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M. Giarrusso

Publications and source records attributed to M. Giarrusso.

At least 19 recordsLinked to original sources

First detection of acoustic-like flux in the middle solar corona

Waves are thought to play a significant role in the heating of the solar atmosphere and the acceleration of the wind. Among the many types of waves observed in the Sun, the so-called p-modes with a 3 mHz frequency peak dominate the lower atmosphere. In the presence of magnetic fields, these waves can be converted into magnetohydrodynamic modes, which then leak into the corona through magnetic conduits. High-resolution off-limb observations have indeed revealed signatures of ubiquitous and global 3 mHz oscillations in the corona, although limited to low heights and to incompressible modes. We present high-cadence, high-resolution observations of the corona in the range 1.7 - 3.6 solar radii taken in broad-band 580-640 nm visible light by the Metis coronagraph aboard Solar Orbiter. These observations were designed to investigate density fluctuations in the middle corona. The data were acquired over several days in March 2022, October 2022, and for two days in April 2023. We selected representative regions of the corona on three sample dates. Analysis of the data in those regions revealed the presence of periodic density fluctuations. By examining several time-distance diagrams, we determined the main properties (apparent propagation speed, amplitude) of those fluctuations. We also show power spectra in selected locations in order to determine the dominant frequencies. We found wave-like, compressible fluctuations of low amplitude - of the order of 0.1 % of the background - in several large-scale regions in the corona at least up to 2.5 solar radii. We also found that the apparent propagation speeds of these perturbations typically fall in the range 150 - 450 km/s. A power spectrum analysis of time series revealed an excess power in the range 2-7 mHz, often with peaks at 3 or 5 mHz, i.e. in a range consistent with p-mode frequencies of the lower solar atmosphere.

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Discovery of the binary nature of the magnetospheric B-type star $\rho$ Oph A

The nearby B-type star $\rho$ Oph A was recently identified as a rapidly rotating magnetic B-type star with variable radio and X-ray emission consistent with a magnetospheric origin. We present a high-resolution spectropolarimetric time series obtained with ESPaDOnS, which we use to perform a magnetic analysis using least-squares deconvolution (LSD). We find that $\rho$ Oph A is a spectroscopic binary consisting of two B-type stars with masses of about 8 and 10 $M_\odot$ on a slightly eccentric 88-day orbit, with the magnetic field being associated with the smaller Ab component. This leads to $\rho$ Oph Ab's 4 kG surface magnetic dipole being approximately twice as strong as the previously reported 2 kG. The oblique rotator model derived from the longitudinal magnetic field curve agrees well with the LSD Stokes $V$ profiles, indicating that the magnetic field is likely to be very nearly dipolar. The orbital and rotational axes appear to be aligned. We report for the first time $\rho$ Oph Ab's magnetospheric H$\alpha$ emission, which is consistent with an origin in a centrifugal magnetosphere. We also demonstrate that $\rho$ Oph Ab's light curve can be recovered from the previously reported {\em Kepler-2} light curve of $\rho$ Oph C, and that it demonstrates prominent magnetospheric eclipses similar to those of $\sigma$ Ori E, and which can be reproduced using a dipolar Rigidly Rotating Magnetosphere model. Both H$\alpha$ and the light curve are indicative of a strongly asymmetric magnetosphere. All indications are that $\rho$ Oph Ab's magnetic field is essentially dipolar, meaning that contributions from higher-order multipoles probably cannot explain the strong asymmetry in the magnetosphere. Only two other stars show comparable degrees of asymmetry, both of which are also close binaries, suggesting that binarity can affect the magnetospheric plasma distributions.

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Super-slowly rotating Ap (ssrAp) stars: Spectroscopic study

