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I. Ribas

Publications and source records attributed to I. Ribas.

At least 145 records · Page 8Linked to original sources

The atmosphere and architecture of WASP-189 b probed by its CHEOPS phase curve

Gas giants orbiting close to hot and massive early-type stars can reach dayside temperatures that are comparable to those of the coldest stars. These "ultra-hot Jupiters" have atmospheres made of ions and atomic species from molecular dissociation and feature strong day-to-night temperature gradients. Photometric observations at different orbital phases provide insights on the planet atmospheric properties. We analyse the photometric observations of WASP-189 acquired with the instrument CHEOPS to derive constraints on the system architecture and the planetary atmosphere. We implement a light curve model suited for asymmetric transit shape caused by the gravity-darkened photosphere of the fast-rotating host star. We also model the reflective and thermal components of the planetary flux, the effect of stellar oblateness and light-travel time on transit-eclipse timings, the stellar activity and CHEOPS systematics. From the asymmetric transit, we measure the size of the ultra-hot Jupiter WASP-189 b, $R_p=1.600^{+0.017}_{-0.016}\,R_J$, with a precision of 1%, and the true orbital obliquity of the planetary system $Ψ_p=89.6\pm1.2°$ (polar orbit). We detect no significant hotspot offset from the phase curve and obtain an eclipse depth $δ_\text{ecl}=96.5^{+4.5}_{-5.0}\,\text{ppm}$, from which we derive an upper limit on the geometric albedo: $A_g<0.48$. We also find that the eclipse depth can only be explained by thermal emission alone in the case of extremely inefficient energy redistribution. Finally, we attribute the photometric variability to the stellar rotation, either through superficial inhomogeneities or resonance couplings between the convective core and the radiative envelope.

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HADES RV Programme with HARPS-N at TNG XV. Planetary occurrence rates around early-M dwarfs

We present the complete Bayesian statistical analysis of the HArps-n red Dwarf Exoplanet Survey (HADES), which monitored the radial velocities of a large sample of M dwarfs with HARPS-N at TNG, over the last 6 years. The targets were selected in a narrow range of spectral types from M0 to M3, $0.3$ M$_\odot < M_\star < 0.71$ M$_\odot$, in order to study the planetary population around a well-defined class of host stars. We take advantage of Bayesian statistics to derive an accurate estimate of the detectability function of the survey. Our analysis also includes the application of Gaussian Process approach to take into account stellar activity induced radial velocity variations, and improve the detection limits, around the most-observed and most-active targets. The Markov chain Monte Carlo and Gaussian process technique we apply in this analysis has proven very effective in the study of M-dwarf planetary systems, helping the detection of most of the HADES planets. From the detectability function we can calculate the occurrence rate of small mass planets around early-M dwarfs, either taking into account only the 11 already published HADES planets or adding also the 5 new planetary candidates discovered in this analysis, and compare them with the previous estimates of planet occurrence around M-dwarf or Solar-type stars: considering only the confirmed planets, we find the highest frequency for low-mass planets ($1$ M$_\oplus < m_p \sin i < 10$ M$_\oplus$) with periods $10$ d$ < P < 100$ d, $f_\text{occ} = 85^{+5}_{-19}\%$, while for short-period planets ($1$ d$ < P < 10$ d) we find a frequency of $f_\text{occ} = 10.3^{+8.4}_{-3.3}\%$, significantly lower than for later-M dwarfs. These results, and their comparison with other surveys focused on different stellar types, confirms the central role that stellar mass plays in the formation and evolution of planetary systems.

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The CARMENES search for exoplanets around M dwarfs: Benchmarking the impact of activity in high-precision radial velocity measurements

Current exoplanet surveys using the radial velocity (RV) technique are targeting M dwarfs because any habitable zone terrestrial-mass planets will induce a high RV and orbit on shorter periods than for more massive stars. One of the main caveats is that M dwarfs show a wide range of activity levels from inactive to very active, which can induce an asymmetry in the line profiles and, consequently, a spurious RV measurement. We aim to benchmark the impact of stellar activity on high-precision RV measurements using regular-cadence CARMENES visible and near-infrared observations of the active M3.5 dwarf EV Lac. We used the newly developed technique of low-resolution Doppler imaging to determine the centre-of-light, or spot-induced RV component, for eight observational epochs. We confirm a statistically significant and strong correlation between the independently measured centre-of-light and the chromatic index, which is a measure of the amplitude variation with wavelength of the RVs. We also find circular closed-loop relations of several activity indices with RV for a subset of data that covers only several rotation periods. We also investigate the implications of large phase gaps in the periodograms of activity indicators. Finally, by removing the spot-induced RV component we improve the planet-mass sensitivity by a factor of at least three. We conclude that for active M stars, a regular-cadence observing strategy is the most efficient way to identify and eliminate sources of correlated noise.

