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I. Ribas

Publications and source records attributed to I. Ribas.

At least 217 records · Page 12Linked to original sources

The CARMENES search for exoplanets around M dwarfs. Two temperate Earth-mass planet candidates around Teegarden's Star

Context. Teegarden's Star is the brightest and one of the nearest ultra-cool dwarfs in the solar neighbourhood. For its late spectral type (M7.0V), the star shows relatively little activity and is a prime target for near-infrared radial velocity surveys such as CARMENES. Aims. As part of the CARMENES search for exoplanets around M dwarfs, we obtained more than 200 radial-velocity measurements of Teegarden's Star and analysed them for planetary signals. Methods. We find periodic variability in the radial velocities of Teegarden's Star. We also studied photometric measurements to rule out stellar brightness variations mimicking planetary signals. Results. We find evidence for two planet candidates, each with $1.1M_\oplus$ minimum mass, orbiting at periods of 4.91 and 11.4 d, respectively. No evidence for planetary transits could be found in archival and follow-up photometry. Small photometric variability is suggestive of slow rotation and old age. Conclusions. The two planets are among the lowest-mass planets discovered so far, and they are the first Earth-mass planets around an ultra-cool dwarf for which the masses have been determined using radial velocities.

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Water vapor detection in the transmission spectra of HD 209458 b with the CARMENES NIR channel

Aims: We aim at detecting H$_2$O in the atmosphere of the hot Jupiter HD 209458 b and perform a multi-band study in the near infrared with CARMENES. Methods: The H$_2$O absorption lines from the planet's atmosphere are Doppler-shifted due to the large change in its radial velocity during transit. This shift is of the order of tens of km s$^{-1}$, whilst the Earth's telluric and the stellar lines can be considered quasi-static. We took advantage of this to remove the telluric and stellar lines using SYSREM, a principal component analysis algorithm. The residual spectra contain the signal from thousands of planetary molecular lines well below the noise level. We retrieve this information by cross-correlating the spectra with models of the atmospheric absorption. Results: We find evidence of H$_2$O in HD 209458 b with a signal-to-noise ratio (S/N) of 6.4. The signal is blueshifted by --5.2 $^{+2.6}_{-1.3}$ km s$^{-1}$, which, despite the error bars, is a firm indication of day-to-night winds at the terminator of this hot Jupiter. Additionally, we performed a multi-band study for the detection of H$_2$O individually from the three NIR bands covered by CARMENES. We detect H$_2$O from its 1.0 $μ$m band with a S/N of 5.8, and also find hints from the 1.15 $μ$m band, with a low S/N of 2.8. No clear planetary signal is found from the 1.4 $μ$m band. Conclusions: Our significant signal from the 1.0 $μ$m band in HD 209458 b represents the first detection of H$_2$O from this band, the bluest one to date. The unfavorable observational conditions might be the reason for the inconclusive detection from the stronger 1.15 and 1.4 $μ$m bands. H$_2$O is detected from the 1.0 $μ$m band in HD 209458 b, but hardly in HD 189733 b, which supports a stronger aerosol extinction in the latter.

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Red Dots: A temperate 1.5 Earth-mass planet in a compact multi-terrestrial planet system around GJ1061

Small low-mass stars are favourable targets for the detection of rocky habitable planets. In particular, planetary systems in the solar neighbourhood are interesting and suitable for precise characterisation. The Red Dots campaigns seek to discover rocky planets orbiting nearby low-mass stars. The 2018 campaign targeted GJ 1061, which is the 20$^{\rm th}$ nearest star to the Sun. For three consecutive months we obtained nightly, high-precision radial velocity measurements with the HARPS spectrograph. We analysed these data together with archival HARPS data. We report the detection of three planet candidates with periods of $3.204\pm 0.001$, $6.689\pm 0.005$ and $13.03\pm 0.03$ days, which is close to 1:2:4 period commensurability. After several considerations related to the properties of the noise and sampling, we conclude that a 4$^{\rm th}$ signal is most likely explained by stellar rotation, although it may be due to a planet. The proposed three-planet system (and the potential four-planet solution) is long-term dynamically stable. Planet-planet gravitational interactions are below our current detection threshold. The minimum masses of the three planets range from $1.4\pm 0.2$ to $1.8\pm 0.3$ M$_\oplus$. Planet d, with $m \sin i = 1.68\pm0.25$ M$_\oplus$, receives a similar amount of energy as Earth receives from the Sun. Consequently it lies within the liquid-water habitable zone of the star and has a similar equilibrium temperature to Earth. GJ 1061 has very similar properties to Proxima Centauri but activity indices point to lower levels of stellar activity.

