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K. Pavlovski

Publications and source records attributed to K. Pavlovski.

At least 19 recordsLinked to original sources

V446 Cephei: a $\beta$ Cep pulsator in a multiple system

$\beta$ Cep stars in eclipsing binary (EB) systems give us an opportunity to put observational constraints on their structure and stellar parameters. We present a comprehensive analysis of the $\beta$ Cep star in the EB V446 Cep, using \textit{TESS} photometry and HERMES spectra. We calculate the stellar and orbital parameters using light curve modelling and spectral disentangling. The EB has an orbital period of $3.808567 \pm 0.000012$ d and a mass ratio of $0.1550 \pm 0.0012$. We find the $\beta$ Cep star to have a mass of $10.68 \pm 0.06$ $\mathrm{M_{\odot}}$, a radius of $5.864 \pm 0.033$ $\mathrm{R}_{\odot}$, and a $T_{\rm eff}$ of $24220 \pm 180$ K. The secondary has a mass of $1.657 \pm 0.017$ $\mathrm{M_{\odot}}$, a radius of $1.530 \pm 0.014$ $\mathrm{R}_{\odot}$, and a $T_{\rm eff}$ of $9080 \pm 390$ K. We also extract the abundances of C, N, O, Mg, and Si for the $\beta$ Cep star, which are found to be consistent with galactic OB binaries. We identified 21 distinct pulsation frequencies, with the dominant mode at 10.24324 d$^{-1}$, which corresponds to a near-harmonic of the system's orbital frequency. The two stars in the EB have asynchronous rotation, with both stars rotating faster than the orbital frequency. We detect a companion to the EB using eclipse timing variations and period changes of the dominant pulsation frequency. We calculate the minimum mass of this tertiary companion to be $4.11 \pm 0.32$ $\mathrm{M_{\odot}}$ which is on an orbit of 2303$\pm$69 d around the EB. Using spectral energy distributions and MIST isochrones, we conclude that V446 Cep is either a co-evolving hierarchical 2+2 quadruple or a triple system where the third body is a compact object.

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Dynamical mass of a solar-like oscillator at the main-sequence turnoff from Gaia astrometry & ground-based spectroscopy

Asteroseismology is widely used for precise determining of masses of solar-like oscillating stars by performing individual-frequency modeling or applying homological scaling relations. However, these methods lack dynamical validation on the main sequence due to the absence of eclipsing double-lined binary system (SB2) as benchmark objects. By providing the orbital inclination, astrometric binary systems from ESA Gaia DR3 offer an abundant alternative for eclipsing systems. We present KIC693187 as the first SB2, hosting a solar-like oscillating post-main-sequence star with dynamical masses. By combining Gaia astrometry with spectroscopic obtained with the Las Cumbres Observatory network (LCO), we find $M_1^\mathrm{dyn}$=0.99$\pm$0.05$M_\odot$ and $M_2^\mathrm{dyn}$=0.89$\pm$0.04$M_\odot$ for the primary and secondary, respectively. Asteroseismic parameters were extracted from photometry of the NASA \Kepler satellite. The mass from individual frequency modeling is $M_1^\mathrm{IF}$=0.92$\pm$0.01$M_\odot$. Taking into account the systematic uncertainty of 0.04$M_\odot$ for best fit models from individual frequency fitting, we find an agreement within 1.2$\sigma$. From scaling relations we obtain a mass range of 0.93 to 0.98$M_\odot$ by using the observed large frequency separations (\dnu) in the scaling relations for the primary. By using standard corrections for departures from the asymptotic regime of \dnu, we obtained a mass range of 0.83 to 1.03$M_\odot$. The upper ends of both ranges agree well with the dynamical mass of the primary. This approach provides the first empirical validation for main-sequence solar-like oscillators and opens a new window for validating asteroseismology. Through a dedicatded program targeting astrometric SB2 binary systems, ESA's PLATO space mission will provide will enlarge the benchmark sample substantially.