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CHEOPS geometric albedo of the hot Jupiter HD 209458b

We report the detection of the secondary eclipse of the hot Jupiter HD 209458b in optical/visible light using the CHEOPS space telescope. Our measurement of 20.4 +/- 3.3 ppm translates into a geometric albedo of A_g = 0.096 +/- 0.016. The previously estimated dayside temperature of about 1500 K implies that our geometric albedo measurement consists predominantly of reflected starlight and is largely uncontaminated by thermal emission. This makes the present result one of the most robust measurements of A_g for any exoplanet. Our calculations of the bandpass-integrated geometric albedo demonstrate that the measured value of A_g is consistent with a cloud-free atmosphere, where starlight is reflected via Rayleigh scattering by hydrogen molecules, and the water and sodium abundances are consistent with stellar metallicity. We predict that the bandpass-integrated TESS geometric albedo is too faint to detect and that a phase curve of HD 209458b observed by CHEOPS would have a distinct shape associated with Rayleigh scattering if the atmosphere is indeed cloud free.

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Transit timing variations of AU Microscopii b and c

Here we report large-amplitude transit timing variations (TTVs) for AU\,Microcopii b and c as detected in combined TESS (2018, 2020) and CHEOPS (2020, 2021) transit observations. AU Mic is a young planetary system with a debris disk and two transiting warm Neptunes. A TTV on the order of several minutes was previously reported for AU Mic b, which was suggested to be an outcome of mutual perturbations between the planets in the system. In 2021, we observed AU Mic b (five transits) and c (three transits) with the CHEOPS space telescope to follow-up the TTV of AU Mic b and possibly detect a TTV for AU Mic c. When analyzing TESS and CHEOPS 2020--2021 measurements together, we find that a prominent TTV emerges with a full span of ~23 minutes between the two TTV extrema. Assuming that the period change results from a periodic process - such as mutual perturbations - we demonstrate that the times of transits in the summer of 2022 are expected to be 30--85 minutes later than predicted by the available linear ephemeris.

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Spi-OPS: Spitzer and CHEOPS confirm the near-polar orbit of MASCARA-1 b and reveal a hint of dayside reflection

The light curves of tidally locked hot Jupiters transiting fast-rotating, early-type stars are a rich source of information about both the planet and star, with full-phase coverage enabling a detailed atmospheric characterisation of the planet. Although it is possible to determine the true spin-orbit angle $Ψ$, a notoriously difficult parameter to measure, from any transit asymmetry resulting from gravity darkening induced by the stellar rotation, the correlations that exist between the transit parameters have led to large disagreements in published values of $Ψ$ for some systems. We aimed to study these phenomena in the light curves of the ultra-hot Jupiter MASCARA-1 b. We obtained optical CHEOPS transit and occultation light curves of MASCARA-1 b, and analysed them jointly with a Spitzer/IRAC 4.5 $μ$m full-phase curve. When fitting the CHEOPS and Spitzer transits together, the degeneracies are greatly diminished and return results consistent with previously published Doppler tomography. Placing priors informed by the tomography achieves even better precision, allowing a determination of $Ψ=72.1^{+2.5}_{-2.4}$ deg. From the occultations and phase variations, we derived dayside and nightside temperatures of $3062^{+66}_{-68}$ K and $1720\pm330$ K, respectively. In addition, we could separately derive geometric albedo $A_g=0.171^{+0.066}_{-0.068}$ and spherical albedo $A_s=0.266^{+0.097}_{-0.100}$ from the CHEOPS data, and Bond albedo $A_B=0.057^{+0.083}_{-0.101}$ from the Spitzer phase curve. Where possible, priors informed by Doppler tomography should be used when fitting transits of fast-rotating stars, though multi-colour photometry may also unlock an accurate measurement of $Ψ$. Our approach to modelling the phase variations at different wavelengths provides a template for how to separate thermal emission from reflected light in spectrally resolved JWST phase curves.