To gain better understanding of the Ap stars with the longest rotation periods, we obtained high resolution spectra of a sample of super-slowly rotating Ap (ssrAp) star candidates identified by a TESS photometric survey, to confirm that they are indeed Ap stars, to check that their v sin i values are compatible with super-slow rotation, and to obtain a first estimate of their magnetic field strengths. We determined whenever possible their mean magnetic field modulus, their mean quadratic magnetic field, and an upper limit of their projected equatorial velocities. Eighteen of the 27 stars studied are typical Ap stars; most of the other nine appear to be misclassified. One of the Ap stars is not a slow rotator; it must be seen nearly pole-on. The properties of the remaining 17 are compatible with moderately to extremely long rotation periods. Eight new stars with resolved magnetically split lines in the visible range were discovered; their mean magnetic field modulus and their mean quadratic magnetic field were measured. The mean quadratic field could also be determined in five more stars. Five new spectroscopic binaries containing an Ap star were identified. Among the misclassified stars, one SB2 system with two similar, sharp-lined Am components was also discovered. The technique that we used to carry out a search for ssrAp star candidates using TESS data is validated, but appears limited by uncertainties in the spectral classification of Ap stars. The new magnetic field measurements obtained as part of this study lend further support to the tentative conclusions of our previous studies: the absence of periods longer than ~150 d in stars with magnetic fields stronger than ~7.5 kG, the lower rate of occurrence of super-slow rotation for field strengths less than ~2 kG than in the range ~3-7.5 kG, and the deficiency of slowly rotating Ap stars with field strengths between ~2 and ~3 kG.

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Study of solar brightness profiles in the 18-26 GHz frequency range with INAF radio telescopes II. Evidence for coronal emission

One of the most important objectives of solar physics is the physical understanding of the solar atmosphere, the structure of which is also described in terms of the density (N) and temperature (T) distributions of the atmospheric matter. Several multi-frequency analyses show that the characteristics of these distributions are still debated, especially for the outer coronal emission. We aim to constrain the T and N distributions of the solar atmosphere through observations in the centimetric radio domain. We employ single-dish observations from two of the INAF radio telescopes at the K-band frequencies (18 - 26 GHz). We investigate the origin of the significant brightness temperature ($T_B$) level that we detected up to the upper corona ($\sim 800$ Mm of altitude with respect to the photospheric solar surface). To probe the physical origin of the atmospheric emission and to constrain instrumental biases, we reproduced the solar signal by convolving specific 2D antenna beam models. The analysis of the solar atmosphere is performed by adopting a physical model that assumes the thermal bremsstrahlung as the emission mechanism, with specific T and N distributions. The modelled $T_B$ profiles are compared with those observed by averaging solar maps obtained during the minimum of solar activity (2018 - 2020). The T and N distributions are compatible (within $25\%$ of uncertainty) with the model up to $\sim 60$ Mm and $\sim 100$ Mm of altitude, respectively. The analysis of the role of the antenna beam pattern on our solar maps proves the physical nature of the atmospheric emission in our images up to the coronal tails seen in our $T_B$ profiles. The challenging analysis of the coronal radio emission at higher altitudes, together with the data from satellite instruments will require further multi-frequency measurements.

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Comprehensive spectroscopic and photometric study of pulsating eclipsing binary star AI Hya

The pulsating eclipsing binaries are remarkable systems that provide an opportunity to probe the stellar interior and to determine the fundamental stellar parameters precisely. Especially the detached eclipsing binary systems with (a) pulsating component(s) are significant objects to understand the nature of the oscillations since the binary effects in these systems are negligible. Recent studies based on space data have shown that the pulsation mechanisms of some oscillating stars are not completely understood. Hence, comprehensive studies of a number of pulsating stars within detached eclipsing binaries are important. In this study, we present a detailed analysis of the pulsating detached eclipsing binary system AI Hya which was studied by two independent groups with different methods. We carried out a spectroscopic survey to estimate the orbital parameters via radial velocity measurements and the atmospheric parameters of each binary component using the composite and/or disentangled spectra. We found that the more luminous component of the system is a massive, cool and chemically normal star while the hotter binary component is a slightly metal-rich object. The fundamental parameters of AI Hya were determined by the analysis of binary variations and subsequently used in the evolutionary modelling. Consequently, we obtained the age of the system as 850 $\pm$ 20 Myr and found that both binary components are situated in the Delta Scuti instability strip. The frequency analysis revealed pulsation frequencies between the 5.5 - 13.0 d$^{-1}$ and we tried to estimate which binary component is the pulsating one. However, it turned out that those frequencies could originate from both binary components.

