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S. Pedraz

Publications and source records attributed to S. Pedraz.

At least 37 records · Page 2Linked to original sources

The CARMENES search for exoplanets around M dwarfs. Two planets on the opposite sides of the radius gap transiting the nearby M dwarf LTT 3780

We present the discovery and characterisation of two transiting planets observed by the Transiting Exoplanet Survey Satellite (TESS) orbiting the nearby (d ~ 22 pc), bright (J ~ 9 mag) M3.5 dwarf LTT 3780 (TOI-732). We confirm both planets and their association with LTT 3780 via ground-based photometry and determine their masses using precise radial velocities measured with the CARMENES spectrograph. Precise stellar parameters determined from CARMENES high resolution spectra confirm that LTT 3780 is a mid-M dwarf with an effective temperature of T_eff = 3360 +\- 51 K, a surface gravity of log(g) = 4.81 +/- 0.04 (cgs), and an iron abundance of [Fe/H] = 0.09 +/- 0.16 dex, with an inferred mass of M_star = 0.379 +/- 0.016 M_sun and a radius of R_star = 0.382 +/- 0.012 R_sun. The ultra-short-period planet LTT 3780 b (P_b = 0.77 d) with a radius of 1.35^{+0.06}_{-0.06} R_earth, a mass of 2.34^{+0.24}_{-0.23} M_earth, and a bulk density of 5.24^{+0.94}_{-0.81} g cm^{-3} joins the population of Earth-size planets with rocky, terrestrial composition. The outer planet, LTT 3780 c, with an orbital period of 12.25 d, radius of 2.42^{+0.10}_{-0.10} R_earth, mass of 6.29^{+0.63}_{-0.61} M_earth, and mean density of 2.45^{+0.44}_{-0.37} g cm^{-3} belongs to the population of dense sub-Neptunes. With the two planets located on opposite sides of the radius gap, this planetary system is an excellent target for testing planetary formation, evolution and atmospheric models. In particular, LTT 3780 c is an ideal object for atmospheric studies with the James Webb Space Telescope.

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The CARMENES search for exoplanets around M dwarfs. Three temperate to warm super-Earths

We announce the discovery of two planets orbiting the M dwarfs GJ 251 ($0.360\pm0.015$ M$_\odot$) and HD 238090 ($0.578\pm0.021$ M$_\odot$) based on CARMENES radial velocity (RV) data. In addition, we independently confirm with CARMENES data the existence of Lalande 21185 b, a planet that has recently been discovered with the SOPHIE spectrograph. All three planets belong to the class of warm or temperate super-Earths and share similar properties. The orbital periods are 14.24 d, 13.67 d, and 12.95 d and the minimum masses are $4.0\pm0.4$ $M_\oplus$, $6.9\pm0.9$ $M_\oplus$, and $2.7\pm0.3$ $M_\oplus$ for GJ 251 b, HD 238090 b, and Lalande 21185 b, respectively. Based on the orbital and stellar properties, we estimate equilibrium temperatures of $351.0\pm1.4$ K for GJ 251 b, $469.6\pm2.6$ K for HD 238090 b, and $370.1\pm6.8$ K for Lalande 21185 b. For the latter we resolve the daily aliases that were present in the SOPHIE data and that hindered an unambiguous determination of the orbital period. We find no significant signals in any of our spectral activity indicators at the planetary periods. The RV observations were accompanied by contemporaneous photometric observations. We derive stellar rotation periods of $122.1\pm2.2$ d and $96.7\pm3.7$ d for GJ 251 and HD 238090, respectively. The RV data of all three stars exhibit significant signals at the rotational period or its first harmonic. For GJ 251 and Lalande 21185, we also find long-period signals around 600 d, and 2900 d, respectively, which we tentatively attribute to long-term magnetic cycles. We apply a Bayesian approach to carefully model the Keplerian signals simultaneously with the stellar activity using Gaussian process regression models and extensively search for additional significant planetary signals hidden behind the stellar activity.

