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A. Quirrenbach

Publications and source records attributed to A. Quirrenbach.

At least 91 records · Page 5Linked to original sources

Large Interferometer For Exoplanets (LIFE): I. Improved exoplanet detection yield estimates for a large mid-infrared space-interferometer mission

One of the long-term goals of exoplanet science is the atmospheric characterization of dozens of small exoplanets in order to understand their diversity and search for habitable worlds and potential biosignatures. Achieving this goal requires a space mission of sufficient scale. We seek to quantify the exoplanet detection performance of a space-based mid-infrared nulling interferometer that measures the thermal emission of exoplanets. For this, we have developed an instrument simulator that considers all major astrophysical noise sources and coupled it with Monte Carlo simulations of a synthetic exoplanet population around main-sequence stars within 20 pc. This allows us to quantify the number (and types) of exoplanets that our mission concept could detect over a certain time period. Two different scenarios to distribute the observing time among the stellar targets are discussed and different apertures sizes and wavelength ranges are considered. Within a 2.5-year initial search phase, an interferometer consisting of four 2 m apertures with a total instrument throughput of 5% covering a wavelength range between 4 and 18.5 $μ$m could detect up to ~550 exoplanets with radii between 0.5 and 6 R$_\oplus$ with an integrated SNR$\ge$7. At least ~160 of the detected exoplanets have radii $\le$1.5 R$_\oplus$. Depending on the observing scenario, ~25-45 rocky exoplanets (objects with radii between 0.5 and 1.5 $_{\oplus}$) orbiting within the empirical habitable zone (eHZ) of their host stars are among the detections. With an aperture size of 3.5 m, the total number of detections can increase to up to ~770, including ~60-80 rocky, eHZ planets. With 1 m aperture size, the maximum detection yield is ~315 exoplanets, including $\le$20 rocky, eHZ planets. In terms of predicted detection yield, such a mission can compete with large single-aperture reflected light missions. (abridged)

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A quarter century of spectroscopic monitoring of the nearby M dwarf Gl 514. A super-Earth on an eccentric orbit moving in and out of the habitable zone

We investigated the presence of planetary companions around the nearby (7.6 pc) and bright ($V=9$ mag) early-type M dwarf Gl 514, analysing 540 radial velocities collected over nearly 25 years with the HIRES, HARPS, and CARMENES spectrographs. The data are affected by time-correlated signals at the level of 2-3 ms$^{-1}$ due to stellar activity, that we filtered out testing three different models based on Gaussian process regression. As a sanity cross-check, we repeated the analyses using HARPS radial velocities extracted with three different algorithms. We used HIRES radial velocities and Hipparcos-Gaia astrometry to put constraints on the presence of long-period companions, and we analysed TESS photometric data. We found strong evidence that Gl 514 hosts a super-Earth on a likely eccentric orbit, residing in the conservative habitable zone for nearly $34\%$ of its orbital period. The planet Gl 514 b has minimum mass $m_b\sin i_b=5.2\pm0.9$ $M_{\rm Earth}$, orbital period $P_b=140.43\pm0.41$ days, and eccentricity $e_b=0.45^{+0.15}_{-0.14}$. No evidence for transits is found in the TESS light curve. There is no evidence for a longer period companion in the radial velocities and, based on astrometry, we can rule out a $\sim0.2$ $M_{\rm Jup}$ planet at a distance of $\sim3-10$ au, and massive giant planets/brown dwarfs out to several tens of au. We discuss the possible presence of a second low-mass companion at a shorter distance from the host than Gl 514 b. Gl 514 b represents an interesting science case to study the habitability of planets on eccentric orbits. We advocate for additional spectroscopic follow-up to get more accurate and precise planetary parameters. Further follow-up is also needed to investigate sub \ms and shorter period signals.

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Magnetism, rotation, and nonthermal emission in cool stars -- Average magnetic field measurements in 292 M dwarfs

Stellar dynamos generate magnetic fields that are of fundamental importance to the variability and evolution of Sun-like and low-mass stars, and for the development of their planetary systems. We report measurements of surface-average magnetic fields in 292 M dwarfs from a comparison with radiative transfer calculations; for 260 of them, this is the first measurement of this kind. Our data were obtained from more than 15,000 high-resolution spectra taken during the CARMENES project. They reveal a relation between average field strength, , and Rossby number, $Ro$, resembling the well-studied rotation-activity relation. Among the slowly rotating stars, we find that magnetic flux, $Φ_\textrm{B}$, is proportional to rotation period, $P$, and among the rapidly rotating stars that average surface fields do not grow significantly beyond the level set by the available kinetic energy. Furthermore, we find close relations between nonthermal coronal X-ray emission, chromospheric H$α$ and Ca H&K emission, and magnetic flux. Taken together, these relations demonstrate empirically that the rotation-activity relation can be traced back to a dependence of the magnetic dynamo on rotation. We advocate the picture that the magnetic dynamo generates magnetic flux on the stellar surface proportional to rotation rate with a saturation limit set by the available kinetic energy, and we provide relations for average field strengths and nonthermal emission that are independent of the choice of the convective turnover time. We also find that Ca H&K emission saturates at average field strengths of $\langle B \rangle \approx 800$ G while H$α$ and X-ray emission grow further with stronger fields in the more rapidly rotating stars. This is in conflict with the coronal stripping scenario predicting that in the most rapidly rotating stars coronal plasma would be cooled to chromospheric temperatures.

