arXiv subjects

M. Kürster

Publications and source records attributed to M. Kürster.

At least 55 records · Page 3Linked to original sources

arXiv2019

A giant exoplanet orbiting a very low-mass star challenges planet formation models

Statistical analyses from exoplanet surveys around low-mass stars indicate that super-Earth and Neptune-mass planets are more frequent than gas giants around such stars, in agreement with core accretion theory of planet formation. Using precise radial velocities derived from visual and near-infrared spectra, we report the discovery of a giant planet with a minimum mass of 0.46 Jupiter masses in an eccentric 204-day orbit around the very low-mass star GJ 3512. Dynamical models show that the high eccentricity of the orbit is most likely explained from planet-planet interactions. The reported planetary system challenges current formation theories and puts stringent constraints on the accretion and migration rates of planet formation and evolution models, indicating that disc instability may be more efficient in forming planets than previously thought.

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arXiv2019

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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arXiv2019

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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arXiv2019

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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arXiv2019

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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arXiv2019

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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arXiv2019

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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arXiv2019

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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arXiv2019

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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arXiv2019

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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arXiv2019

The CARMENES search for exoplanets around M dwarfs. Period search in H$α$, Na I D, and Ca II IRT lines

We use spectra from CARMENES, the Calar Alto high-Resolution search for M dwarfs with Exo-earths with Near-infrared and optical Echelle Spectrographs, to search for periods in chromospheric indices in 16 M0 to M2 dwarfs. We measure spectral indices in the H$α$, the Ca II infrared triplet (IRT), and the Na I D lines to study which of these indices are best-suited to find rotation periods in these stars. Moreover, we test a number of different period-search algorithms, namely the string length method, the phase dispersion minimisation, the generalized Lomb-Scargle periodogram, and the Gaussian process regression with quasi-periodic kernel. We find periods in four stars using H$α$ and in five stars using the Ca II IRT, two of which have not been found before. Our results show that both H$α$ and the Ca II IRT lines are well suited for period searches, with the Ca II IRT index performing slightly better than H$α$. Unfortunately, the Na I D lines are strongly affected by telluric airglow, and we could not find any rotation period using this index. Further, different definitions of the line indices have no major impact on the results. Comparing the different search methods, the string length method and the phase dispersion minimisation perform worst, while Gaussian process models produce the smallest numbers of false positives and non-detections.

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arXiv2019

The CARMENES search for exoplanets around M dwarfs - The enigmatic planetary system GJ 4276: One eccentric planet or two planets in a 2:1 resonance?

We report the detection of a Neptune-mass exoplanet around the M4.0 dwarf GJ 4276 (G 232-070) based on radial velocity (RV) observations obtained with the CARMENES spectrograph. The RV variations of GJ 4276 are best explained by the presence of a planetary companion that has a minimum mass of $m_{\rm b}\sin i \approx 16\, M_\oplus$ on a $P_{\rm b}=13.35$ day orbit. The analysis of the activity indicators and spectral diagnostics exclude stellar induced RV perturbations and prove the planetary interpretation of the RV signal. We show that a circular single-planet solution can be excluded by means of a likelihood ratio test. Instead, we find that the RV variations can be explained either by an eccentric orbit or interpreted as a pair of planets on circular orbits near a period ratio of 2:1. Although the eccentric single-planet solution is slightly preferred, our statistical analysis indicates that none of these two scenarios can be rejected with high confidence using the RV time series obtained so far. Based on the eccentric interpretation, we find that GJ 4276 b is the most eccentric ($e_{\rm b} = 0.37$) exoplanet around an M dwarf with such a short orbital period known today.

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arXiv2018

Detection of He I $\lambda10830$ Å absorption on HD 189733 b with CARMENES high-resolution transmission spectroscopy

