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.

The evolution of binary systems consisting of an asymptotic giant branch star of mass equal to 3M ⊙ or 5M ⊙ , and a main sequence star of mass equal to 0.4M ⊙ or 0.6M ⊙ with orbital periods ∼ > 200 days has been followed from the onset through the late stages of the common envelope phase. Using a nested grid technique, the three-dimensional hydrodynamical simulations of an asymptotic giant branch star with radii ∼ 1 A.U. indicate that a significant fraction of the envelope gas is unbound (∼ 31% and 23% for binaries of 3M ⊙ and 0.4M ⊙ , and 5M ⊙ and 0.6M ⊙ respectively) by the ends of the simulations, and that the efficiency of the mass ejection process ∼ 40%. During an intermediate phase, a differentially rotating structure resembling a thick disk surrounds the remnant binary briefly before energy input from the orbits of the companion and remnant core drive the mass away. While the original volume of the giant is virtually evacuated in the late stages, most of the envelope gas remains marginally bound on the grid. At the ends of our simulations, when the orbital decay timescale exceeds about 5 years, the giant core and companion orbit one another with a period of ∼ 1 day (2.4 days for a binary involving a more evolved giant), although this is an upper limit to the final orbital period. For a binary of 5M ⊙ and 0.4M ⊙ , the common envelope may not be completely ejected. The results are not found to be sensitive to the degree to which the initial binary system departs from the synchronous state.

▪ Abstract  The common envelope phase of binary star evolution plays an essential role in the formation of short period systems containing a compact object. In this process, significant mass and angular momentum are lost, transforming a wide progenitor system into a close remnant binary. The pathways leading to this phase and the outcomes are described. Emphasis is placed on the conditions that are required for survival of the binary according to the results of three-dimensional hydrodynamics calculations. The evolution of high-mass systems containing neutron stars is discussed, including double neutron stars, binary pulsars, Thorne-Zytkow objects, and high- and low-mass X-ray binaries.

We present new BV I photometry for the halo globular cluster M5 (NGC 5904 = C1516+022), and examine the B-and I-band luminosity functions (LFs), based on over 20,000 stars -one of the largest samples ever gathered for a cluster luminosity function. Extensive artificial star tests have been conducted to quantify incompleteness as a function of magnitude and cluster radius. We do not see evidence in the LF of a "subgiant excess" or of a discrepancy in the relative numbers of stars on the red-giant branch and main sequence, both of which have been claimed in more metal-poor clusters.Enhancements of α-element have been taken into account in our analysis. This improves the agreement between the observed and predicted positions of the "red-giant bump". Depending on the average α-element enhancement among globular clusters and the distance calibration, the observed discrepancy between the theoretical and observed position for a large number of clusters ) can be almost completely removed.The helium abundance of M5, as determined by the population ratio R, is found to be Y = 0.19 ± 0.02. However, there is no other indication that the helium abundance is different from other clusters of similar metallicity, and values calculated for other helium indicators are consistent with Y ≈ 0.23.The relative ages of M5, Palomar 5, M4, NGC 288, NGC 362, NGC 1261, NGC 1851 and NGC 2808 are derived via the ∆V HB T O method using M5's horizontal branch (HB) as a bridge to compare clusters with very different HB morphology. We conclude that at the level of ∼ 1.5 Gyr these clusters of comparable metallicity are the same age with the possible exception of NGC 288 (older by 3.5 ± 1.5 if the reddest NGC 288 HB stars are on the zero-age horizontal branch) and Palomar 5 (which may be marginally younger). Even with NGC 288 set aside, there is a large range in HB morphology between the remaining clusters which appears to eliminate age as the sole second parameter determining HB morphology in the case of constant mass loss between RGB and HB (although a Reimers' mass-loss relation weakens this statement considerably).We are unable to chose between the two competing values for M5's (absolute) metallicity: [Fe/H] = −1.40 (Zinn & West 1984) and −1.17 (Sneden et al. 1992) based on recent high-dispersion spectroscopy. This level of discrepancy has a signifcant effect on the derivation of the distance modulus and absolute age of M5. From subdwarf fitting to the main sequence of the cluster, we find an apparent distance modulus (m − M ) V = 14.41 ± 0.07 for [Fe/H] M5 = −1.40, and 14.50 ± 0.07 if [Fe/H] M5 = −1.17. From comparisons with theoretical isochrones and luminosity functions, we find an absolute age for M5 of 13.5 ± 1 Gyr (internal error, assuming perfect models and no [M /H] error) for the Zinn & West abundance scale and 11 ± 1 Gyr for the higher abundance value.

We have calibrated and combined an extensive set of BVI observations of M67 to produce a colour–magnitude diagram of stars measured with high relative precision. We have selected stars that are most likely to be single‐star members of the cluster using proper motion, radial velocity, and variability information from the literature, and an examination of the most probable colour–magnitude diagram locations of unresolved stellar blends. We have made detailed comparisons of our photometry of the selected stars with theoretical models, and discuss the most notable discrepancies. Observations of M67 turn‐off stars are a severe test of algorithms attempting to describe convective cores in the limit of small extent, and we find strong evidence of a ‘hook’ just fainter than the turn‐off gap. The stars in M67 support assertions that the degree of convective core overshooting decreases to zero for stars with masses in the range 1.0 < (M/M⊙) ≤ 1.5, but that the degree of overshoot is smaller than currently used in published isochrones. We also verify that all current theoretical models for the lower main sequence (with the exception of Baraffe et al. 1998) are too blue for MV≳ 6, even when the sequences are shifted to match M67 near the MV of the Sun, probably due to a combination of problems with colour–Teff transformations and realistic surface boundary conditions for models. Finally, we identify a subset of cluster members with unusual photometry (candidate red giant binaries, blue straggler stars, and triple systems) deserving of further study.