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Orbital and Physical Properties of the Pleiades Binary 27 Tau (Atlas)

We report new spectroscopic and interferometric observations of the Pleiades binary star Atlas, which played an important role nearly three decades ago in settling the debate over the distance to the cluster from ground-based and space-based determinations. We use the new measurements, together with other published and archival astrometric observations, to improve the determination of the 291-day orbit and the distance to Atlas ($136.2 \pm 1.4$ pc). We also derive the main properties of the components, including their absolute masses ($5.04 \pm 0.17 M_{\odot}$ and $3.64 \pm 0.12 M_{\odot}$), sizes, effective temperatures, projected rotational velocities, and chemical composition. We find that the more evolved primary star is rotationally distorted, and are able to estimate its oblateness and the approximate orientation of its spin axis from the interferometric observations. The spin axis may well be aligned with the orbital axis. Models of stellar evolution from MESA that account for rotation provide a good match to all of the primary's global properties, and point to an initial angular rotation rate on the zero-age main sequence of about 55% of the breakup velocity. The current location of the star in the H-R diagram is near the very end of the hydrogen-burning main sequence, at an age of about 105 Myr, according to these models. Our spectroscopic analysis of the more slowly-rotating secondary indicates that it is a helium-weak star, with other chemical anomalies.

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Observational mapping of the mass discrepancy in eclipsing binaries: Selection of the sample and its photometric and spectroscopic properties

Abridged. Eclipsing spectroscopic double-lined binaries are the prime source of precise and accurate measurements of masses and radii of stars. These measurements provide a stringent test of models of stellar evolution that are persistently reported to contain major shortcomings. The mass discrepancy observed for the eclipsing spectroscopic double-lined binaries is one of the manifestations of shortcomings in stellar evolution models. Our ultimate goal is to provide an observational mapping of the mass discrepancy and propose a recipe for its solution. We initiate a spectroscopic monitoring campaign of 573 candidate eclipsing binaries of which 83 are analysed in this work with the methods of least-squares deconvolution and spectral disentangling. TESS light curves are used to provide photometric classification of the systems according to the type of their intrinsic variability. We confirm 69 systems as either spectroscopic binaries or higher-order multiple systems. Twelve stars are classified as single and two more objects are found at the interface of their line profile variability being interpreted as due to binarity and intrinsic variability of the star. Moreover, 20 eclipsing binaries are found to contain at least one component that exhibits stellar oscillations. The sample presented in this work contains both detached and semi-detached systems and covers a range in the effective temperature and mass of the star of Teff = [7000,30000] K and M = [1.5,15] M_Sun, respectively. We conclude an appreciable capability of the spectral disentangling method to deliver precise and accurate spectroscopic orbital elements from as few as 6-8 orbital phase-resolved spectroscopic observations. Orbital solutions obtained this way are accurate enough to deliver age estimates with accuracy of 10% or better, an important resource for calibration of stellar evolution models.

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High-mass eclipsing binaries: a testbed for models of interior structure and evolution -- Accurate fundamental properties and surface chemical composition for V1034 Sco, GL Car, V573 Car and V346 Cen

The surface chemical compositions of stars are affected by physical processes which bring the products of thermonuclear burning to the surface. Despite their potential in understanding the structure and evolution of stars, elemental abundances are available for only a few high-mass binary stars. We aim to enlarge this sample by determining the physical properties and photospheric abundances for four eclipsing binary systems containing high-mass stars: V1034 Sco, GL Car, V573 Car and V346 Cen. The components have masses 8-17 Msun and effective temperatures from 22500 to 32200 K, and are all on the main sequence. We present new high-resolution and high signal-to-noise spectroscopy from HARPS, and analyse them using spectral disentangling and NLTE spectral synthesis. We model existing light curves and new photometry from the TESS satellite, We measure the stellar masses to 0.6-2.0 percent precision, radii to 0.8-1.7 percent precision, effective temperatures to 1.1-1.6 percent precision, and abundances of C, N, O, Mg and Si. The abundances are similar to those found in our previous studies of high-mass eclipsing binaries; our sample now comprises 25 high-mass stars in 13 binary systems. We also find tidally-excited pulsations in V346 Cen. We reinforce our previous conclusions: interior chemical element transport is not as efficient in binary star components as in their single-star counterparts in the same mass regime and evolutionary stage, possibly due to the effects of tidal forces. Our ultimate goal is to provide a larger sample of OB-type stars in binaries which would enable a thorough comparison to stellar evolutionary models, as well as to single high-mass stars.