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Stellar activity analysis of Barnard's Star: Very slow rotation and evidence for long-term activity cycle

The search for Earth-like planets around late-type stars using ultra-stable spectrographs requires a very precise characterization of the stellar activity and the magnetic cycle of the star, since these phenomena induce radial velocity (RV) signals that can be misinterpreted as planetary signals. Among the nearby stars, we have selected Barnard's Star (Gl 699) to carry out a characterization of these phenomena using a set of spectroscopic data that covers about 14.5 years and comes from seven different spectrographs: HARPS, HARPS-N, CARMENES, HIRES, UVES, APF, and PFS; and a set of photometric data that covers about 15.1 years and comes from four different photometric sources: ASAS, FCAPT-RCT, AAVSO, and SNO. We have measured different chromospheric activity indicators (H$α$, Ca~{\sc II}~HK and Na I D), as well as the FWHM of the cross-correlation function computed for a sub-set of the spectroscopic data. The analysis of Generalized Lomb-Scargle periodograms of the time series of different activity indicators reveals that the rotation period of the star is 145 $\pm$ 15 days, consistent with the expected rotation period according to the low activity level of the star and previous claims. The upper limit of the predicted activity-induced RV signal corresponding to this rotation period is about 1 m/s. We also find evidence of a long-term cycle of 10 $\pm$ 2 years that is consistent with previous estimates of magnetic cycles from photometric time series in other M stars of similar activity levels. The available photometric data of the star also support the detection of both the long-term and the rotation signals.

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He I $λ$ 10830 Å in the transmission spectrum of HD 209458 b

Context: Recently, the He I triplet at 10830 Å has been rediscovered as an excellent probe of the extended and possibly evaporating atmospheres of close-in transiting planets. This has already resulted in detections of this triplet in the atmospheres of a handful of planets, both from space and from the ground. However, while a strong signal is expected for the hot Jupiter HD 209458 b, only upper limits have been obtained so far. Aims: Our goal is to measure the helium excess absorption from HD 209458 b and assess the extended atmosphere of the planet and possible evaporation. Methods: We obtained new high-resolution spectral transit time-series of HD 209458 b using CARMENES at the 3.5 m Calar Alto telescope, targeting the He I triplet at 10830 Å at a spectral resolving power of 80 400. The observed spectra were corrected for stellar absorption lines using out of transit data, for telluric absorption using the molecfit software, and for the sky emission lines using simultaneous sky measurements through a second fibre. Results: We detect He I absorption at a level of 0.91 $\pm$ 0.10 % (9 $σ$) at mid-transit. The absorption follows the radial velocity change of the planet during transit, unambiguously identifying the planet as the source of the absorption. The core of the absorption exhibits a net blueshift of 1.8 $\pm$ 1.3 km s$^{-1}$. Possible low-level excess absorption is seen further blueward from the main absorption near the centre of the transit, which could be caused by an extended tail. However, this needs to be confirmed. Conclusions: Our results further support a close relationship between the strength of planetary absorption in the helium triplet lines and the level of ionising, stellar X-ray and extreme-UV irradiation.

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Planetary system around the nearby M dwarf GJ 357 including a transiting, hot, Earth-sized planet optimal for atmospheric characterization

We report the detection of a transiting Earth-size planet around GJ 357, a nearby M2.5V star, using data from the Transiting Exoplanet Survey Satellite (TESS). GJ 357 b (TOI-562.01) is a transiting, hot, Earth-sized planet (Teq=525+-11 K) with a radius of Rb=1.217+-0.084 Re and an orbital period of Pb=3.93 d. Precise stellar radial velocities from CARMENES and PFS, as well as archival data from HIRES, UVES, and HARPS also display a 3.93-day periodicity, confirming the planetary nature and leading to a planetary mass of Mb=1.84+-0.31 Me. In addition to the radial velocity signal for GJ 357 b, more periodicities are present in the data indicating the presence of two further planets in the system: GJ 357 c, with a minimum mass of Mc=3.40+-0.46 Me in a 9.12 d orbit, and GJ 357 d, with a minimum mass of Md=6.1+-1.0 Me in a 55.7 d orbit inside the habitable zone. The host is relatively inactive and exhibits a photometric rotation period of Prot=78+-2 d. GJ 357 b is to date the second closest transiting planet to the Sun, making it a prime target for further investigations such as transmission spectroscopy. Therefore, GJ 357 b represents one of the best terrestrial planets suitable for atmospheric characterization with the upcoming JWST and ground-based ELTs.

