Asteroseismology of solar-like oscillations in giant stars allow the derivation of their masses and radii. For members of open clusters this allows an age estimate of the cluster which should be identical to the age estimate from the colour-magnitude diagram, but independent of the uncertainties that are present for that type of analysis. Thus, a more precise and accurate age estimate can be obtained. We aim to measure asteroseismic properties of oscillating giant members of the open cluster NGC 6866 and utilise these for a cluster age estimate. Model comparisons allow constraints on the stellar physics, and here we investigate the efficiency of convective-core overshoot and effects of rotation during the main-sequence, which has a significant influence on the age for these relatively massive giants. We identify six giant members of NGC 6866 and derive asteroseismic measurements for five of them. This constrains the convective-core overshoot and enables a more precise and accurate age estimate than previously possible. Asteroseismology establishes the helium-core burning evolutionary phase for the giants, which have a mean mass of 2.8 $M_{\odot}$. Their radii are significantly smaller than predicted by current 1D stellar models unless the amount of convective-core overshoot on the main sequence is reduced to $\alpha_{ov} \leq 0.1 H_p$ in the step-overshoot description. Our measurements also suggest that rotation has affected the evolution of the stars in NGC 6866 in a way that is consistent with 3D simulations but not with current 1D stellar models. The cluster age is estimated to be 0.43 $\pm$ 0.05 Gyr, significantly younger and more precise than most previous estimates. We derive a precise cluster age while constraining convective-core overshooting and effects of rotation in the models. We uncover potential biases for automated age estimates of helium-core burning stars.

Asteroseismic scaling relations can provide high-precision measurements of mass and radius for red giant (RG) stars displaying solar-like oscillations. Their accuracy can be validated and potentially improved using independent and accurate observations of mass, radius, effective temperature and metallicity. We seek to achieve this using long period SB2 eclipsing binaries hosting oscillating RGs. We explore KIC 8430105, for which a previous study found significant asteroseismic overestimation of mass and radius when compared with eclipsing binary measurements. We measured dynamical masses and radii for both components to be significantly lower than previously established, increasing the discrepancy between asteroseismic and dynamical measurements. Our dynamical measurements of the RG component were compared to corresponding measurements of mass and radius using asteroseismic scaling relations. Uncorrected scaling relations overestimated the mass of the RG by 26%, the radius by 11%, and the average density by 7%, in agreement with studies for other systems. However, using a theoretical correction to $\Delta \nu$, we managed to obtain an asteroseismic average density that is $1\sigma$ consistent with our dynamical result. We obtained several measurements of $\nu_{max}$ that are not fully consistent. With $\nu_{max} = 76.78 \pm 0.81\mu $Hz, the $\Delta \nu$ correction provided $2 \sigma$ consistent mass and radius for the giant. The age of the system was estimated to be $3.7 \pm 0.4$ Gyr.

Context. Eclipsing binary stars with an oscillating giant component allow accurate stellar parameters to be derived and asteroseismic methods to be tested and calibrated. To this aim, suitable systems need to be firstly identified and secondly measured precisely and accurately. KIC 4054905 is one such system, which has been identified, but with measurements of a relatively low precision and with some confusion regarding its parameters and evolutionary state. Aims. Our aim is to provide a detailed and precise characterisation of the system and to test asteroseismic scaling relations. Methods. Dynamical and asteroseismic parameters of KIC 4054905 were determined from Kepler time-series photometry and multi-epoch high-resolution spectra from FIES at the Nordic Optical Telescope. Results. KIC 4054905 was found to belong to the thick disk and consist of two lower red giant branch (RGB) components with nearly identical masses of 0.95 M-& ODOT; and an age of 9.9 & PLUSMN; 0.6 Gyr. The most evolved star with R & SIME; 8.4 R-& ODOT; displays solar-like oscillations. These oscillations suggest that the star belongs to the RGB, supported also by the radius, which is significantly smaller than the red clump phase for this mass and metallicity. Masses and radii from corrected asteroseismic scaling relations can be brought into full agreement with the dynamical values if the RGB phase is assumed, but a best scaling method could not be identified. Conclusions. The dynamical masses and radii were measured with a precision better than 1.0%. We firmly establish the evolutionary nature of the system to be that of two early RGB stars with an age close to 10 Gyr, unlike previous findings. The metallicity and Galactic velocity suggest that the system belongs to the thick disk of the Milky Way. We investigate the agreement between dynamical and asteroseismic parameters for KIC 4054905 measured in various ways. This suggests that consistent solutions exist, but the need to analyse more of these systems continues in order to establish the accuracy of asteroseismic methods.