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The CARMENES search for exoplanets around M dwarfs: Rubidium abundances in nearby cool stars

In this study, abundances of the neutron-capture elements Rb, Sr, and Zr are derived, for the first time, in a sample of nearby M dwarfs. We focus on stars in the metallicity range -0.5<[Fe/H]<+0.3, an interval poorly explored for Rb abundances in previous analyses. To do this we use high-resolution, high-signal-to-noise-ratio, optical and near-infrared spectra of 57 M dwarfs observed with CARMENES. The resulting [Sr/Fe] and [Zr/Fe] ratios for most M dwarfs are almost constant at about the solar value, and are identical to those found in GK dwarfs of the same metallicity. However, for Rb we find systematic underabundances ([Rb/Fe]<0.0) by a factor two on average. Furthermore, a tendency is found for Rb-but not for other heavy elements (Sr, Zr) -to increase with increasing metallicity such that [Rb/Fe]>0.0 is attained at metallicities higher than solar. These are surprising results, never seen for any other heavy element, and are difficult to understand within the formulation of the s- and r-processes, both contributing sources to the Galactic Rb abundance. We discuss the reliability of these findings for Rb in terms of non-LTE effects, stellar activity, or an anomalous Rb abundance in the Solar System, but no explanation is found. We then interpret the full observed [Rb/Fe] versus [Fe/H] trend within the framework of theoretical predictions from state-of-the-art chemical evolution models for heavy elements, but a simple interpretation is not found either. In particular, the possible secondary behaviour of the [Rb/Fe] ratio at super-solar metallicities would require a much larger production of Rb than currently predicted in AGB stars through the s-process without overproducing Sr and Zr.

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Precise mass and radius of a transiting super-Earth planet orbiting the M dwarf TOI-1235: a planet in the radius gap?

We report the confirmation of a transiting planet around the bright, inactive M0.5 V star TOI-1235 (TYC 4384-1735-1, V = 11.5 mag), whose transit signal was detected in the photometric time series of Sectors 14, 20, and 21 of the TESS space mission. We confirm the planetary nature of the transit signal, which has a period of 3.44 d, by using precise radial velocity measurements with CARMENES and HARPS-N spectrographs. A comparison of the properties derived for TOI-1235 b's with theoretical models reveals that the planet has a rocky composition, with a bulk density slightly higher than Earth's. In particular, we measure a mass of M_p = 5.9+/-0.6 M_Earth and a radius of R_p = 1.69+/-0.08 R_Earth, which together result in a density of rho_p = 6.7+1.3-1.1 g/cm3. When compared with other well-characterized exoplanetary systems, the particular combination of planetary radius and mass puts our discovery in the radius gap, a transition region between rocky planets and planets with significant atmospheric envelopes, with few known members. While the exact location of the radius gap for M dwarfs is still a matter of debate, our results constrain it to be located at around 1.7 R_Earth or larger at the insolation levels received by TOI-1235 b (~60 S_Earth), which makes it an extremely interesting object for further studies of planet formation and atmospheric evolution.

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The CARMENES search for exoplanets around M dwarfs. Radial velocities and activity indicators from cross-correlation functions with weighted binary masks

For years, the standard procedure to measure radial velocities (RVs) of spectral observations consisted in cross-correlating the spectra with a binary mask, that is, a simple stellar template that contains information on the position and strength of stellar absorption lines. The cross-correlation function (CCF) profiles also provide several indicators of stellar activity. We present a methodology to first build weighted binary masks and, second, to compute the CCF of spectral observations with these masks from which we derive radial velocities and activity indicators. These methods are implemented in a python code that is publicly available. To build the masks, we selected a large number of sharp absorption lines based on the profile of the minima present in high signal-to-noise ratio (S/N) spectrum templates built from observations of reference stars. We computed the CCFs of observed spectra and derived RVs and the following three standard activity indicators: full-width-at-half-maximum as well as contrast and bisector inverse slope.We applied our methodology to CARMENES high-resolution spectra and obtain RV and activity indicator time series of more than 300 M dwarf stars observed for the main CARMENES survey. Compared with the standard CARMENES template matching pipeline, in general we obtain more precise RVs in the cases where the template used in the standard pipeline did not have enough S/N. We also show the behaviour of the three activity indicators for the active star YZ CMi and estimate the absolute RV of the M dwarfs analysed using the CCF RVs.