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Kepler Object of Interest Network III. Kepler-82f: A new non-transiting $21 M_\bigoplus$ planet from photodynamical modelling

Context. The Kepler Object of Interest Network (KOINet) is a multi-site network of telescopes around the globe organised for follow-up observations of transiting planet candidate Kepler objects of interest (KOIs) with large transit timing variations (TTVs). The main goal of KOINet is the completion of their TTV curves as the Kepler telescope stopped observing the original Kepler field in 2013. Aims. We ensure a comprehensive characterisation of the investigated systems by analysing Kepler data combined with new ground-based transit data using a photodynamical model. This method is applied to the Kepler-82 system leading to its first dynamic analysis. Methods. In order to provide a coherent description of all observations simultaneously, we combine the numerical integration of the gravitational dynamics of a system over the time span of observations with a transit light curve model. To explore the model parameter space, this photodynamical model is coupled with a Markov chain Monte Carlo algorithm. Results. The Kepler-82b/c system shows sinusoidal TTVs due to their near 2:1 resonance dynamical interaction. An additional chopping effect in the TTVs of Kepler-82c hints to a further planet near the 3:2 or 3:1 resonance. We photodynamically analysed Kepler long- and short-cadence data and three new transit observations obtained by KOINet between 2014 and 2018. Our result reveals a non-transiting outer planet with a mass of $m_f=20.9\pm1.0\;M_\bigoplus$ near the 3:2 resonance to the outermost known planet, Kepler-82c. Furthermore, we determined the densities of planets b and c to the significantly more precise values $ρ_b=0.98_{-0.14}^{+0.10}\;\text{g cm}^{-3}$ and $ρ_c=0.494_{-0.077}^{+0.066}\;\text{g cm}^{-3}$.

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The CARMENES search for exoplanets around M dwarfs -- Photospheric parameters of target stars from high-resolution spectroscopy. II. Simultaneous multiwavelength range modeling of activity insensitive lines

We present precise photospheric parameters of 282 M dwarfs determined from fitting the most recent version of PHOENIX models to high-resolution CARMENES spectra in the visible (0.52 - 0.96 $μ$m) and near-infrared wavelength range (0.96 - 1.71 $μ$m). With its aim to search for habitable planets around M dwarfs, several planets of different masses have been detected. The characterization of the target sample is important for the ability to derive and constrain the physical properties of any planetary systems that are detected. As a continuation of previous work in this context, we derived the fundamental stellar parameters effective temperature, surface gravity, and metallicity of the CARMENES M-dwarf targets from PHOENIX model fits using a $χ^2$ method. We calculated updated PHOENIX stellar atmosphere models that include a new equation of state to especially account for spectral features of low-temperature stellar atmospheres as well as new atomic and molecular line lists. We show the importance of selecting magnetically insensitive lines for fitting to avoid effects of stellar activity in the line profiles. For the first time, we directly compare stellar parameters derived from multiwavelength range spectra, simultaneously observed for the same star. In comparison with literature values we show that fundamental parameters derived from visible spectra and visible and near-infrared spectra combined are in better agreement than those derived from the same spectra in the near-infrared alone.

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The CARMENES search for exoplanets around M dwarfs Detection of a mini-Neptune around LSPM J2116+0234 and refinement of orbital parameters of a super-Earth around GJ 686 (BD+18 3421)