We present three transit observations of HD 189733 b obtained with the high-resolution spectrograph CARMENES at Calar Alto. A strong absorption signal is detected in the near-infrared He I triplet at 10830 Å in all three transits. During mid-transit, the mean absorption level is $0.88\pm0.04$ % measured in a $\pm$10 km s$^{-1}$ range at a net blueshift of $-3.5\pm0.4$ km s$^{-1}$ (10829.84--10830.57 Å). The absorption signal exhibits radial velocities of $+6.5\pm3.1$ km s$^{-1}$ and $-12.6\pm1.0$ km s$^{-1}$ during ingress and egress, respectively; measured in the planetary rest frame. We show that stellar activity related pseudo-signals interfere with the planetary atmospheric absorption signal. They could contribute as much as 80% of the observed signal and might also affect the radial velocity signature, but pseudo-signals are very unlikely to explain the entire signal. The observed line ratio between the two unresolved and the third line of the He I triplet is $2.8\pm0.2$, which strongly deviates from the value expected for an optically thin atmospheres. When interpreted in terms of absorption in the planetary atmosphere, this favors a compact helium atmosphere with an extent of only 0.2 planetary radii and a substantial column density on the order of $4\times 10^{12}$ cm$^{-2}$. The observed radial velocities can be understood either in terms of atmospheric circulation with equatorial superrotation or as a sign of an asymmetric atmospheric component of evaporating material. We detect no clear signature of ongoing evaporation, like pre- or post-transit absorption, which could indicate material beyond the planetary Roche lobe, or radial velocities in excess of the escape velocity. These findings do not contradict planetary evaporation, but only show that the detected helium absorption in HD 189733 b does not trace the atmospheric layers that show pronounced escape signatures.

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arXiv2018

A candidate super-Earth planet orbiting near the snow line of Barnard's star

At a distance of 1.8 parsecs, Barnard's star (Gl 699) is a red dwarf with the largest apparent motion of any known stellar object. It is the closest single star to the Sun, second only to the alpha Centauri triple stellar system. Barnard's star is also among the least magnetically active red dwarfs known and has an estimated age older than our Solar System. Its properties have made it a prime target for planet searches employing techniques such as radial velocity, astrometry, and direct imaging, all with different sensitivity limits but ultimately leading to disproved or null results. Here we report that the combination of numerous measurements from high-precision radial velocity instruments reveals the presence of a low-amplitude but significant periodic signal at 233 days. Independent photometric and spectroscopic monitoring, as well as the analysis of instrumental systematic effects, show that this signal is best explained as arising from a planetary companion. The candidate planet around Barnard's star is a cold super-Earth with a minimum mass of 3.2 Earth masses orbiting near its snow-line. The combination of all radial velocity datasets spanning 20 years additionally reveals a long-term modulation that could arise from a magnetic activity cycle or from a more distant planetary object. Because of its proximity to the Sun, the proposed planet has a maximum angular separation of 220 milli-arcseconds from Barnard's star, making it an excellent target for complementary direct imaging and astrometric observations.

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arXiv2018

Multiple water band detections in the CARMENES near-infrared transmission spectrum of HD 189733 b

Aims: We explore the capabilities of CARMENES for characterizing hot-Jupiter atmospheres by targeting multiple water bands, in particular, those at 1.15 and 1.4 $μ$m. Hubble Space Telescope observations suggest that this wavelength region is relevant for distinguishing between hazy/cloudy and clear atmospheres. Methods: We observed one transit of the hot Jupiter HD 189733 b with CARMENES. Telluric and stellar absorption lines were removed using Sysrem, which performs a principal component analysis including proper error propagation. The residual spectra were analysed for water absorption with cross-correlation techniques using synthetic atmospheric absorption models. Results: We report a cross-correlation peak at a signal-to-noise ratio (SNR) of 6.6, revealing the presence of water in the transmission spectrum of HD 189733 b. The absorption signal appeared slightly blueshifted at -3.9 $\pm$ 1.3 kms$^{-1}$. We measured the individual cross-correlation signals of the water bands at 1.15 and 1.4 $μ$m, finding cross-correlation peaks at SNRs of 4.9 and 4.4, respectively. The 1.4 $μ$m feature is consistent with that observed with the Hubble Space Telescope. Conclusions: The water bands studied in this work have been mainly observed in a handful of planets from space. The ability of also detecting them individually from the ground at higher spectral resolution can provide insightful information to constrain the properties of exoplanet atmospheres. Although the current multiband detections can not yet constrain atmospheric haze models for HD 189733 b, future observations at higher signal-to-noise ratio could provide an alternative way to achieve this aim.