Context. The derivation of accurate and precise masses and radii is possible for eclipsing binary stars, allowing for insights into their evolution. When residing in star clusters, they provide measurements of even greater precision, along with additional information on their properties. Asteroseismic investigations of solar-like oscillations offers similar possibilities for single stars.Aims. We wish to improve the previously established properties of the Hyades eclipsing binary HD 27130 and re-assess the asteroseismic properties of the giant star E Tau. The physical properties of these members of the Hyades can be used to constrain the helium content and age of the cluster.Methods. New multi-colour light curves were combined with multi-epoch radial velocities to yield masses and radii of HD 27130. Measurements of T-eff were derived from spectroscopy and photometry, and verified using the Gaia parallax. We estimated the cluster age from re-evaluated asteroseismic properties of E Tau while using HD 27130 to constrain the helium content.Results. The masses, radii, and T-eff of HD 27130 were found to be M=1.0245 0.0024 M-circle dot, R=0.9226 +/- 0.015 R-circle dot, T-eff=5650 +/- 50 K for the primary, and M=0.7426 +/- 0.0016 M-circle dot, R=0.7388 +/- 0.026 R-circle dot, T-eff=4300 +/- 100 K for the secondary component. Our re-evaluation of E Tau suggests that the previous literature estimates are trustworthy and that the HIPPARCOS parallax is more reliable than the Gaia DR2 parallax.Conclusions. The helium content of HD 27130 and, thus, of the Hyades is found to be Y=0.27 but with a significant model dependency. Correlations with the adopted metallicity result in a robust helium enrichment law, with Delta Y/Delta Z close to 1.2 We estimate the age of the Hyades to be 0.9 +/- 0.1 (stat) +/- 0.1 (sys) Gyr, which is in slight tension with recent age estimates based on the cluster white dwarfs. The precision of the age estimate can be much improved via asteroseismic investigations of the other Hyades giants and by future improvements to the Gaia parallax for bright stars.

We perform an asteroseismic investigation of giant stars in the field of NGC 6791 with previous indications of atypical evolution. The analysis makes use of observations from Kepler and Gaia in combination with ground-based photometry, a literature radialvelocity study, and measurements of eclipsing binaries in the cluster. We derive mass, radius, effective temperature, evolutionary stage and apparent distance modulus of each target. Among the investigated cluster giants we find clear evidence of overmassive and undermassive members, and non-members with strong hints of potential past membership. Our results indicate that about 10% of the red giants in the cluster have experiencedmass-transfer or a merger. High-resolutionhigh-S/N spectroscopic follow-up could confirm potential past membership of the non-members, and reveal whether certain element abundances might expose the non-standard evolution of overmassive and undermassive stars. If so, field stars of similar type could be identified as what they are, i.e. overor undermassive stars, and not mistakenly classified as younger or older than they are.