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The CARMENES search for exoplanets around M dwarfs. Characterization of the nearby ultra-compact multiplanetary system YZ Ceti

The nearby ultra-compact multiplanetary system YZ Ceti consists of at least three planets. The orbital period of each planet is the subject of discussion in the literature due to strong aliasing in the radial velocity data. The stellar activity of this M dwarf also hampers significantly the derivation of the planetary parameters. With an additional 229 radial velocity measurements obtained since the discovery publication, we reanalyze the YZ Ceti system and resolve the alias issues. We use model comparison in the framework of Bayesian statistics and periodogram simulations based on a method by Dawson and Fabrycky to resolve the aliases. We discuss additional signals in the RV data, and derive the planetary parameters by simultaneously modeling the stellar activity with a Gaussian process regression model. To constrain the planetary parameters further we apply a stability analysis on our ensemble of Keplerian fits. We resolve the aliases: the three planets orbit the star with periods of $2.02$ d, $3.06$ d, and $4.66$ d. We also investigate an effect of the stellar rotational signal on the derivation of the planetary parameters, in particular the eccentricity of the innermost planet. Using photometry we determine the stellar rotational period to be close to $68$ d. From the absence of a transit event with TESS, we derive an upper limit of the inclination of $i_\mathrm{max} = 87.43$ deg. YZ Ceti is a prime example of a system where strong aliasing hindered the determination of the orbital periods of exoplanets. Additionally, stellar activity influences the derivation of planetary parameters and modeling them correctly is important for the reliable estimation of the orbital parameters in this specific compact system. Stability considerations then allow additional constraints to be placed on the planetary parameters.

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CAFE2: an upgrade to the CAFE high-resolution spectrograph. Commissioning results and new public pipeline

The Calar Alto Fiber-fed Échelle spectrograph (CAFE) is a high-resolution spectrographs with high-precision radial velocity capabilities mounted in the 2.2m telescope of Calar Alto Observatory. It suffered from strong degradation after 4 years of operations and it has now been upgraded. The upgrades of the instrument (now named CAFE$_2$) aimed at improving the throughput and stability thanks to the inclusion of a new grating, an active temperature control in the isolated coudé room, and a new scrambling system among other minor changes. In this paper, we present the results of the re-commissioning of the instrument and a new pipeline (CAFExtractor) that provides the user with fully reduced data including radial velocity measurements of FGK dwarf stars. We have monitored the upgraded instrument for several months to characterize its main properties and test the new pipeline. It uses part of the CERES code, improves the wavelength calibration and radial velocity extraction (using the HARPS masks adapted), applies nightly drift corrections. The finally reduced spectra are presented in FITS files. The commissioning results show a clear improvement in the instrument performance with respect to the degraded status before the intervention. The room temperature is now stabilized down to 5 mK during one night and below 50 mK over two months. CAFE$_2$ now provides 3 m/s precision on the reference ThAr frames and the on-sky tests provide a radial velocity precision of 8 m/s during one night (for S/N>50). The throughput of the instrument is now back to nominal values with an efficiency of around 15% at 550 nm. The limiting magnitude of the instrument for a 1h exposure and S/N=20 is V=15. With all these properties, CAFE$_2$ enters into the small family of high-resolution spectrographs mounted on 2-4 meter-class telescopes capable of reaching radial velocity precisions below 10 m/s.

