transiting Exoplanet Survey Satellite ({\it TESS}) provides an opportunity to survey most of the known exoplanet systems in a systematic fashion to detect possible transits of their planets. HD~136352 (Nu$^2$~Lupi) is a naked-eye ($V = 5.78$) G-type main-sequence star that was discovered to host three planets with orbital periods of 11.6, 27.6, and 108.1 days via RV monitoring with the HARPS spectrograph. We present the detection and characterization of transits for the two inner planets of the HD~136352 system, revealing radii of $1.482^{+0.058}_{-0.056}$~$R_\oplus$ and $2.608^{+0.078}_{-0.077}$~$R_\oplus$ for planets b and c, respectively. We combine new HARPS observations with RV data from Keck/HIRES and the AAT, along with {\it TESS} photometry from Sector 12, to perform a complete analysis of the system parameters. The combined data analysis results in extracted bulk density values of $ρ_b = 7.8^{+1.2}_{-1.1}$~gcm$^{-3}$ and $ρ_c = 3.50^{+0.41}_{-0.36}$~gcm$^{-3}$ for planets b and c, respectively, thus placing them on either side of the radius valley. The combination of the multi-transiting planet system, the bright host star, and the diversity of planetary interiors and atmospheres means this will likely become a cornerstone system for atmospheric and orbital characterization of small worlds.

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