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arXiv2018

The CARMENES search for exoplanets around M dwarfs: The warm super-Earths in twin orbits around the mid-type M dwarfs Ross 1020 (GJ 3779) and LP 819-052 (GJ 1265)

We announce the discovery of two planetary companions orbiting around the low mass stars Ross 1020 (GJ 3779, M4.0V) and LP 819-052 (GJ 1265, M4.5V). The discovery is based on the analysis of CARMENES radial velocity observations in the visual channel as part of its survey for exoplanets around M dwarfs. In the case of GJ 1265, CARMENES observations were complemented with publicly available Doppler measurements from HARPS. The datasets reveal one planetary companion for each star that share very similar properties: minimum masses of $8.0\pm0.5$ M$_{\oplus}$ and $7.4\pm0.5$ M$_{\oplus}$ in low-eccentricity orbits with periods of $3.023\pm0.001$ d and $3.651\pm0.001$ d for GJ 3779 b and GJ 1265 b, respectively. The periodic signals around three days found in the radial velocity data have no counterpart in any spectral activity indicator. Besides, we collected available photometric data for the two host stars, which confirm that the additional Doppler variations found at periods around 95 d can be attributed to the rotation of the stars. The addition of these planets in a mass-period diagram of known planets around M dwarfs suggests a bimodal distribution with a lack of short-period low-mass planets in the range of 2-5 M$_{\oplus}$. It also indicates that super-Earths (> 5 M$_{\oplus}$) currently detected by radial velocity and transit techniques around M stars are usually found in systems dominated by a single planet.

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arXiv2018

The CARMENES search for exoplanets around M dwarfs: Nine new double-line spectroscopic binary stars

Context. The CARMENES spectrograph is surveying ~300 M dwarf stars in search for exoplanets. Among the target stars, spectroscopic binary systems have been discovered, which can be used to measure fundamental properties of stars. Aims. Using spectroscopic observations, we determine the orbital and physical properties of nine new double-line spectroscopic binary systems by analysing their radial velocity curves. Methods. We use two-dimensional cross-correlation techniques to derive the radial velocities of the targets, which are then employed to determine the orbital properties. Photometric data from the literature are also analysed to search for possible eclipses and to measure stellar variability, which can yield rotation periods. Results. Out of the 342 stars selected for the CARMENES survey, 9 have been found to be double-line spectroscopic binaries, with periods ranging from 1.13 to ~8000 days and orbits with eccentricities up to 0.54. We provide empirical orbital properties and minimum masses for the sample of spectroscopic binaries. Absolute masses are also estimated from mass-luminosity calibrations, ranging between ~0.1 and ~0.6 Msol . Conclusions. These new binary systems increase the number of double-line M dwarf binary systems with known orbital parameters by 15%, and they have lower mass ratios on average.

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arXiv2018

The CARMENES search for exoplanets around M dwarfs. A Neptune-mass planet traversing the habitable zone around HD 180617

Despite their activity, low-mass stars are of particular importance for the search of exoplanets by the means of Doppler spectroscopy, as planets with lower masses become detectable. We report on the discovery of a planetary companion around HD 180617, a bright J = 5.58 mag, low-mass M = 0.45 M_{sun} star of spectral type M2.5 V. The star, located at a distance of 5.9 pc, is the primary of the high proper motion binary system containing vB 10, a star with one of the lowest masses known in most of the twentieth century. Our analysis is based on new radial velocity (RV) measurements made at red-optical wavelengths provided by the high-precision spectrograph CARMENES, which was designed to carry out a survey for Earth-like planets around M dwarfs. The available CARMENES data are augmented by archival Doppler measurements from HIRES and HARPS. Altogether, the RVs span more than 16 years. The modeling of the RV variations, with a semi-amplitude of K = 2.85-0.25/+0.16m/s yields a Neptune-like planet with a minimum mass of 12.2-1.4/+1.0 M_{Earth} on a 105.90-0.10/+0.09d circumprimary orbit, which is partly located in the host star's habitable zone. The analysis of time series of common activity indicators does not show any dependence on the detected RV signal. The discovery of HD 180617 b not only adds information to a currently hardly filled region of the mass-period diagram of exoplanets around M dwarfs, but the investigated system becomes the third known binary consisting of M dwarfs and hosting an exoplanet in an S-type configuration. Its proximity makes it an attractive candidate for future studies.

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