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Discovery and mass measurement of the hot, transiting, Earth-sized planet GJ 3929 b

We report the discovery of GJ 3929 b, a hot Earth-sized planet orbiting the nearby M3.5 V dwarf star, GJ 3929 (G 180--18, TOI-2013). Joint modelling of photometric observations from TESS sectors 24 and 25 together with 73 spectroscopic observations from CARMENES and follow-up transit observations from SAINT-EX, LCOGT, and OSN yields a planet radius of $R_b = 1.150 +/- 0.040$ R$_{earth}$, a mass of $M_b = 1.21 +/- 0.42$ M$_{earth}$, and an orbital period of $P_b = 2.6162745 +/- 0.0000030$ d. The resulting density of $ρ_b= 4.4 +/- 1.6$ g/cm$^{-3}$ is compatible with the Earth's mean density of about 5.5 g/cm$^{-3}$. Due to the apparent brightness of the host star (J=8.7 mag) and its small size, GJ 3929 b is a promising target for atmospheric characterisation with the JWST. Additionally, the radial velocity data show evidence for another planet candidate with $P_{[c]} = 14.303 +/- 0.035$ d, which is likely unrelated to the stellar rotation period, $P_{rot} = 122+/-13$ d, which we determined from archival HATNet and ASAS-SN photometry combined with newly obtained TJO data.

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A tentative detection of He I in the atmosphere of GJ 1214b

The $\ion{He}{I}$ 10833\,$Å$ triplet is a powerful tool for characterising the upper atmosphere of exoplanets and tracing possible mass loss. Here, we analysed one transit of GJ\,1214\,b observed with the CARMENES high-resolution spectrograph to study its atmosphere via transmission spectroscopy around the $\ion{He}{I}$ triplet. Although previous studies using lower resolution instruments have reported non-detections of $\ion{He}{I}$ in the atmosphere of GJ\,1214\,b, we report here the first potential detection. We reconcile the conflicting results arguing that previous transit observations did not present good opportunities for the detection of $\ion{He}{I}$, due to telluric H$_2$O absorption and OH emission contamination.We simulated those earlier observations, and show evidence that the planetary signal was contaminated. From our single non-telluric-contaminated transit, we determined an excess absorption of 2.10$^{+0.45}_{-0.50}$\,\% (4.6\,$σ$) with a full width at half maximum (FWHM) of 1.30$^{+0.30}_{-0.25}$\,Å. The detection of \ion{He}{I} is statistically significant at the 4.6\,$σ$ level, but repeatability of the detection could not be confirmed due to the availability of only one transit. By applying a hydrodynamical model and assuming an H/He composition of 98/2, we found that GJ\,1214\,b would undergo hydrodynamic escape in the photon-limited regime, losing its primary atmosphere with a mass-loss rate of (1.5--18)\,$\times$\,10$^{10}$\,g\,s$^{-1}$ and an outflow temperature in the range of 2900--4400\,K. Our $\ion{He}{I}$ excess absorption is the first tentative detection of a chemical species in the atmosphere of this benchmark sub-Neptune planet.

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Detection of iron emission lines and a temperature inversion on the dayside of the ultra-hot Jupiter KELT-20b

Ultra-hot Jupiters (UHJs) are gas giants with very high equilibrium temperatures. In recent years, multiple chemical species, including various atoms and ions, have been discovered in their atmospheres. Most of these observations have been performed with transmission spectroscopy, although UHJs are also ideal targets for emission spectroscopy due to their strong thermal radiation. We present high-resolution thermal emission spectroscopy of the transiting UHJ KELT-20b/MASCARA-2b. The observation was performed with the CARMENES spectrograph at orbital phases before and after the secondary eclipse. We detected atomic Fe using the cross-correlation technique. The detected Fe lines are in emission, which unambiguously indicates a temperature inversion on the dayside hemisphere. We furthermore retrieved the temperature structure with the detected Fe lines. The result shows that the atmosphere has a strong temperature inversion with a temperature of $4900\pm{700}$ K and a pressure of $10^{-4.8_{-1.1}^{+1.0}}$ bar at the upper layer of the inversion. A joint retrieval of the CARMENES data and the TESS secondary eclipse data returns a temperature of $2550_{-250}^{+150}$ K and a pressure of $10^{-1.5_{-0.6}^{+0.7}}$ bar at the lower layer of the temperature inversion. The detection of such a strong temperature inversion is consistent with theoretical simulations that predict an inversion layer on the dayside of UHJs. The joint retrieval of the CARMENES and TESS data demonstrates the power of combing high-resolution emission spectroscopy with secondary eclipse photometry in characterizing atmospheric temperature structures.