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The CARMENES search for exoplanets around M dwarfs: Two Saturn-mass planets orbiting active stars

The CARMENES radial-velocity survey is currently searching for planets in a sample of 387 M dwarfs. Here we report on two Saturn-mass planets orbiting TYC 2187-512-1 ($M_\star = 0.50 M_\odot$) and TZ Ari ($M_\star = 0.15 M_\odot$), respectively. We obtained supplementary photometric time series, which we use along with spectroscopic information to determine the rotation periods of the two stars. In both cases, the radial velocities also show strong modulations at the respective rotation period. We thus modeled the radial velocities as a Keplerian orbit plus a Gaussian process representing the stellar variability. TYC 2187-512-1 is found to harbor a planet with a minimum mass of 0.33 $M_{\rm Jup}$ in a near-circular 692-day orbit. The companion of TZ Ari has a minimum mass of 0.21 $M_{\rm Jup}$, orbital period of 771 d, and orbital eccentricity of 0.46. We provide an overview of all known giant planets in the CARMENES sample, from which we infer an occurrence rate of giant planets orbiting M dwarfs with periods up to 2 years in the range between 2% to 6%. TZ Ari b is only the second giant planet discovered orbiting a host with mass less than 0.3 $M_\odot$. These objects occupy an extreme location in the planet mass versus host mass plane. It is difficult to explain their formation in core-accretion scenarios, so they may possibly have been formed through a disk fragmentation process.

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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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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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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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ISPY -- NaCo Imaging Survey for Planets around Young stars. CenteR: the impact of centering and frame selection

Abridged: Direct imaging has made significant progress over the past decade leading to the detection of several giant planets. Observing strategies and data rates vary from instrument to instrument and wavelength, and can result in tens of thousands of images to be combined. We here present a new approach, tailored for VLT/NaCo observations performed with the Annular Groove Phase Mask (AGPM) coronagraph at $L'$ filter. Our pipeline aims at improving the post-processing of the observations on two fronts: identifying the location of the star behind the AGPM to better align the science frames and performing frame selection. Our method relies on finding the position of the AGPM in the sky frame observations, and correlate it with the circular aperture of the coronagraphic mask. This relationship allows us to retrieve the location of the AGPM in the science frames, in turn allowing us to estimate the position of the star. In the process we also gather additional information useful for our frame selection approach. We tested our pipeline on several targets, and find that we improve the S/N of companions around $β$ Pictoris and R CrA by $24\pm3$ \% and $117\pm11$ \% respectively, compared to other state-of-the-art reductions. The astrometry of the point sources is slightly different but remains compatible within $3σ$ compared to published values. Finally, we find that even for NaCo observations with tens of thousands of frames, frame selection yields just marginal improvement for point sources but may improve the final images for objects with extended emission such as disks. We proposed a novel approach to identify the location of the star behind a coronagraph even when it cannot easily be determined by other methods, leading to better S/N for nearby point sources, and led a thorough study on the importance of frame selection, concluding that the improvements are marginal in most case.

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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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The CARMENES search for exoplanets around M dwarfs -- Planet occurrence rates from a subsample of 71 stars

The CARMENES exoplanet survey of M dwarfs has obtained more than 18 000 spectra of 329 nearby M dwarfs over the past five years as part of its guaranteed time observations (GTO) program. We determine planet occurrence rates with the 71 stars from the GTO program for which we have more than 50 observations. We use injection-and-retrieval experiments on the radial-velocity (RV) time series to measure detection probabilities. We include 27 planets in 21 planetary systems in our analysis. We find 0.06+0.04-0.03 giant planets (100 M_Earth < M_pl sin i < 1000 M_Earth) per star in periods of up to 1000 d, but due to a selection bias this number could be up to a factor of five lower in the whole 329-star sample. The upper limit for hot Jupiters (orbital period of less than 10 d) is 0.03 planets per star, while the occurrence rate of planets with intermediate masses (10 M_Earth < M_pl sin i < 100 M_Earth) is 0.18+0.07-0.05 planets per star. Less massive planets with 1 M_Earth < M_pl sin i < 10 M_Earth are very abundant, with an estimated rate of 1.32+0.33-0.31 planets per star for periods of up to 100 d. When considering only late M dwarfs with masses M_star < 0.34 M_sol, planets more massive than 10 M_Earth become rare. Instead, low-mass planets with periods shorter than 10 d are significantly overabundant. For orbital periods shorter than 100 d, our results confirm the known stellar mass dependences from the Kepler survey: M dwarfs host fewer giant planets and at least two times more planets with M_pl sin i < 10 M_Earth than G-type stars. In contrast to previous results, planets around our sample of very low-mass stars have a higher occurrence rate in short-period orbits of less than 10 d. Our results demonstrate the need to take into account host star masses in planet formation models.

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