Although M dwarfs are known for high levels of stellar activity, they are ideal targets for the search of low-mass exoplanets with the radial velocity (RV) method. We report the discovery of a planetary-mass companion around LSPM J2116+0234 (M3.0 V) and confirm the existence of a planet orbiting GJ 686 (BD+18 3421; M1.0 V). The discovery of the planet around LSPM J2116+0234 is based on CARMENES RV observations in the visual and near-infrared channels. We confirm the planet orbiting around GJ 686 by analyzing the RV data spanning over two decades of observations from CARMENES VIS, HARPS-N, HARPS, and HIRES. We find planetary signals at 14.44 and 15.53 d in the RV data for LSPM J2116+0234 and GJ 686, respectively. Additionally, the RV, photometric time series, and various spectroscopic indicators show hints of variations of 42 d for LSPM J2116+0234 and 37 d for GJ 686, which we attribute to the stellar rotation periods. The orbital parameters of the planets are modeled with Keplerian fits together with correlated noise from the stellar activity. A mini-Neptune with a minimum mass of 11.8 Me orbits LSPM J2116+0234 producing an RV semi-amplitude of 6.19 m/s, while a super-Earth of mass 6.6 Me orbits GJ 686 and produces an RV semi-amplitude of 3.0 m/s. Both LSPM J2116+0234 and GJ 686 have planetary companions populating the regime of exoplanets with masses lower than 15 Me and orbital periods <20 d.

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K2-295 b and K2-237 b: two transiting hot Jupiters

We report the discovery from K2 of two transiting hot Jupiter systems. K2-295 (observed in Campaign 8) is a K5 dwarf which hosts a planet slightly smaller than Jupiter, orbiting with a period of 4.0 d. We have made an independent discovery of K2-237 b (Campaign 11), which orbits an F6 dwarf every 2.2 d and has an inflated radius 50 - 60 per cent larger than that of Jupiter. We use high-precision radial velocity measurements, obtained using the HARPS and FIES spectrographs, to measure the planetary masses. We find that K2-295 b has a similar mass to Saturn, while K2-237 b is a little more massive than Jupiter.

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Magnetic fields in M dwarfs from the CARMENES survey

M dwarfs are known to generate the strongest magnetic fields among main-sequence stars with convective envelopes, but the link between the magnetic fields and underlying dynamo mechanisms, rotation, and activity still lacks a consistent picture. In this work we measure magnetic fields from the high-resolution near-infrared spectra taken with the CARMENES radial-velocity planet survey in a sample of 29 active M dwarfs and compare our results against stellar parameters. We use the state-of-the-art radiative transfer code to measure total magnetic flux densities from the Zeeman broadening of spectral lines and filling factors. We detect strong kG magnetic fields in all our targets. In 16 stars the magnetic fields were measured for the first time. Our measurements are consistent with the magnetic field saturation in stars with rotation periods P<4d. The analysis of the magnetic filling factors reveal two different patterns of either very smooth distribution or a more patchy one, which can be connected to the dynamo state of the stars and/or stellar mass. Our measurements extend the list of M dwarfs with strong surface magnetic fields. They also allow us to better constrain the interplay between the magnetic energy, stellar rotation, and underlying dynamo action. The high spectral resolution and observations at near-infrared wavelengths are the beneficial capabilities of the CARMENES instrument that allow us to address important questions about the stellar magnetism.

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The CARMENES search for exoplanets around M dwarfs: Different roads to radii and masses of the target stars

We determine the radii and masses of 293 nearby, bright M dwarfs of the CARMENES survey. This is the first time that such a large and homogeneous high-resolution (R>80 000) spectroscopic survey has been used to derive these fundamental stellar parameters. We derived the radii using Stefan-Boltzmann's law. We obtained the required effective temperatures $T_{\rm eff}$ from a spectral analysis and we obtained the required luminosities L from integrated broadband photometry together with the Gaia DR2 parallaxes. The mass was then determined using a mass-radius relation that we derived from eclipsing binaries known in the literature. We compared this method with three other methods: (1) We calculated the mass from the radius and the surface gravity log g, which was obtained from the same spectral analysis as $T_{\rm eff}$. (2) We used a widely used infrared mass-magnitude relation. (3) We used a Bayesian approach to infer stellar parameters from the comparison of the absolute magnitudes and colors of our targets with evolutionary models. Between spectral types M0V and M7V our radii cover the range $0.1\,R_{\normalsize\odot}<R<0.6\,R_{\normalsize\odot}$ with an error of 2-3% and our masses cover $0.09\,{\mathcal M}_{\normalsize\odot}<{\mathcal M}<0.6\,{\mathcal M}_{\normalsize\odot}$ with an error of 3-5%. We find good agreement between the masses determined with these different methods for most of our targets. Only the masses of very young objects show discrepancies. This can be well explained with the assumptions that we used for our methods.