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Twenty-year monitoring of the surface magnetic fields of chemically peculiar stars

Magnetic chemically peculiar stars of the main sequence can present rotational periods as long as many decades. Here we report the results of an observational campaign started in 2001 aimed at establishing these very long periods from the variability of the integrated magnetic field modulus, the so-called surface magnetic field $B_s$, as measured from the Zeeman splitting of the Fe{\sc ii}\,6149.258\,Å spectral line. Thirty-six stars have been monitored with various high-resolution spectrographs at different telescopes, totalling 412 newly collected spectra. To improve the phase coverage, we have also exploited all public archives containing high-resolution spectra, many not yet published. On the basis of these new $B_s$ variability curves, we 1) confirm or revisit the periods of 24 stars, 2) extend the lower limits to the periods of HD\,55719 ($P > 38$\,yr), HD\,165474 ($P > 27$\,yr), HD\,177765 ($P > 37$\,yr), 3) establish for the first time the periods of HD\,29578 ($P = 10.95$\,yr), HD\,47103 ($P = 17.683$\,d), HD\,150562 ($P = 5.7$\,yr), HD\,216018 ($P = 34.044$\,d), and 4) set lower limits to the periods of HD\,75445 ($P >> 14$\,yr), HD\,110066 ($P >> 29$\,yr), HD\,116114 ($P > 48$\,yr), and HD\,137949 ($P > 27$\,yr). As to $γ$\,Equ, whose period must exceed 90 years, we point out a clear decrease in the field modulus, the maximum of which coincides within the uncertainties with the minimum of the variation in the integrated longitudinal field.

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Discovery and origin of the radio emission from the multiple stellar system KQVel

KQVel is a binary system composed of a slowly rotating magnetic Ap star with a companion of unknown nature. In this paper, we report the detection of its radio emission. We conducted a multi-frequency radio campaign using the ATCA interferometer (band-names: 16cm, 4cm, and 15mm). The target was detected in all bands. The most obvious explanation for the radio emission is that it originates in the magnetosphere of the Ap star, but this is shown unfeasible. The known stellar parameters of the Ap star enable us to exploit the scaling relationship for non-thermal gyro-synchrotron emission from early-type magnetic stars. This is a general relation demonstrating how radio emission from stars with centrifugal magnetospheres is supported by rotation. Using KQVel's parameters the predicted radio luminosity is more than five orders of magnitudes lower than the measured one. The extremely long rotation period rules out the Ap star as the source of the observed radio emission. Other possible explanations for the radio emission from KQVel, involving its unknown companion, have been explored. A scenario that matches the observed features (i.e. radio luminosity and spectrum, correlation to X-rays) is a hierarchical stellar system, where the possible companion of the magnetic star is a close binary (possibly of RSCVn type) with at least one magnetically active late-type star. To be compatible with the total mass of the system, the last scenario places strong constraints on the orbital inclination of the KQVel stellar system.

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New, late-type spectroscopic binaries with X-ray emission

In this paper we present a spectroscopic study of six double-lined binaries, five of which were recently discovered in a high-resolution spectroscopic survey of optical counterparts of stellar X-ray sources. Thanks to high-resolution spectra acquired with CAOS spectropolarimeter during seven years, we were able to measure the radial velocities of their components and determine their orbital elements. We have applied our code COMPO2 to determine the spectral types and atmospheric parameters of the components of these spectroscopic binaries and found that two of these systems are composed of main sequence stars, while the other four contain at least one evolved (giant or subgiant) component, similar to other well-known RS CVn systems. The subtraction of a photospheric template built up with spectra of non-active stars of the same spectral type as those of the components of each system has allowed us to investigate the chromospheric emission that fills in the H$α$ cores. We found that the colder component is normally the one with the largest H$α$ emission. None of the systems show a detectable LiI$λ$6708 line, with the exception of TYC 4279-1821-1, which exhibits high photospheric abundances in both components. Photometric time series from the literature allowed us to assess that the five systems with a nearly circular orbit have also photometric periods close or equal to the orbital ones, indicating spin-orbit synchronization. For the system with a highly eccentric orbit, a possible pseudo-synchronization with the periastron velocity is suggested.