Context. Models of stellar structure and evolution can be constrained using accurate measurements of the parameters of eclipsing binary members of open clusters. Multiple binary stars provide the means to tighten the constraints and, in turn, to improve the precision and accuracy of the age estimate of the host cluster. In the previous two papers of this series, we have demonstrated the use of measurements of multiple eclipsing binaries in the old open cluster NGC 6791 to set tighter constraints on the properties of stellar models than was previously possible, thereby improving both the accuracy and precision of the cluster age. Aims. We identify and measure the properties of a non-eclipsing cluster member, V56, in NGC 6791 and demonstrate how this provides additional model constraints that support and strengthen our previous findings. Methods. We analyse multi-epoch spectra of V56 from FLAMES in conjunction with the existing photometry and measurements of eclipsing binaries in NGC6971. Results. The parameters of the V56 components are found to be Mp = 1.103 ± 0.008M⊙ and Ms = 0.974 ± 0.007M⊙, Rp = 1.764 ± 0.099R⊙ and Rs = 1.045 ± 0.057R⊙, Teff,p = 5447 ± 125 K and Teff,s = 5552 ± 125 K, and surface [Fe/H]=+0.29 ± 0.06 assuming that they have the same abundance. Conclusions. The derived properties strengthen our previous best estimate of the cluster age of 8.3 ± 0.3 Gyr and the mass of stars on the lower red giant branch (RGB), which is MRGB = 1.15 ± 0.02 M⊙ for NGC 6791. These numbers therefore continue to serve as verification points for other methods of age and mass measures, such as asteroseismology.

Accurate stellar parameters of stars in open clusters can help constrain models of stellar structure and evolution. Here we wish to determine the age and metallicity content of the open cluster NGC 2506. To this end we investigated three detached eclipsing binaries (DEBs; V2032, V4, and V5) for which we determined their masses and radii, as well as four red giant branch stars for which we determined their effective temperatures, surface gravities, and metallicities. Three of the stars in the DEBs have masses close to the cluster turn-off mass, allowing for extremely precise age determination. Comparing the values for the masses and radii of the binaries to BaSTI isochrones we estimated a cluster age of $2.01 \pm 0.10$ Gyr. This does depend on the models used in the comparison, where we have found that the inclusion of convective core-overshooting is necessary to properly model the cluster. From red giant branch stars we determined values for the effective temperatures, the surface gravities, and the metallicities. From these we find a cluster metallicity of $-0.36 \pm 0.10$ dex. Using this value and the values for the effective temperatures we determine the reddening to be E$(b - y) = 0.057 \pm 0.004$ mag. Furthermore, we derived the distance to the cluster from Gaia parallaxes and found $3.101 \pm 0.017$ kpc, and we have performed a radial velocity membership determination for stars in the field of the cluster. Finally, we report on the detection of oscillation signals in $\gamma$ Dor and $\delta$ Scuti members in data from the TESS mission, including the possible detection of solar-like oscillations in two of the red giants.

Context. Asteroseismic analysis of solar-like stars allows us to determine physical parameters such as stellar mass, with a higher precision compared to most other methods. Even in a well-studied cluster such as the Hyades, the masses of the red giant stars are not well known, and previous mass estimates are based on model calculations (isochrones). The four known red giants in the Hyades are assumed to be clump (core-helium-burning) stars based on their positions in colour-magnitude diagrams, however asteroseismology offers an opportunity to test this assumption. Aims. Using asteroseismic techniques combined with other methods, we aim to derive physical parameters and the evolutionary stage for the planet hosting star ǫ Tau, which is one of the four red giants located in the Hyades. Methods. We analysed time-series data from both ground and space to perform the asteroseismic analysis. By combining high signalto-noise (S/N) radial-velocity data from the ground-based SONG network with continuous space-based data from the revised Kepler mission K2, we derive and characterize 27 individual oscillation modes for ǫ Tau, along with global oscillation parameters such as the large frequency separation ∆ν and the ratio between the amplitude of the oscillations measured in radial velocity and intensity as a function of frequency. The latter has been measured previously for only two stars, the Sun and Procyon. Combining the seismic analysis with interferometric and spectroscopic measurements, we derive physical parameters for ǫ Tau, and discuss its evolutionary status. Results. Along with other physical parameters, we derive an asteroseismic mass for ǫ Tau of M = 2.458± 0.073 M⊙, which is slightly lower than previous estimates, and which leads to a revised minimum mass of the planetary companion. Noting that the SONG and K2 data are non-simultaneous, we estimate the amplitude ratio between intensity and radial velocity to be 42.2±2.3 ppm m−1 s, which is higher than expected from scaling relations.