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KIC 7955301: a hierarchical triple system with eclipse timing variations and an oscillating red giant

KIC 7955301 is a hierarchical triple system with eclipse timing and depth variations discovered by the Kepler mission. It is composed of a non-eclipsing primary star at the bottom of the red giant branch on a 209-day orbit with a K/G-type main-sequence inner eclipsing binary, orbiting in 15.3 days. This system was noted for the large amplitude of its eclipse timing variations (4 hours), and the clear solar-like oscillations of the red-giant component, including p-modes of degree up to l=3 and mixed l=1 modes. The system is a single-lined spectroscopic triple. We perform a dynamical model by combining the Kepler photometric data, eclipse timing variations, and radial-velocity data obtained at Apache Point (ARCES) and Haute Provence (SOPHIE) observatories. The dynamical mass of the red-giant is determined with a 2% precision at 1.30 (+0.03,-0.02) solar mass. We perform asteroseismic modeling based on the global seismic parameters and on the individual frequencies. Both methods lead to a mass of the red giant that matches the dynamical mass within the uncertainties. Asteroseismology also reveals the rotation rate of the core (15 days), the envelope (150 days), and the inclination (75 deg) of the red giant. Three different approaches lead to an age between 3.3 and 5.8 Gyr, which highlights the difficulty of determining stellar ages despite the exceptional wealth of available information. On short timescales, the inner binary exhibits eclipses with varying depths during a 7.3-year long interval, and no eclipses during the consecutive 11.9 years. This is why Kepler could detect its eclipses, TESS will not, and the future ESA PLATO mission should. Over the long term, the system owes its evolution to the evolution of its individual components. It could end its current smooth evolution by merging by the end of the red giant or the asymptotic giant branch of the primary star.

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Dynamical parallax, physical parameters and evolutionary status of the components of the bright eclipsing binary α Draconis

Altough both components of the bright eclipsing binary $α$ Dra having been resolved using long baseline interferometry and the secondary component shown to contribute some 15\% of the total flux, a spectroscopic detection of the companion star was so far unsuccessful. To achieve our goals, we use a combined data set from interferometry with the Navy Precision Optical Interferometer (NPOI), photometry with the TESS space observatory, and high-resolution spectroscopy with the HERMES fibre-fed spectrograph at the La Palma observatory. We use the method of spectral disentangling to search for the contribution of a companion star in the observed composite HERMES spectra, to separate the spectral contributions of both components, and to determine orbital elements of the $α$ Dra system. TESS light curves are analysed in an iterative fashion with spectroscopic inference of stellar atmospheric parameters to determine fundamental stellar properties and their uncertainties. Finally, NPOI interferometric measurements are used for determination of the orbital parameters of the system and angular diameters of both binary components. We report the first firm spectroscopic detection of the secondary component in $α$ Dra and deliver disentangled spectra of both binary components. The inferred near-core mixing properties of both components do not support a dependence of the convective core overshooting on the stellar mass. At the same time, the $α$ Dra system provides extra support to hypothesise that the mass discrepancy in eclipsing spectroscopic double-lined binaries is associated with inferior atmospheric modelling of intermediate- and high-mass stars, and less so with the predictive power of stellar structure and evolution models as to the amount of near-core mixing and mass of the convective core. (abridged abstract)

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The surface brightness - colour relations based on eclipsing binary stars and calibrated with Gaia EDR3

The surface brightness -- colour relation (SBCR) is a basic tool in establishing precise and accurate distances within the Local Group. Detached eclipsing binary stars with accurately determined radii and trigonometric parallaxes allow for a calibration of the SBCRs with unprecedented accuracy. We analysed four nearby eclipsing binary stars containing late F-type main sequence components: AL Ari, AL Dor, FM Leo and BN Scl. We determined very precise spectroscopic orbits and combined them with high precision ground- and space-based photometry. We derived the astrophysical parameters of their components with mean errors of 0.1% for mass and 0.4% for radius. We combined those four systems with another 24 nearby eclipsing binaries with accurately known radii from the literature for which $Gaia$ EDR3 parallaxes are available, in order to derive the SBCRs. The resulting SBCRs cover stellar spectral types from B9 V to G7 V. For calibrations we used Johnson optical $B$ and $V$, $Gaia$ $G_{\rm BP}$ and $G$ and 2MASS $JHK$ bands. The most precise relations are calibrated using the infrared $K$ band and allow to predict angular diameters of A-, F-, and G-type dwarf and subgiant stars with a precision of 1%.