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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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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. 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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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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The CARMENES search for exoplanets around M dwarfs - Photospheric parameters of target stars from high-resolution spectroscopy

The new CARMENES instrument comprises two high-resolution and high-stability spectrographs that are used to search for habitable planets around M dwarfs in the visible and near-infrared regime via the Doppler technique. Characterising our target sample is important for constraining the physical properties of any planetary systems that are detected. The aim of this paper is to determine the fundamental stellar parameters of the CARMENES M-dwarf target sample from high-resolution spectra observed with CARMENES. We also include several M-dwarf spectra observed with other high-resolution spectrographs, that is CAFE, FEROS, and HRS, for completeness. We used a {chi}^2 method to derive the stellar parameters effective temperature T_eff, surface gravity log g, and metallicity [Fe/H] of the target stars by fitting the most recent version of the PHOENIX-ACES models to high-resolution spectroscopic data. These stellar atmosphere models incorporate a new equation of state to describe spectral features of low-temperature stellar atmospheres. Since T_eff, log g, and [Fe/H] show degeneracies, the surface gravity is determined independently using stellar evolutionary models. We derive the stellar parameters for a total of 300 stars. The fits achieve very good agreement between the PHOENIX models and observed spectra. We estimate that our method provides parameters with uncertainties of {sigma} T_eff = 51 K, {sigma} log g = 0.07, and {sigma} [Fe/H] = 0.16, and show that atmosphere models for low-mass stars have significantly improved in the last years. Our work also provides an independent test of the new PHOENIX-ACES models, and a comparison for other methods using low-resolution spectra. In particular, our effective temperatures agree well with literature values, while metallicities determined with our method exhibit a larger spread when compared to literature results.

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PISCO: The Pmas/ppak Integral-field Supernova hosts COmpilation

We present the Pmas/ppak Integral-field Supernova hosts COmpilation (PISCO) which comprises Integral Field Spectroscopy (IFS) of 232 supernova (SN) host galaxies, that hosted 272 SNe, observed over several semesters with the 3.5m telescope at the Calar Alto Observatory (CAHA). PISCO is the largest collection of SN host galaxies observed with wide-field IFS, totaling 466,347 individual spectra covering a typical spatial resolution of $\sim$380 pc. While focused studies regarding specific SN Ia- related topics will be published elsewhere, this paper aims to present the properties of the SN environments with stellar population (SP) synthesis and the gas-phase ISM, providing additional results separating stripped-envelope SNe into their subtypes. With 11,270 HII regions detected in all galaxies, we present for the first time an HII region statistical analysis, that puts HII regions that have hosted SNe in context with all other SF clumps within their galaxies. SNe Ic are associated to more metal-rich, higher EW(Hα) and higher SF rate environments within their host galaxies than the mean of all HII regions detected within each host, on contrary SNe IIb occur at the most different environments compared to other CC SNe types. We find two clear components of young and old SP at SNe IIn locations. We find that SNe II fast-decliners (IIL) tend to explode at locations where ΣSFR is more intense. Finally, we outline how a future dedicated IFS survey of galaxies in parallel to an untargeted SN search would overcome the biases in current environmental studies.

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CAFE: Calar Alto Fiber-fed Echelle spectrograph

We present here CAFE, the Calar Alto Fiber-fed Echelle spectrograph, a new instrument built at the Centro Astronomico Hispano Alemán (CAHA). CAFE is a single fiber, high-resolution ($R\sim$70000) spectrograph, covering the wavelength range between 3650-9800Å. It was built on the basis of the common design for Echelle spectrographs. Its main aim is to measure radial velocities of stellar objects up to $V\sim$13-14 mag with a precision as good as a few tens of $m s^{-1}$. To achieve this goal the design was simplified at maximum, removing all possible movable components, the central wavelength is fixed, so the wavelentgth coverage; no filter wheel, one slit and so on, with a particular care taken in the thermal and mechanical stability. The instrument is fully operational and publically accessible at the 2.2m telescope of the Calar Alto Observatory. In this article we describe (i) the design, summarizing its manufacturing phase; (ii) characterize the main properties of the instrument; (iii) describe the reduction pipeline; and (iv) show the results from the first light and commissioning runs. The preliminar results indicate that the instrument fulfill the specifications and it can achieve the foreseen goals. In particular, they show that the instrument is more efficient than anticipated, reaching a $S/N\sim$20 for a stellar object as faint as $V\sim$14.5 mag in $\sim$2700s integration time. The instrument is a wonderful machine for exoplanetary research (by studying large samples of possible systems cotaining massive planets), galactic dynamics (high precise radial velocities in moving groups or stellar associations) or astrochemistry.

