Context. Models of stellar structure and evolution can be constrained by measuring accurate parameters of detached eclipsing binaries in open clusters. Multiple binary stars provide the means to determine helium abundances in these old stellar systems, and in turn, to improve estimates of their age. Aims. In the first paper of this series, we demonstrated how measurements of multiple eclipsing binaries in the old open cluster NGC 6791 sets tighter constraints on the properties of stellar models than has previously been possible, thereby potentially improving both the accuracy and precision of the cluster age. Here we add additional constraints and perform an extensive model comparison to determine the best estimates of the cluster age and helium content, employing as many observational constraints as possible. Methods. We improve our photometry and correct empirically for differential reddening effects. We then perform an extensive comparison of the new colour-magnitude diagrams (CMDs) and eclipsing binary measurements to Victoria and DSEP isochrones in order to estimate cluster parameters. We also reanalyse a spectrum of the star 2-17 to improve [Fe/H] constraints. Results. We find a best estimate of the age of ∼8.3 Gyr for NGC 6791 while demonstrating that remaining age uncertainty is dominated by uncertainties in the CNO abundances. The helium mass fraction is well constrained at Y = 0.30 ± 0.01 resulting in ΔY/ΔZ ∼ 1.4 assuming that such a relation exists. During the analysis we firmly identify blue straggler stars, including the star 2-17, and find indications for the presence of their evolved counterparts. Our analysis supports the RGB mass-loss found from asteroseismology and we determine precisely the absolute mass of stars on the lower RGB, M RGB = 1.15 ± 0.02 M . This will be an important consistency check for the detailed asteroseismology of cluster stars. Conclusions. Using multiple, detached eclipsing binaries for determining stellar cluster ages, it is now possible to constrain parameters of stellar models, notably the helium content, which were previously out of reach. By observing a suitable number of detached eclipsing binaries in several open clusters, it will be possible to calibrate the age-scale and the helium enrichment parameter Δ Y/Δ Z, and provide firm constraints that stellar models must reproduce.

Asteroseismic constraints on K giants make it possible to infer radii, masses and ages of tens of thousands of field stars. Tests against independent estimates of these properties are however scarce, especially in the metal-poor regime. Here, we report the detection of solar-like oscillations in 8 stars belonging to the red-giant branch and red-horizontal branch of the globular cluster M4. The detections were made in photometric observations from the K2 Mission during its Campaign 2. Making use of independent constraints on the distance, we estimate masses of the 8 stars by utilising different combinations of seismic and non-seismic inputs. When introducing a correction to the ∆ν scaling relation as suggested by stellar models, for RGB stars we find excellent agreement with the expected masses from isochrone fitting, and with a distance modulus derived using independent methods. The offset with respect to independent masses is lower, or comparable with, the uncertainties on the average RGB mass (4 − 10%, depending on the combination of constraints used). Our results lend confidence to asteroseismic masses in the metal poor regime. We note that a larger sample will be needed to allow more stringent tests to be made of systematic uncertainties in all the observables (both seismic and non-seismic), and to explore the properties of RHB stars, and of different populations in the cluster.

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 solarlike 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 modeling. We found that asteroseismic scaling relations without corrections to ∆ν systematically overestimate the masses of the three red giants by 11.7%, 13.7%, and 18.9%, respectively. However, by applying theoretical correction factors f ∆ν 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.

We confirm the Kepler planet candidate Kepler-410b (KOI-42b) as a Neptune sized exoplanet on a 17.8 day, eccentric orbit around the bright (K p = 9.4) star Kepler-410A. This is the third brightest confirmed planet host star in the Kepler field and one of the brightest hosts of all currently known transiting exoplanets. Kepler-410 consists of a blend between the fast rotating planet host star (Kepler-410A) and a fainter star (Kepler-410B), which has complicated the confirmation of the planetary candidate. Employing asteroseismology, using constraints from the transit light curve, adaptive optics and speckle images, and Spitzer transit observations, we demonstrate that the candidate can only be an exoplanet orbiting Kepler-410A. Via asteroseismology we determine the following stellar and planetary parameters with high precision; M = 1.214±0.033 M , R = 1.352±0.010 R , Age = 2.76±0.54 Gyr, planetary radius (2.838±0.054 R ⊕ ), and orbital eccentricity (0.17 +0.07 −0.06 ). In addition, rotational splitting of the pulsation modes allows for a measurement of Kepler-410A's inclination and rotation rate. Our measurement of an inclination of 82.5 +7.5 −2.5 [ • ] indicates a low obliquity in this system. Transit timing variations indicate the presence of at least one additional (non-transiting) planet in the system.

About 1% of giant stars have been shown to have large surface Li abundances, which is unexpected according to standard stellar evolution models. Several scenarios for lithium production have been proposed, but it is still unclear why these Li-rich giants exist. A missing piece in this puzzle is the knowledge of the exact stage of evolution of these stars. Using low-and-high-resolution spectroscopic observations, we have undertaken a survey of lithium-rich giants in the Kepler field. In this letter, we report the finding of the first confirmed Li-rich corehelium-burning giant, as revealed by asteroseismic analysis. The evolutionary timescales constrained by its mass suggest that Li-production most likely took place through non-canonical mixing at the RGB-tip, possibly during the helium flash.