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Stellar Population Astrophysics (SPA) with the TNG: Stock 2, a little-studied open cluster with an eMSTO

Stock 2 is a little-studied open cluster that shows an extended main-sequence turnoff (eMSTO). In order to investigate this phenomenon and characterise the cluster itself we performed high-resolution spectroscopy in the framework of the Stellar Population Astrophysics (SPA) project. We employed the High Accuracy Radial velocity Planet Searcher in North hemisphere spectrograph (HARPS-N) at the Telescopio Nazionale Galileo (TNG). We completed our observations with additional spectra taken with the Catania Astrophysical Observatory Spectrograph (CAOS). In total we observed 46 stars (dwarfs and giants), which represent, by far, the largest sample collected for this cluster to date. We provide the stellar parameters, extinction, radial and projected rotational velocities for most of the stars. Chemical abundances for 21 species with atomic numbers up to 56 have also been derived. We notice a differential reddening in the cluster field whose average value is 0.27 mag. It seems to be the main responsible for the observed eMSTO, since it cannot be explained as the result of different rotational velocities, as found in other clusters. We estimate an age for Stock 2 of 450$\pm$150 Ma which corresponds to a MSTO stellar mass of $\approx$2.8 M$_{\odot}$. The cluster mean radial velocity is around 8.0 km s$^{-1}$. We find a solar-like metallicity for the cluster, [Fe/H]=$-$0.07$\pm$0.06, compatible with its Galactocentric distance. MS stars and giants show chemical abundances compatible within the errors, with the exceptions of Barium and Strontium, which are clearly overabundant in giants, and Cobalt, which is only marginally overabundant. Finally, Stock 2 presents a chemical composition fully compatible with that observed in other open clusters of the Galactic thin disc.

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A scaling relationship for non-thermal radio emission from ordered magnetospheres: from the top of the Main Sequence to planets

In this paper, we present the analysis of incoherent non-thermal radio emission from a sample of hot magnetic stars, ranging from early-B to early-A spectral type. Spanning a wide range of stellar parameters and wind properties, these stars display a commonality in their radio emission which presents new challenges to the wind scenario as originally conceived. It was thought that relativistic electrons, responsible for the radio emission, originate in current sheets formed where the wind opens the magnetic field lines. However, the true mass-loss rates from the cooler stars are too small to explain the observed non-thermal broadband radio spectra. Instead, we suggest the existence of a radiation belt located inside the inner-magnetosphere, similar to that of Jupiter. Such a structure explains the overall indifference of the broadband radio emissions on wind mass-loss rates. Further, correlating the radio luminosities from a larger sample of magnetic stars with their stellar parameters, the combined roles of rotation and magnetic properties have been empirically determined. Finally, our sample of early-type magnetic stars suggests a scaling relationship between the non-thermal radio luminosity and the electric voltage induced by the magnetosphere's co-rotation, which appears to hold for a broader range of stellar types with dipole-dominated magnetospheres (like the cases of the planet Jupiter and the ultra-cool dwarf stars and brown dwarfs). We conclude that well-ordered and stable rotating magnetospheres share a common physical mechanism for supporting the generation of non-thermal electrons.

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Long-term photospheric instabilities and envelopes dynamics in the post-AGB binary system 89 Herculis

We present a long-term optical spectroscopic study of the post-AGB binary system 89 Herculis, with the aim to characterize the relationship between photospheric instabilities and dynamics in the close circumstellar environment of the system. This study is based on spectra acquired with the high-resolution Catania Astrophysical Observatory Spectropolarimeter and archive data, covering a time interval between 1978 and 2018. We find long-term changes in the radial velocity curve of the system, occurring mostly in amplitude, which correlate with the variability observed in the blue-shifted absorption component of the P Cygni like H$α$ profile. Two possible scenarios are discussed. We also find strong splitting in the s-process elements of \ion{Ba}{ii} $6141.713$ Å and $6496.898$ Å\,lines, with short-term morphological variations. A Gaussian decomposition of such profiles allows us to distinguish four shell components, two expanding and two in-falling toward the central star, which are subject to the orbital motion of the system and are not affected by the long-term instabilities. Finally, we find that the numerous metal lines in emission could originate in regions of a structured circumbinary disk that have sizes proportional to the energy of the corresponding upper level transition $\rm E_{up}$. This study demonstrates the potential of long-term high-resolution spectroscopy in linking together the instability processes occurring during the late evolutionary stages of post-AGBs and the subsequent phase of PNe.