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The Calar Alto Observatory: current status and future instrumentation

The Calar Alto Observatory, located at 2168m height above the sea level in continental Europe, holds a significant number of astronomical telescopes and experiments, covering a large range of the electromagnetic domain, from gamma-ray to near-infrared. It is a very well characterized site, with excellent logistics. Its main telescopes includes a large suite of instruments. At the present time, new instruments, namely CAFE, PANIC and Carmenes, are under development. We are also planning a new operational scheme in order to optimize the observatory resources.

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The magnetically-active, low-mass, triple system WDS 19312+3607

Aims: We investigated in detail the system WDS 19312+3607, whose primary is an active M4.5Ve star previously thought to be young (tau ~ 300-500 Ma) based on high X-ray luminosity. Methods: We collected intermediate- and low-resolution optical spectra taken with 2 m-class telescopes, photometric data from the $B$ to 8 mum bands, and eleven astrometric epochs with a time baseline of over 56 years for the two components in the system, G 125-15 and G 125-14. Results: We derived M4.5V spectral types for both stars, confirmed their common proper motion, estimated the heliocentric distance and projected physical separation, determined the galactocentric space velocities, and deduced a most-probable age older than 600 Ma. We discovered that the primary, G 125-15, is in turn an inflated, double-lined, spectroscopic binary with a short period of photometric variability of P ~ 1.6 d, which we associated to orbital synchronisation. The observed X-ray and Halpha emissions, photometric variability, and abnormal radius and effective temperature of G 125-15 AB indicate strong magnetic activity, possibly due to fast rotation. Besides, the estimated projected physical separation between G 125-15 AB and G 125-14 of about 1200 AU makes WDS 19312+3607 to be one of the widest systems with intermediate M-type primaries. Conclusions: G 125-15 AB is a nearby (d ~ 26 pc), bright (J ~ 9.6 mag), active spectroscopic binary with a single proper-motion companion of the same spectral type at a wide separation. They are thus ideal targets for specific follow-ups to investigate wide and close multiplicity or stellar expansion and surface cooling due to reduced convective efficiency.

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Kinematic properties as probes of the evolution of dwarf galaxies in the Virgo cluster

We present new observational results on the kinematical, morphological, and stellar population properties of a sample of 21 dEs located both in the Virgo cluster and in the field, which show that 52% of the dEs i) are rotationally supported, ii) exhibit structural signs of typical rotating systems such as discs, bars or spiral arms, iii) are younger (~3 Gyr) than non-rotating dEs, and iv) are preferentially located either in the outskirts of Virgo or in the field. This evidence is consistent with the idea that rotationally supported dwarfs are late type spirals or irregulars that recently entered the cluster and lost their gas through a ram pressure stripping event, quenching their star formation and becoming dEs through passive evolution. We also find that all, but one, galaxies without photometric hints for hosting discs are pressure supported and are all situated in the inner regions of the cluster. This suggests a different evolution from the rotationally supported systems. Three different scenarios for these non-rotating galaxies are discussed (in situ formation, harassment and ram pressure stripping).

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A new stellar library in the region of the CO index at 2.3 $μ$m. New index definition and empirical fitting functions

Context: The analysis of unresolved stellar populations demands evolutionary synthesis models with realistic physical ingredients and extended wavelength coverage. Aims: To obtain a quantitative description of the first CO bandhead at 2.3 $μ$m, to allow stellar population models to provide improved predictions in this wavelength range. Methods: We have observed a new stellar library with a better coverage of the stellar atmospheric parameter space than preceding works. We have performed a detailed analysis of the robustness of previous CO index definitions with spectral resolution, wavelength calibration, signal-to-noise ratio, and flux calibration. Results: We define a new line-strength index for the first CO bandhead at 2.3 $μ$m, D$_{\rm CO}$, better suited for stellar population studies than previous index definitions. We compute empirical fitting functions for the CO feature as a function of the stellar parameters (T$_{\rm eff}$, $\log g$ and [Fe/H]), showing a detailed quantitative metallicity dependence.

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