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Ariel mission planning. Scheduling the survey of a thousand exoplanets

Automatic scheduling techniques are becoming a crucial tool for the efficient planning of large astronomical surveys. A specific scheduling method is being designed and developed for the Atmospheric Remote-sensing Infrared Exoplanet Large-survey (Ariel) mission planning based on a hybrid meta-heuristic algorithm with global optimization capability to ensure obtaining satisfying results fulfilling all mission constraints. We used this method to simulate the Ariel mission plan, to assess the feasibility of its scientific goals, and to study the outcome of different science scenarios. We conclude that Ariel will be able to fulfill the scientific objectives, i.e. characterizing ~1000 exoplanet atmospheres, with a total exposure time representing about 75-80% of the mission lifetime. We demonstrate that it is possible to include phase curve observations for a sample of targets or to increase the number of studied exoplanets within the mission lifetime. Finally, around 12-15% of the time can still be used for non-time constrained observations.

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Silicon in the dayside atmospheres of two ultra-hot Jupiters

Atmospheres of highly irradiated gas giant planets host a large variety of atomic and ionic species. Here we observe the thermal emission spectra of the two ultra-hot Jupiters WASP-33b and KELT-20b/MASCARA-2b in the near-infrared wavelength range with CARMENES. Via high-resolution Doppler spectroscopy, we searched for neutral silicon (Si) in their dayside atmospheres. We detect the Si spectral signature of both planets via cross-correlation with model spectra. Detection levels of 4.8$\mathrmσ$ and 5.4$\mathrmσ$, respectively, are observed when assuming a solar atmospheric composition. This is the first detection of Si in exoplanet atmospheres. The presence of Si is an important finding due to its fundamental role in cloud formation and, hence, for the planetary energy balance. Since the spectral lines are detected in emission, our results also confirm the presence of an inverted temperature profile in the dayside atmospheres of both planets.

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Metallicities in M dwarfs: Investigating different determination techniques

Deriving metallicities for solar-like stars follows well-established methods, but for cooler stars such as M dwarfs, the determination is much more complicated due to forests of molecular lines that are present. Several methods have been developed in recent years to determine accurate stellar parameters for these cool stars ($T_{\rm eff} \lesssim$ 4000 K). However, significant differences can be found at times when comparing metallicities for the same star derived using different methods. In this work, we determine the effective temperatures, surface gravities, and metallicities of 18 well-studied M dwarfs observed with the CARMENES high-resolution spectrograph following different approaches, including synthetic spectral fitting, analysis of pseudo-equivalent widths, and machine learning. We analyzed the discrepancies in the derived stellar parameters, including metallicity, in several analysis runs. Our goal is to minimize these discrepancies and find stellar parameters that are more consistent with the literature values. We attempted to achieve this consistency by standardizing the most commonly used components, such as wavelength ranges, synthetic model spectra, continuum normalization methods, and stellar parameters. We conclude that although such modifications work quite well for hotter main-sequence stars, they do not improve the consistency in stellar parameters for M dwarfs, leading to mean deviations of around 50-200 K in temperature and 0.1-0.3 dex in metallicity. In particular, M dwarfs are much more complex and a standardization of the aforementioned components cannot be considered as a straightforward recipe for bringing consistency to the derived parameters. Further in-depth investigations of the employed methods would be necessary in order to identify and correct for the discrepancies that remain.

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A multi-planetary system orbiting the early-M dwarf TOI-1238