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The HADES RV Programme with HARPS-N at TNG XI. GJ 685 b: a warm super-Earth around an active M dwarf

Small rocky planets seem to be very abundant around low-mass M-type stars. Their actual planetary population is however not yet precisely understood. Currently several surveys aim to expand the statistics with intensive detection campaigns, both photometric and spectroscopic. We analyse 106 spectroscopic HARPS-N observations of the active M0-type star GJ 685 taken over the past five years. We combine these data with photometric measurements from different observatories to accurately model the stellar rotation and disentangle its signals from genuine Doppler planetary signals in the RV data. We run an MCMC analysis on the RV and activity indexes time series to model the planetary and stellar signals present in the data, applying Gaussian Process regression technique to deal with the stellar activity signals. We identify three periodic signals in the RV time series, with periods of 9, 24, and 18 d. Combining the analyses of the photometry of the star with the activity indexes derived from the HARPS-N spectra, we identify the 18 d and 9 d signals as activity-related, corresponding to the stellar rotation period and its first harmonic respectively. The 24 d signals shows no relations with any activity proxy, so we identify it as a genuine planetary signal. We find the best-fit model describing the Doppler signal of the newly-found planet, GJ 685\,b, corresponding to an orbital period $P_b = 24.160^{+0.061}_{-0.047}$ d and a minimum mass $M_P \sin i = 9.0^{+1.7}_{-1.8}$ M$_\oplus$. We also study a sample of 70 RV-detected M-dwarf planets, and present new statistical evidence of a difference in mass distribution between the populations of single- and multi-planet systems, which can shed new light on the formation mechanisms of low-mass planets around late-type stars.

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HD219666b: A hot-Neptune from TESS Sector 1

We report on the confirmation and mass determination of a transiting planet orbiting the old and inactive G7 dwarf star HD219666 (Mstar = 0.92 +/- 0.03 MSun, Rstar = 1.03 +/- 0.03 RSun, tau_star = 10 +/- 2 Gyr). With a mass of Mb = 16.6 +/- 1.3 MEarth, a radius of Rb = 4.71 +/- 0.17 REarth, and an orbital period of P ~ 6 days, HD219666b is a new member of a rare class of exoplanets: the hot-Neptunes. The Transiting Exoplanet Survey Satellite (TESS) observed HD219666 (also known as TOI-118) in its Sector 1 and the light curve shows four transit-like events, equally spaced in time. We confirmed the planetary nature of the candidate by gathering precise radial-velocity measurements with HARPS@ESO3.6m. We used the co-added HARPS spectrum to derive the host star fundamental parameters (Teff = 5527 +/- 65 K, log g = 4.40 +/- 0.11 (cgs), [Fe/H]= 0.04 +/- 0.04 dex, log R'HK = -5.07 +/- 0.03), as well as the abundances of many volatile and refractory elements. The host star brightness (V = 9.9) makes it suitable for further characterisation by means of in-transit spectroscopy. The determination of the planet orbital obliquity, along with the atmospheric metal-to-hydrogen content and thermal structure could provide us with important clues on the formation mechanisms of this class of objects.

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HADES RV Programme with HARPS-N at TNG. X. The non-saturated regime of the stellar activity-rotation relationship for M-Dwarfs

Aims. We aim to extend the relationship between X-ray luminosity (Lx) and rotation period (Prot) found for main-sequence FGK stars and test whether it also holds for early-M dwarfs, especially in the non-saturated regime (Lx α P_{rot}^{-2}) which corresponds to slow rotators. Methods. We use the luminosity coronal activity indicator (Lx) of a sample of 78 early-M dwarfs with masses in the range from 0.3 to 0.75 Msun from the HArps-N red Dwarf Exoplanet Survey (HADES) radial velocity (RV) programme collected from ROSAT and XMM-Newton. The determination of the rotation periods (P_{rot}) was done by analysing time-series of high-resolution spectroscopy of the Ca ii H & K and Hα activity indicators. Our sample principally covers the slow rotation regime with rotation periods from 15 to 60 days. Results. Our work extends to the low mass regime the observed trend for more massive stars showing a continuous shift of the Lx/Lbol vs. Prot power-law towards longer rotation period values and includes the determination, in a more accurate way, of the value of the rotation period at which the saturation occurs (P_{sat}) for M dwarf stars. Conclusions. We conclude that the relations between coronal activity and stellar rotation for FGK stars also hold for early-M dwarfs in the non-saturated regime, indicating that the rotation period is sufficient to determine the ratio Lx/Lbol.

