We present a rapid binary evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single star evolution, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks and angular momentum loss mechanisms are included. In particular, circularization and synchronization of the orbit by tidal interactions are calculated for convective, radiative and degenerate damping mechanisms. We use this algorithm to study the formation and evolution of various binary systems. We also investigate the effect that tidal friction has on the outcome of binary evolution. Using the rapid binary code, we generate a series of large binary populations and evaluate the formation rate of interesting individual species and events. By comparing the results for populations with and without tidal friction we quantify the hitherto ignored systematic effect of tides and show that modelling of tidal evolution in binary systems is necessary in order to draw accurate conclusions from population synthesis work. Tidal synchronism is important but because orbits generally circularize before Roche-lobe overflow the outcome of the interactions of systems with the same semi-latus rectum is almost independent of eccentricity. It is not necessary to include a distribution of eccentricities in population synthesis of interacting binaries, however, the initial separations should be distributed according to the observed distribution of semi-latera recta rather than periods or semi-major axes.Comment: 36 pages, 12 figures, to be published in the Monthly Notices of the Royal Astronomical Societ

A B S T R A C TWe present analytic formulae that approximate the evolution of stars for a wide range of mass M and metallicity Z. Stellar luminosity, radius and core mass are given as a function of age, M and Z, for all phases from the zero-age main sequence up to, and including, the remnant stages. For the most part we find continuous formulae accurate to within 5 per cent of detailed models. These formulae are useful for purposes such as population synthesis that require very rapid but accurate evaluation of stellar properties, and in particular for use in combination with N-body codes. We describe a mass-loss prescription that can be used with these formulae, and investigate the resulting stellar remnant distribution.

To compare the chemistries of stars in the Milky Way dwarf spheroidal satellite galaxies (dSph) with stars in the Galaxy, we have compiled a large sample of Galactic stellar abundances from the literature. When kinematic information is available, we have assigned the stars to standard Galactic components through Bayesian classification based on Gaussian velocity ellipsoids. As found in previous studies, the [α/Fe] ratios 1 This work was completed while visiting the Institute

We have calculated a grid of empirically well tested evolutionary tracks with masses M between 0.5 and 50 M⊙, spaced by approximately 0.1 in log M, and with metallicities Z = 0.0001, 0.0003, 0.001, 0.004, 0.01, 0.02 and 0.03. We use a robust and fast evolution code with a self‐adaptive non‐Lagrangian mesh, which employs the mixing‐length theory but treats convective mixing as a diffusion process, solving simultaneously for the structure and the chemical composition. The hydrogen and helium abundances are chosen as functions of the metallicity: X = 0.76 − 3.0ZY = 0.24 + 2.0Z.  Two sets of models were computed, one without and one with a certain amount of enhanced mixing or ‘overshooting’. This amount has been empirically chosen by means of various sensitive tests for overshooting: (1) the luminosity of core helium burning (blue loop) giants of well‐known mass, (2) the width of the main sequence as defined by double‐lined eclipsing binaries with well‐measured masses and radii, and (3) the shape and implied stellar distribution of isochrones of various open clusters. The first two tests have been the subject of previous papers, the third test is discussed in this paper. On the basis of these tests, we recommend the use of the overshooting models for masses above about 1.5M ⊙.  We describe here the characteristics of the models, the procedure for constructing isochrones for arbitrary age and metallicity from the models, and the performance of these isochrones for several intermediate‐age and old open clusters. All original models are available in electronic form and we describe the means by which they may be obtained.

We compare our latest single and binary stellar model results from the Cambridge stars code to several sets of observations. We examine four stellar population ratios: the number of blue to red supergiants, the number of Wolf–Rayet stars to O supergiants, the number of red supergiants to Wolf–Rayet stars and the relative number of Wolf–Rayet subtypes, WC to WN stars. These four ratios provide a quantitative measure of nuclear burning lifetimes and the importance of mass loss during various stages of the stars' lifetimes. In addition, we compare our models to the relative rate of Type Ib/c to Type II supernovae to measure the amount of mass lost over the entire lives of all stars. We find reasonable agreement between the observationally inferred values and our predicted values by mixing single and binary star populations. However, there is evidence that extra mass loss is required to improve the agreement further, to reduce the number of red supergiants and increase the number of Wolf–Rayet stars.

We present a simple and e cient, yet reasonably accurate, equation of state, which at the moderately low temperatures and high densities found in the interiors of stars less massive than the Sun is substantially more accurate than its predecessor by Eggleton, Faulkner & Flannery. Along with the most recently available values in tabular form of opacities, neutrino loss rates, and nuclear reaction rates for a selection of the most important reactions, this provides a convenient package of input physics for stellar modelling. We brie y discuss a few results obtained with the updated stellar evolution code.

The old open cluster M67 is an ideal testbed for current cluster evolution models because of its dynamically evolved structure and rich stellar populations that show clear signs of interaction between stellar, binary and cluster evolution. Here, we present the first truly direct N‐body model for M67, evolved from zero age to 4 Gyr taking full account of cluster dynamics as well as stellar and binary evolution. Our preferred model starts with 36 000 stars (12 000 single stars and 12 000 binaries) and a total mass of nearly 19 000 M⊙, placed in a Galactic tidal field at 8.0 kpc from the Galactic Centre. Our choices for the initial conditions and for the primordial binary population are explained in detail. At 4 Gyr, the age of M67, the total mass has reduced to 2000 M⊙ as a result of mass loss and stellar escapes. The mass and half‐mass radius of luminous stars in the cluster are a good match to observations, although the model is more centrally concentrated than observations indicate. The stellar mass and luminosity functions (LFs) are significantly flattened by preferential escape of low‐mass stars. We find that M67 is dynamically old enough that information about the initial mass function (IMF) is lost, both from the current LF and from the current mass fraction in white dwarfs (WDs). The model contains 20 blue stragglers (BSs) at 4 Gyr, which is slightly less than the 28 observed in M67. Nine are in binaries. The blue stragglers were formed by a variety of means and we find formation paths for the whole variety observed in M67. Both the primordial binary population and the dynamical cluster environment play an essential role in shaping the population. A substantial population of short‐period primordial binaries (with periods less than a few days) is needed to explain the observed number of BSs in M67. The evolution and properties of two‐thirds of the BSs, including all found in binaries, have been altered by cluster dynamics and nearly half would not have formed at all outside the cluster environment. On the other hand, the cluster environment is also instrumental in destroying potential BSs from the primordial binary population, so that the total number is in fact slightly smaller than what would be expected from evolving the same binary stars in isolation.

We present maps of the nature of single star progenitors of supernovae and their remnants in mass and metallicity space. We find our results are similar to others but we have gone further in varying the amount of mixing and using various mass-loss schemes to see how the maps change. We find that extra mixing, in the form of convective overshooting, moves boundaries such as the minimum mass for a supernova or Wolf-Rayet (WR) star to lower masses. We also find that the pre-WR mass loss determines the shape of our maps. We find that different mass-loss rates lead to quite different results. We find that the rise in luminosity at second dredge-up places quite tight constraints on the masses of some progenitors and in particular the progenitor of supernova 2003gd.