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A beta Cephei pulsator and a changing orbital inclination in the high-mass eclipsing binary system VV Orionis

We present an analysis of the high-mass eclipsing binary system VV Ori based on photometry from the TESS satellite. The primary star (B1V, 9.5 Msun) shows beta Cephei pulsations and the secondary (B7V, 3.8 Msun) is possibly a slowly-pulsating B star. We detect 51 significant oscillation frequencies, including two multiplets with separations equal to the orbital frequency, indicating that the pulsations are tidally perturbed. We analyse the TESS light curve and published radial velocities to determine the physical properties of the system. Both stars are only the second of their pulsation type with a precisely-measured mass. The orbital inclination is also currently decreasing, likely due to gravitational interactions with a third body.

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Discovery of $β$ Cep pulsations in the eclipsing binary V453 Cygni

V453 Cyg is an eclipsing binary containing 14 Msun and 11 Msun stars in an eccentric short-period orbit. We have discovered $β$ Cep-type pulsations in this system using TESS data. We identify seven significant pulsation frequencies, between 2.37 and 10.51 d$^{-1}$, in the primary star. These include six frequencies which are separated by yet significantly offset from harmonics of the orbital frequency, indicating they are tidally-perturbed modes. We have determined the physical properties of the system to high precision: V453 Cyg A is the first $β$ Cep pulsator with a precise mass measurement. The system is a vital tracer of the physical processes that govern the evolution of massive single and binary stars.

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The mass discrepancy in intermediate- and high-mass eclipsing binaries: the need for higher convective core masses

(Abridged) Eclipsing, spectroscopic double-lined binary star systems (SB2) are excellent laboratories for calibrating theories of stellar interior structure and evolution. We aim to investigate the mass discrepancy in binary stars. We study the effect of near-core mixing on the mass of the convective core of the stars and interpret the results in the context of the mass discrepancy. Two scenarios are considered, where individual stellar components of a binary system are treated independent of each other and where they are forced to have the same age and initial chemical composition. We find that the mass discrepancy is present in our sample and that it is anti-correlated with the surface gravity of the star. No correlations are found with other fundamental and atmospheric parameters, including the stellar mass. The mass discrepancy can be partially accounted for by increasing the amount of near-core mixing in stellar evolution models. We also find that ignoring the microturbulent velocity and turbulent pressure in stellar atmosphere models of hot evolved stars results in overestimation of their effective temperature by up to 8%. Together with enhanced near-core mixing, this can almost entirely account for the 30% mass discrepancy found for the evolved primary component of V380 Cyg. We find a strong link between the mass discrepancy and the convective core mass. The mass discrepancy can be solved by considering the combined effect of extra near-core boundary mixing and consistent treatment in the spectrum analysis of hot evolved stars. Our binary modelling results in convective core masses between 17 and 35% of the stellar mass, in excellent agreement with results from gravity-mode asteroseismology of single stars. This implies larger helium core masses near the end of the main sequence than anticipated so far.

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Modelling of the B-type binaries CW Cep and U Oph: A critical view on dynamical masses, core boundary mixing, and core mass

Context: Intermediate-Mass stars are often overlooked as they are not supernova progenitors but still host convective cores and complex atmospheres which require computationally expensive treatment. Due to this, there is a general lack of such stars modelled by state of the art stellar structure and evolution codes. Aims: This paper aims to use high-quality spectroscopy to update the dynamically obtained stellar parameters and produce a new evolutionary assessment of the bright B0.5+B0.5 and B5V+B5V binary systems CW Cep and U Oph. Methods: We use new spectroscopy obtained with the Hermes spectrograph to revisit the photometric binary solution of the two systems. The updated mass ratio and effective temperatures are incorporated to obtain new dynamical masses for the primary and secondary. With these, we perform isochrone-cloud based evolutionary modelling to investigate the core properties of these stars. Results: We report the first abundances for CW Cep and U Oph as well as report an updated dynamical solution for both systems. We find that we cannot uniquely constrain the amount of core boundary mixing in any of the stars we consider. Instead, we report their core masses and compare our results to previous studies. Conclusions: We find that the per-cent level precision on fundamental stellar quantities are accompanied with core mass estimates to between ~ 5-15%. We find that differences in analysis techniques can lead to substantially different evolutionary mode

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Evidence for conservative mass transfer in the classical Algol system $δ$ Librae from its surface carbon-to-nitrogen abundance ratio