Two transiting planet candidates with super-Earth radii around the nearby K7--M0 dwarf star TOI-1238 were announced by TESS. We aim to validate their planetary nature using precise radial velocities (RV) taken with the CARMENES spectrograph. We obtained 55 CARMENES RV data that span 11 months. For a better characterization of the parent star's activity, we also collected contemporaneous optical photometric observations and retrieved archival photometry from the literature. We performed a combined TESS+CARMENES photometric and spectroscopic analysis by including Gaussian processes and Keplerian orbits to account for the stellar activity and planetary signals simultaneously. We estimate that TOI-1238 has a rotation period of 40 $\pm$ 5 d based on photometric and spectroscopic data. The combined analysis confirms the discovery of two transiting planets, TOI-1238 b and c, with orbital periods of $0.764597^{+0.000013}_{-0.000011}$ d and $3.294736^{+0.000034}_{-0.000036}$ d, masses of 3.76$^{+1.15}_{-1.07}$ M$_{\oplus}$ and 8.32$^{+1.90}_{-1.88}$ M$_{\oplus}$, and radii of $1.21^{+0.11}_{-0.10}$ R$_{\oplus}$ and $2.11^{+0.14}_{-0.14}$ R$_{\oplus}$. They orbit their parent star at semimajor axes of 0.0137$\pm$0.0004 au and 0.036$\pm$0.001 au, respectively. The two planets are placed on opposite sides of the radius valley for M dwarfs and lie between the star and the inner border of TOI-1238's habitable zone. The inner super-Earth TOI-1238 b is one of the densest ultra-short-period planets ever discovered ($ρ=11.7^{+4.2}_{-3.4}$ g $\rm cm^{-3}$). The CARMENES data also reveal the presence of an outer, non-transiting, more massive companion with an orbital period and radial velocity amplitude of $\geq$600 d and $\geq$70 m s$^{-1}$, which implies a likely mass of $M \geq 2 \sqrt{1-e^2}$ M$_{\rm Jup}$ and a separation $\geq$1.1 au from its parent star.

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Rapid contraction of giant planets orbiting the 20 million-years old star V1298 Tau

Current theories of planetary evolution predict that infant giant planets have large radii and very low densities before they slowly contract to reach their final size after about several hundred million years. These theoretical expectations remain untested to date, despite the increasing number of exoplanetary discoveries, as the detection and characterisation of very young planets is extremely challenging due to the intense stellar activity of their host stars. However, the recent discoveries of young planetary transiting systems allow to place initial constraints on evolutionary models. With an estimated age of 20 million years, V1298\,Tau is one of the youngest solar-type stars known to host transiting planets: it harbours a multiple system composed of two Neptune-sized, one Saturn-sized, and one Jupiter-sized planets. Here we report the analysis of an intense radial velocity campaign, revealing the presence of two periodic signals compatible with the orbits of two of its planets. We find that planet b, with an orbital period of 24 days, has a mass of 0.64 Jupiter masses and a density similar to the giant planets of the Solar System and other known giant exoplanets with significantly older ages. Planet e, with an orbital period of 40 days, has a mass of 1.16 Jupiter masses and a density larger than most giant exoplanets. This is unexpected for planets at such a young age and suggests that some giant planets might evolve and contract faster than anticipated, thus challenging current models of planetary evolution.

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The CARMENES search for exoplanets around M dwarfs. Diagnostic capabilities of strong K I lines for photosphere and chromosphere

There are several strong K I lines found in the spectra of M dwarfs, among them the doublet near 7700 AA and another doublet near 12 500 AA. We study these optical and near-infrared doublets in a sample of 324 M dwarfs, observed with CARMENES, the high-resolution optical and near-infrared spectrograph at Calar Alto, and investigate how well the lines can be used as photospheric and chromospheric diagnostics. Both doublets have a dominant photospheric component in inactive stars and can be used as tracers of effective temperature and gravity. For variability studies using the optical doublet, we concentrate on the red line component because this is less prone to artefacts from telluric correction in individual spectra. The optical doublet lines are sensitive to activity, especially for M dwarfs later than M5.0 V where the lines develop an emission core. For earlier type M dwarfs, the red component of the optical doublet lines is also correlated with H$α$ activity. We usually find positive correlation for stars with H$α$ in emission, while early-type M stars with H$α$ in absorption show anti-correlation. During flares, the optical doublet lines can exhibit strong fill-in or emission cores for our latest spectral types. On the other hand, the near-infrared doublet lines very rarely show correlation or anti-correlation to H$α$ and do not change line shape significantly even during the strongest observed flares. Nevertheless, the near-infrared doublet lines show notable resolved Zeeman splitting for about 20 active stars which allows to estimate the magnetic fields B.