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The auroral radio emission of the magnetic B-type star rho OphC

The non-thermal radio emission of main-sequence early-type stars is a signature of stellar magnetism. We present multi-wavelength (1.6-16.7 GHz) ATCA measurements of the early-type magnetic star rho OphC, which is a flat-spectrum non-thermal radio source. The rho OphC radio emission is partially circularly polarized with a steep spectral dependence: the fraction of polarized emission is about 60% at the lowest frequency sub-band (1.6 GHz) while is undetected at 16.7 GHz. This is clear evidence of coherent Auroral Radio Emission (ARE) from the rho OphC magnetosphere. Interestingly, the detection of the rho OphC's ARE is not related to a peculiar rotational phase. This is a consequence of the stellar geometry, which makes the strongly anisotropic radiation beam of the amplified radiation always pointed towards Earth. The circular polarization sign evidences mainly amplification of the ordinary mode of the electromagnetic wave, consistent with a maser amplification occurring within dense regions. This is indirect evidence of the plasma evaporation from the polar caps, a phenomenon responsible for the thermal X-ray aurorae. rho OphC is not the first early-type magnetic star showing the O-mode dominated ARE but is the first star with the ARE always on view.

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The single-sided pulsator CO~Camelopardalis

CO~Cam (TIC 160268882) is the second ``single-sided pulsator'' to be discovered. These are stars where one hemisphere pulsates with a significantly higher amplitude than the other side of the star. CO~Cam is a binary star comprised of an Am $δ$~Sct primary star with $T_{\rm eff} = 7070 \pm 150$\,K, and a spectroscopically undetected G main-sequence secondary star. The dominant pulsating side of the primary star is centred on the L$_1$ point. We have modelled the spectral energy distribution combined with radial velocities, and independently the {\em TESS} light curve combined with radial velocities. Both of these give excellent agreement and robust system parameters for both stars. The $δ$~Sct star is an oblique pulsator with at least four low radial overtone (probably) f~modes with the pulsation axis coinciding with the tidal axis of the star, the line of apsides. Preliminary theoretical modelling indicates that the modes must produce much larger flux perturbations near the L$_1$ point, although this is difficult to understand because the pulsating star does not come near to filling its Roche lobe. More detailed models of distorted pulsating stars should be developed. These newly discovered single-sided pulsators offer new opportunities for astrophysical inference from stars that are oblique pulsators in close binary stars.

astro-ph.SR

Evidence for radio and X-ray auroral emissions from the magnetic B-type star rho Oph A

We present new ATCA multi-wavelength radio measurements (range 2.1-21.2 GHz) of the early-type magnetic star rho Oph A, performed in March 2019 during 3 different observing sessions. These new ATCA observations evidence a clear rotational modulation of the stellar radio emission and the detection of coherent auroral radio emission from rho Oph A at 2.1 GHz. We collected high-resolution optical spectra of rho Oph A acquired by several instruments over a time span of about ten years. We also report new magnetic field measurements of rho Oph A that, together with the radio light curves and the temporal variation of the equivalent width of the HeI line (lambda=5015 Angstrom), were used to constrain the rotation period and the stellar magnetic field geometry. The above results have been used to model the stellar radio emission, modelling that allowed us to constrain the physical condition of rho Oph A's magnetosphere. Past XMM measurements showed periodic X-ray pulses from rho Oph A. We correlate the X-ray light curve with the magnetic field geometry of rho Oph A. The already published XMM data have been re-analyzed showing that the X-ray spectra of rho Oph A are compatible with the presence of a non-thermal X-ray component. We discuss a scenario where the emission phenomena occurring at the extremes of the electromagnetic spectrum, radio and X-ray, are directly induced by the same plasma process. We interpret the observed X-ray and radio features of rho Oph A as having an auroral origin.

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The solar-like "Second Spectrum" and the polarised metal lines in emission of the post-AGB binary 89 Herculis

We studied the polarised spectrum of the post-AGB binary system 89\,Herculis on the basis of data collected with the high resolution \emph{Catania Astrophysical Observatory Spectropolarimeter}, \emph{HArps-North POlarimeter} and \emph{Echelle SpectroPolarimetric Device for the Observation of Stars}. We find the existence of linear polarisation in the strongest metal lines in absorption and with low excitation potentials. Signals are characterized by complex Q and U morphologies varying with the orbital period. As possible origin of this "Second Solar Spectrum"-like behaviour, we rule out magnetic fields, continuum depolarisation due pulsations and hot spots. { The linear polarisation we detected also in the Ca{\sc ii}\,8662Å\, line is a clear evidence of optical pumping polarisation and it rules out the scattering polarisation from free electrons of the circumbinary environment.} In the framework of optical pumping due to the secondary star, the observed periodic properties of the spectral line polarisation can be justied by two jets, flow velocity of few tens of km\,s$^{-1}$, at the basis of that hour-glass structure characterising 89\,Herculis. We also discovered linear polarisation across the emission profile of metal lines. Numerical simulations show that these polarised profiles could be formed in an undisrupted circumbinary disk rotating at $\le$10 km\,s$^{-1}$ and whose orientation in the sky is in agreement with optical and radio interferometric results. We conclude that the study of those aspherical enevlopes, whose origin is not yet completely understood, of PNe and already present in the post-AGB's, can benefit of high resolution spectropolarimetry and that this technique can shape envelopes still too far for interferometry.