Context . We present the first high-cadence multiwavelength radial-velocity observations of the Sun-as-a-star, carried out during 57 consecutive days using the stellar échelle spectrograph at the Hertzsprung SONG Telescope operating at the Teide Observatory. Aims . Our aim was to produce a high-quality data set and reference values for the global helioseismic parameters ν max, ⊙ and Δ ν ⊙ of the solar p -modes using the SONG instrument. The obtained data set or the inferred values should then be used when the scaling relations are applied to other stars showing solar-like oscillations observed with SONG or similar instruments. Methods . We used different approaches to analyse the power spectrum of the time series to determine ν max, ⊙ : simple Gaussian fitting and heavy smoothing of the power spectrum. We determined Δ ν ⊙ using the method of autocorrelation of the power spectrum. The amplitude per radial mode was determined using the method described in Kjeldsen et al. (2008, ApJ, 682, 1370). Results . We found the following values for the solar oscillations using the SONG spectrograph: ν max, ⊙ = 3141 ± 12 μ Hz, Δ ν ⊙ = 134.98 ± 0.04 μ Hz, and an average amplitude of the strongest radial modes of 16.6 ± 0.4 cm s −1 . These values are consistent with previous measurements with other techniques.

Asteroseismic analysis of solar-like stars allows us to determine physical parameters such as stellar mass, with a higher precision compared to most other methods. Even in a well-studied cluster such as the Hyades, the masses of the red giant stars are not well known, and previous mass estimates are based on model calculations (isochrones). The four known red giants in the Hyades are assumed to be clump (core-helium-burning) stars based on their positions in colour-magnitude diagrams, however asteroseismology offers an opportunity to test this assumption. Using asteroseismic techniques combined with other methods, we aim to derive physical parameters and the evolutionary stage for the planet hosting star epsilon Tau, which is one of the four red giants located in the Hyades. We analysed time-series data from both ground and space to perform the asteroseismic analysis. By combining high signal-to-noise (S/N) radial-velocity data from the ground-based SONG network with continuous space-based data from the revised Kepler mission K2, we derive and characterize 27 individual oscillation modes for epsilon Tau, along with global oscillation parameters such as the large frequency separation and the ratio between the amplitude of the oscillations measured in radial velocity and intensity as a function of frequency. The latter has been measured previously for only two stars, the Sun and Procyon. Combining the seismic analysis with interferometric and spectroscopic measurements, we derive physical parameters for epsilon Tau, and discuss its evolutionary status.

We aim to establish and improve the accuracy level of asteroseismic estimates of mass, radius, and age of giant stars. This can be achieved by measuring independent, accurate, and precise masses, radii, effective temperatures and metallicities of long period eclipsing binary stars with a red giant component that displays solar-like oscillations. We measured precise properties of the three eclipsing binary systems KIC 7037405, KIC 9540226, and KIC 9970396 and estimated their ages be 5.3 +/- 0.5, 3.1 +/- 0.6, and 4.8 +/- 0.5 Gyr. The measurements of the giant stars were compared to corresponding measurements of mass, radius, and age using asteroseismic scaling relations and grid modelling. We found that asteroseismic scaling relations without corrections to Ay systematically overestimate the masses of the three red giants by 11.7 per cent, 13.7 per cent, and 18.9 per cent, respectively. However, by applying theoretical correction factors f Delta nu according to Rodrigues et al. (2017), we reached general agreement between dynamical and asteroseismic mass estimates, and no indications of systematic differences at the precision level of the asteroseismic measurements. The larger sample investigated by Gaulme et al. (2016) showed a much more complicated situation, where some stars show agreement between the dynamical and corrected asteroseismic measures while others suggest significant overestimates of the asteroseismic measures. We found no simple explanation for this, but indications of several potential problems, some theoretical, others observational. Therefore, an extension of the present precision study to a larger sample of eclipsing systems is crucial for establishing and improving the accuracy of asteroseismology of giant stars.