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H$α$ and He I absorption in HAT-P-32 b observed with CARMENES -- Detection of Roche lobe overflow and mass loss

We analyze two high-resolution spectral transit time series of the hot Jupiter HAT-P-32 b obtained with the CARMENES spectrograph. Our new XMM-Newton X-ray observations of the system show that the fast-rotating F-type host star exhibits a high X-ray luminosity of 2.3e29~erg/s (5-100 A), corresponding to a flux of 6.9e4 erg/cm**2/s at the planetary orbit, which results in an energy-limited escape estimate of about 1e13 g/s for the planetary mass-loss rate. The spectral time series show significant, time-dependent absorption in the Halpha and He I triplet lines with maximum depths of about 3.3% and 5.3%. The mid-transit absorption signals in the Halpha and He I lines are consistent with results from one-dimensional hydrodynamic modeling, which also yields mass-loss rates on the order of 1e13 g/s. We observe an early ingress of a redshifted component of the transmission signal, which extends into a redshifted absorption component, persisting until about the middle of the optical transit. While a super-rotating wind can explain redshifted ingress absorption, we find that an up-orbit stream, transporting planetary mass in the direction of the star, also provides a plausible explanation for the pre-transit signal. This makes HAT-P-32 a benchmark system for exploring atmospheric dynamics via transmission spectroscopy.

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TOI-1201 b: A mini-Neptune transiting a bright and moderately young M dwarf

We present the discovery of a transiting mini-Neptune around TOI-1201, a relatively bright and moderately young early M dwarf ($J \approx$ 9.5 mag, $\sim$600-800 Myr) in an equal-mass $\sim$8 arcsecond-wide binary system, using data from the Transiting Exoplanet Survey Satellite (TESS), along with follow-up transit observations. With an orbital period of 2.49 d, TOI-1201 b is a warm mini-Neptune with a radius of $R_\mathrm{b} = 2.415\pm0.090 R_\oplus$. This signal is also present in the precise radial velocity measurements from CARMENES, confirming the existence of the planet and providing a planetary mass of $M_\mathrm{b} = 6.28\pm0.88 M_\oplus$ and, thus, an estimated bulk density of $2.45^{+0.48}_{-0.42}$ g cm$^{-3}$. The spectroscopic observations additionally show evidence of a signal with a period of 19 d and a long periodic variation of undetermined origin. In combination with ground-based photometric monitoring from WASP-South and ASAS-SN, we attribute the 19 d signal to the stellar rotation period ($P_{rot}=$ 19-23 d), although we cannot rule out that the variation seen in photometry belongs to the visually close binary companion. We calculate precise stellar parameters for both TOI-1201 and its companion. The transiting planet is an excellent target for atmosphere characterization (the transmission spectroscopy metric is $97^{+21}_{-16}$) with the upcoming James Webb Space Telescope. It is also feasible to measure its spin-orbit alignment via the Rossiter-McLaughlin effect using current state-of-the-art spectrographs with submeter per second radial velocity precision.

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Probing the atmosphere of WASP-69 b with low- and high-resolution transmission spectroscopy

Consideration of both low- and high-resolution transmission spectroscopy is key for obtaining a comprehensive picture of exoplanet atmospheres. In studies of transmission spectra, the continuum information is well established with low-resolution spectra, while the shapes of individual lines are best constrained with high-resolution observations. In this work, we aim to merge high- with low-resolution transmission spectroscopy. We present the analysis of three primary transits of WASP-69b in the VIS channel of the CARMENES instrument and perform a combined low- and high-resolution analysis using additional data from HARPS-N, OSIRIS/GTC, and WFC3/HST already available in the literature. During the first CARMENES observing night, we detected the planet Na D$_{2}$ and D$_{1}$ lines at $\sim 7σ$ and $\sim 3σ$ significance levels, respectively. We measured a D$_{2}$/D$_{1}$ intensity ratio of 2.5$\pm$0.7, which is in agreement with previous HARPS-N observations. Our modelling of WFC3 and OSIRIS data suggests strong Rayleigh scattering, solar to super-solar water abundance, and a highly muted Na feature in the atmosphere of this planet, in agreement with previous investigations of this target. We use the continuum information retrieved from the low-resolution spectroscopy as a prior to break the degeneracy between the Na abundance, reference pressure, and thermosphere temperature for the high-resolution spectroscopic analysis. We fit the Na D$_{1}$ and D$_{2}$ lines individually and find that the posterior distributions of the model parameters agree with each other within 1$σ$. Our results suggest that local thermodynamic equilibrium processes can explain the observed D$_{2}$/D$_{1}$ ratio because the presence of haze opacity mutes the absorption features.

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