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The CARMENES search for exoplanets around M dwarfs. Chromospheric modeling of M2-3 V stars with PHOENIX

Chromospheric modeling of observed differences in stellar activity lines is imperative to fully understand the upper atmospheres of late-type stars. We present one-dimensional parametrized chromosphere models computed with the atmosphere code PHOENIX using an underlying photosphere of 3500 K. The aim of this work is to model chromospheric lines of a sample of 50 M2-3 dwarfs observed in the framework of the CARMENES, the Calar Alto high-Resolution search for M dwarfs with Exo-earths with Near-infrared and optical Echelle Spectrographs, exoplanet survey. The spectral comparison between observed data and models is performed in the chromospheric lines of Na I D2, H$α$, and the bluest Ca II infrared triplet line to obtain best-fit models for each star in the sample. We find that for inactive stars a single model with a VAL C-like temperature structure is sufficient to describe simultaneously all three lines adequately. Active stars are rather modeled by a combination of an inactive and an active model, also giving the filling factors of inactive and active regions. Moreover, the fitting of linear combinations on variable stars yields relationships between filling factors and activity states, indicating that more active phases are coupled to a larger portion of active regions on the surface of the star.

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HADES RV program with HARPS-N at TNG. IX. A super-Earth around the M dwarf Gl686

The HArps-n red Dwarf Exoplanet Survey is providing a major contribution to the widening of the current statistics of low-mass planets, through the in-depth analysis of precise radial velocity measurements in a narrow range of spectral sub-types. As part of that program, we obtained radial velocity measurements of Gl 686, an M1 dwarf at d = 8.2 pc. The analysis of data obtained within an intensive observing campaign demonstrates that the excess dispersion is due to a coherent signal, with a period of 15.53 d. Almost simultaneous photometric observations were carried out within the APACHE and EXORAP programs to characterize the stellar activity and to distinguish periodic variations related to activity from signals due to the presence of planetary companions, complemented also with ASAS photometric data. We took advantage of the available radial velocity measurements for this target from other observing campaigns. The analysis of the radial velocity composite time series from the HIRES, HARPS and HARPS-N spectrographs, consisting of 198 measurements taken over 20 years, enabled us to address the nature of periodic signals and also to characterize stellar physical parameters (mass, temperature, and rotation). We report the discovery of a super-Earth orbiting at a distance of 0.092 AU from the host star Gl 686. Gl 686 b has a minimum mass of 7.1 +/- 0.9 MEarth and an orbital period of 15.532 +/- 0.002 d. The analysis of the activity indexes, correlated noise through a Gaussian process framework and photometry, provides an estimate of the stellar rotation period at 37 d, and highlights the variability of the spot configuration during the long timespan covering 20 yrs. The observed periodicities around 2000 d likely point to the existence of an activity cycle.

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The CARMENES search for exoplanets around M dwarfs. Activity indicators at visible and near-infrared wavelengths

The CARMENES survey is searching for Earth-like planets orbiting M dwarfs using the radial velocity method. Studying the stellar activity of the target stars is important to avoid false planet detections and to improve our understanding of the atmospheres of late-type stars. In this work we present measurements of activity indicators at visible and near-infrared wavelengths for 331 M dwarfs observed with CARMENES. Our aim is to identify the activity indicators that are most sensitive and easiest to measure, and the correlations among these indicators. We also wish to characterise their variability. Using a spectral subtraction technique, we measured pseudo-equivalent widths of the He I D3, H$α$, He I $λ$10833 Å, and Pa$β$ lines, the Na I D doublet, and the Ca II infrared triplet, which have a chromospheric component in active M dwarfs. In addition, we measured an index of the strength of two TiO and two VO bands, which are formed in the photosphere. We also searched for periodicities in these activity indicators for all sample stars using generalised Lomb-Scargle periodograms. We find that the most slowly rotating stars of each spectral subtype have the strongest H$α$ absorption. H$α$ is correlated most strongly with He I D3, whereas Na I D and the Ca II infrared triplet are also correlated with H$α$. He I $λ$10833 Å and Pa$β$ show no clear correlations with the other indicators. The TiO bands show an activity effect that does not appear in the VO bands. We find that the relative variations of H$α$ and He I D3 are smaller for stars with higher activity levels, while this anti-correlation is weaker for Na I D and the Ca II infrared triplet, and is absent for He I $λ$10833 Å and Pa$β$. Periodic variation with the rotation period most commonly appears in the TiO bands, H$α$, and in the Ca II infrared triplet.

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