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The multi-line slope method for the measure of the effective magnetic field of the cool stars: an application to the solar like cycle of ε Eri

A method for the determination of integrated longitudinal stellar fields from low-resolution spectra is the so-called slope method, which is based on the regression of the Stokes V signal against the first derivative of Stokes I. Here we investigate the possibility to extend this technique to measure the magnetic fields of cool stars from high resolution spectra. For this purpose we developed a multi-line modification to the slope method, called multi-line slope method. We tested this technique by analysing synthetic spectra computed with the COSSAM code and real observations obtained with the high resolution spectropolarimeters Narval, HARPSpol and Catania Astrophysical Observatory Spectropolarimeter (CAOS). We show that the multi-line slope method is a fast alternative to the Least Squares Deconvolution (LSD) technique for the measurement of the effective magnetic fields of cool stars. Using a Fourier transform on the effective magnetic field variations of the star $ε$ Eri, we find that the long term periodicity of the field corresponds to the 2.95 yr period of the stellar dynamo, revealed by the variation of the activity index.

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Kepler observations of A-F pre-main sequence stars in Upper Scorpius: Discovery of six new $δ$~Scuti and one $γ$~Doradus stars

We present light curves and periodograms for 27 stars in the young Upper Scorpius association (age=$11 \pm 1$\,Myr) obtained with the Kepler spacecraft. This association is only the second stellar grouping to host several pulsating pre-main sequence (PMS) stars which have been observed from space. From an analysis of the periodograms, we identify six $δ$~Scuti variables and one $γ$~Doradus star. These are most likely PMS stars or else very close to the zero-age main sequence. Four of the $δ$~Scuti variables were observed in short-cadence mode, which allows us to resolve the entire frequency spectrum. For these four stars, we are able to infer some qualitative information concerning their ages. For the remaining two $δ$~Scuti stars, only long-cadence data are available, which means that some of the frequencies are likely to be aliases. One of the stars appears to be a rotational variable in a hierarchical triple system. This is a particularly important object, as it allows the possibility of an accurate mass determination when radial velocity observations become available. We also report on new high-resolution echelle spectra obtained for some of the stars of our sample.

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CAOS spectroscopy of Am stars Kepler targets

The {\it Kepler} space mission and its {\it K2} extension provide photometric time series data with unprecedented accuracy. These data challenge our current understanding of the metallic-lined A stars (Am stars) for what concerns the onset of pulsations in their atmospheres. It turns out that the predictions of current diffusion models do not agree with observations. To understand this discrepancy, it is of crucial importance to obtain ground-based spectroscopic observations of Am stars in the {\it Kepler} and {\it K2} fields in order to determine the best estimates of the stellar parameters. In this paper, we present a detailed analysis of high-resolution spectroscopic data for seven stars previously classified as Am stars. We determine the effective temperatures, surface gravities, projected rotational velocities, microturbulent velocities and chemical abundances of these stars using spectral synthesis. These spectra were obtained with {\it CAOS}, a new instrument recently installed at the observing station of the Catania Astrophysical Observatory on Mt. Etna. Three stars have already been observed during quarters Q0-Q17, namely: HD\,180347, HD\,181206, and HD\,185658, while HD\,43509 was already observed during {\it K2} C0 campaign. We confirm that HD\,43509 and HD\,180347 are Am stars, while HD 52403, HD\,50766, HD\,58246, HD\,181206 and HD\,185658 are marginal Am stars. By means of non-LTE analysis, we derived oxygen abundances from O{\sc I}$λ$7771--5Å triplet and we also discussed the results obtained with both non-LTE and LTE approaches.

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