The Stellar Observation Network Group (SONG) is an initiative to build a worldwide network of 1m telescopes with highprecision radial-velocity spectrographs. Here we analyse the first radial-velocity time series of a red-giant star measured by the SONG telescope at Tenerife. The asteroseismic results demonstrate a major increase in the achievable precision of the parameters for redgiant stars obtainable from ground-based observations. Reliable tests of the validity of these results are needed, however, before the accuracy of the parameters can be trusted. We analyse the first SONG time series for the star 46 LMi, which has a precise parallax and an angular diameter measured from interferometry, and therefore a good determination of the stellar radius. We use asteroseismic scaling relations to obtain an accurate mass, and modelling to determine the age. A 55-day time series of high-resolution, high S/N spectra were obtained with the first SONG telescope. We derive the asteroseismic parameters by analysing the power spectrum. To give a best guess on the large separation of modes in the power spectrum, we have applied a new method which uses the scaling of Kepler red-giant stars to 46 LMi. Several methods have been applied: classical estimates, seismic methods using the observed time series, and model calculations to derive the fundamental parameters of 46 LMi. Parameters determined using the different methods are consistent within the uncertainties. We find the following values for the mass M (scaling), radius R (classical), age (modelling), and surface gravity (combining mass and radius): M = 1.09 +- 0.04Msun, R = 7.95 +- 0.11 Rsun, age t = 8.2 +- 1.9Gy, and log g = 2.674 +- 0.013.

We determine the properties of the binary star V106 in the old open cluster NGC 6791. We identify the system to be a blue straggler cluster member by using a combination of ground-based and Kepler photometry and multi-epoch spectroscopy. The properties of the primary component are found to be M-p similar to 1.67 M-circle dot, more massive than the cluster turn-off, with R-p similar to 1.91 R-circle dot and T-eff = 7110 +/- 100 K. The secondary component is highly oversized and overluminous for its low mass with M-s similar to 0.182 M-circle dot, R-s similar to 0.864 R-circle dot, and T-eff = 6875 +/- 200 K. We identify this secondary star as a bloated (proto) extremely low-mass helium white dwarf. These properties of V106 suggest that it represents a typical Algol-paradox system and that it evolved through a mass-transfer phase, which provides insight into its past evolution. We present a detailed binary stellar evolution model for the formation of V106 using the MESA code and find that the mass-transfer phase only ceased about 40 Myr ago. Due to the short orbital period (P = 1.4463 d), another mass-transfer phase is unavoidable once the current primary star evolves towards the red giant phase. We argue that V106 will evolve through a common-envelope phase within the next 100 Myr and merge to become a single overmassive giant. The high mass will make it appear young for its true age, which is revealed by the cluster properties. Therefore, V106 is potentially a prototype progenitor of old field giants masquerading as young.

Using data from the NASA spacecraft Kepler, we study solar-like oscillations in red-giant stars in the open cluster NGC6811. We determine oscillation frequencies, frequency separations, period spacings of mixed modes and mode visibilities for eight cluster giants. The oscillation parameters show that these stars are helium-core-burning red giants. The eight stars form two groups with very different oscillation power spectra; the four stars with lowest Delta_nu-values display rich sets of mixed l=1 modes, while this is not the case for the four stars with higher Delta_nu. For the four stars with lowest Delta_nu, we determine the asymptotic period spacing of the mixed modes, DeltaP, which together with the masses we derive for all eight stars suggest that they belong to the so-called secondary clump. Based on the global oscillation parameters, we present initial theoretical stellar modeling which indicate that we can constrain convective-core overshoot on the main sequence and in the helium-burning phase for these ~2M_sun stars. Finally, our results indicate less mode suppression than predicted by recent theories for magnetic suppression of certain oscillation modes in red giants.