Algol-type binary systems are the product of rapid mass transfer between the initially more massive component to its companion. It is still unknown whether the process is conservative, or whether substantial mass is lost from the system. The history of a system prior to mass exchange is imprinted in the photospheric chemical composition, in particular in the carbon-to-nitrogen (C/N) ratio. We use this to trace the efficiency of mass-transfer processes in the components of a classical Algol-type system, $δ$ Librae. The present analysis is based on new spectroscopic data (ground-based high-resolution échelle spectra) and extracted archival photometric observations (space-based measurements from the STEREO satellites). In the orbital solution, non-Keplerian effects on the radial-velocity variations were taken into account. This reduces the primary's mass by 1.1 \Msun\ ($\sim$23\%) significantly in comparison to previous studies, and removes a long-standing discrepancy between the radius and effective temperature. A spectral disentangling technique is applied to the échelle observations and the spectra of the individual components are separated. Atmospheric and abundance analyses are performed for the mass-gaining component and we found C/N $= 1.55 \pm 0.40$ for this star. An extensive set of evolutionary models ($3.5\times10^6$) for both components are calculated from which the best-fitting model is derived. It is found that $β$, the parameter which quantifies the efficiency of mass-loss from a binary system, is close to zero. This means that the mass-transfer in $δ$ Lib is mostly conservative with little mass loss from the system.

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Physical properties and CNO abundances for high-mass stars in four main-sequence detached eclipsing binaries: V478 Cyg, AH Cep, V453 Cyg and V578 Mon

A prerequisite for probing theortical evolutionary models for high-mass stars is the determination of stellar physical properties with a high accuracy. We do this for three binary systems containing components with masses above 10 Msun: V478 Cyg, AH Cep and V453 Cyg. New high-resolution and high-S/N echelle spectra were secured and analysed using spectral disentangling, yielding improved orbital elements and the individual spectra for the component stars. In conjuction with a re-analysis of archival light curves, the stellar masses and radii were measured to accuracies of 1.5-2.5% and 1.0-1.9%, respectively. Detailed spectroscopic analysis then yielded atmospheric parameters and abundances for C, N, O, Mg and Si. Abundances were also deter- mined for V578 Mon. These results allowed a detailed comparison to the predictions of stellar evolutionary models. No star in our sample fits its position on the evolutionary track for its dynamical mass, leaving mass discrepancy (or alternatively overluminosity) an open problem in theoretical modelling. Moreover, the CNO abundances cluster around the initial values with mean values log(N/C) = -0.56 +/- 0.06 and log(N/O) = -1.01 +/- 0.06. No trend in the CNO abundances for single OB stars are found for the eight high-mass stars analysed here, as well in an extended sample including literature results. This opens an important question on the role of binarity in terms of tides on damping internal mixing in stars residing in binary systems.

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Oscillating red giants in eclipsing binary systems: empirical reference value for asteroseismic scaling relation

The internal structures and properties of oscillating red-giant stars can be accurately inferred through their global oscillation modes (asteroseismology). Based on 1460 days of Kepler observations we perform a thorough asteroseismic study to probe the stellar parameters and evolutionary stages of three red giants in eclipsing binary systems. We present the first detailed analysis of individual oscillation modes of the red-giant components of KIC 8410637, KIC5640750 and KIC9540226. We obtain estimates of their asteroseismic masses, radii, mean densities and logarithmic surface gravities by using the asteroseismic scaling relations as well as grid-based modelling. As these red giants are in double-lined eclipsing binaries, it is possible to derive their independent dynamical masses and radii from the orbital solution and compare it with the seismically inferred values. For KIC 5640750 we compute the first spectroscopic orbit based on both components of this system. We use high-resolution spectroscopic data and light curves of the three systems to determine up-to-date values of the dynamical stellar parameters. With our comprehensive set of stellar parameters we explore consistencies between binary analysis and asteroseismic methods, and test the reliability of the well-known scaling relations. For the three red giants under study, we find agreement between dynamical and asteroseismic stellar parameters in cases where the asteroseismic methods account for metallicity, temperature and mass dependence as well as surface effects. We are able to attain agreement from the scaling laws in all three systems if we use $Δν_{\rm ref,emp} = 130.8 \pm 0.9\,μ$Hz instead of the usual solar reference value.

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Seismic probing of the first dredge-up event through the eccentric red-giant & red-giant spectroscopic binary KIC9163796

Binaries in double-lined spectroscopic systems provide a homogeneous set of stars. Differences of parameters, such as age or initial conditions, which otherwise would have strong impact on the stellar evolution, can be neglected. The observed differences are determined by the difference in stellar mass between the two components. The mass ratio can be determined with much higher accuracy than the actual stellar mass. In this work, we aim to study the eccentric binary system KIC9163796, whose two components are very close in mass and both are low-luminosity red-giant stars from four years of Kepler space photometry and high-resolution spectroscopy with Hermes. Mass and radius of the primary were determined through asteroseismology to be 1.39+/-0.06 Mo and 5.35+/-0.09 Ro, resp. From spectral disentangling the mass ratio was found to be 1.015+/-0.005 and that the secondary is ~600K hotter than the primary. Evolutionary models place both components, in the early and advanced stage of the first dredge-up event on the red-giant branch. From theoretical models of the primary, we derived the internal rotational gradient. From a grid of models, the measured difference in lithium abundance is compared with theoretical predictions. The surface rotation of the primary is determined from the Kepler light curve and resembles the orbital period within 10 days. The radial rotational gradient between the surface and core is found to be 6.9+2.0/-1.0. The agreement between the surface rotation with the seismic result indicates that the full convective envelope is rotating quasi-rigidly. The models of the lithium abundance are compatible with a rigid rotation in the radiative zone during the main sequence. Because of the many constraints offered by oscillating stars in binary systems, such objects are important test beds of stellar evolution.

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Constraining stellar physics from red-giant stars in binaries - stellar rotation, mixing processes and stellar activity

The unparalleled photometric data obtained by NASA's Kepler Space Telescope has led to an improved understanding of stellar structure and evolution - in particular for solar-like oscillators in this context. Binary stars are fascinating objects. Because they were formed together, binary systems provide a set of two stars with very well constrained parameters. Those can be used to study properties and physical processes, such as the stellar rotation, dynamics and rotational mixing of elements and allows us to learn from the differences we find between the two components. In this work, we discussed a detailed study of the binary system KIC9163796, discovered through Kepler photometry. The ground-based follow-up spectroscopy showed that this system is a double-lined spectroscopic binary, with a mass ratio close to unity. However, the fundamental parameters of the components of this system as well as their lithium abundances differ substantially. Kepler photometry of this system allows to perform a detailed seismic analysis as well as to derive the orbital period and the surface rotation rate of the primary component of the system. Indications of the seismic signature of the secondary are found. The differing parameters are best explained with both components located in the early and the late phase of the first dredge up at the bottom of the red-giant branch. Observed lithium abundances in both components are in good agreement with prediction of stellar models including rotational mixing. By combining observations and theory, a comprehensive picture of the system can be drawn.

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A solar twin in the eclipsing binary LL Aqr

In the course of a project to study eclipsing binary stars in vinicity of the Sun, we found that the cooler component of LL Aqr is a solar twin candidate. This is the first known star with properties of a solar twin existing in a non-interacting eclipsing binary, offering an excellent opportunity to fully characterise its physical properties with very high precision. We used extensive multi-band, archival photometry and the Super-WASP project and high-resolution spectroscopy obtained from the HARPS and CORALIE spectrographs. The spectra of both components were decomposed and a detailed LTE abundance analysis was performed. The light and radial velocity curves were simultanously analysed with the Wilson-Devinney code. The resulting highly precise stellar parameters were used for a detailed comparison with PARSEC, MESA, and GARSTEC stellar evolution models. LL Aqr consists of two main-sequence stars (F9 V + G3 V) with masses of M1 = 1.1949$\pm$0.0007 and M2=1.0337$\pm$0.0007 $M_\odot$, radii R1 = 1.321$\pm$0.006 and R2 = 1.002$\pm$0.005 $R_\odot$, temperatures T1=6080$\pm$45 K and T2=5703$\pm$50 K and solar chemical composition [M/H]=0.02$\pm$0.05 dex. The absolute dimensions, radiative and photometric properties, and atmospheric abundances of the secondary are all fully consistent with being a solar twin. Both stars are cooler by about 3.5 $σ$ or less metal abundant by 5$σ$ than predicted by standard sets of stellar evolution models. When advanced modelling was performed, we found that full agreement with observations can only be obtained for values of the mixing length and envelope overshooting parameters that are hard to accept. The most reasonable and physically justified model fits found with MESA and GARSTEC codes still have discrepancies with observations but only at the level of 1$σ$.

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