Evolution of binary stars and the effect of tides on binary populations

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

Carbon Rich Extremely Metal Poor Stars: Signatures of Population-III AGB stars in Binary Systems

We use the Cambridge stellar evolution code STARS to model the evolution and nucleosynthesis of zero-metallicity intermediate-mass stars. We investigate the effect of duplicity on the nucleosynthesis output of these systems and the potential abundances of the secondaries. The surfaces of zero-metallicity stars are enriched in CNO elements after second dredge up. During binary interaction, such as Roche lobe overflow or wind accretion, metals can be released from these stars and the secondaries enriched in CNO isotopes. We investigate the formation of the two most metal poor stars known, HE 0107-5240 and HE 1327-2326. The observed carbon and nitrogen abundances of HE 0107-5240 can be reproduced by accretion of material from the companion-enhanced wind of a seven solar star after second dredge-up, though oxygen and sodium are underproduced. We speculate that HE 1327-2326, which is richer in nitrogen and strontium, may similarly be formed by wind accretion in a later AGB phase after third dredge-up.Comment: 16 pages, 1 figure, 7 tables, accepted by MNRA

Investigation of the processes required for the automation of stitchmarking in shoe manufacture

This thesis describes a novel approach to the high speed automatic stitchmarking of shoe upper components by integrating an electrographic printer with a shape recognition system. A critical review of recognition system parameters selects the currently known shape parameters which are most suitable for use in a high speed recognition system with the large number of different shoe components found in a typical shoe factory. These are compared with the parameters actually used in the previously developed recognition system to be used for stitchmarking. A discussion of printing technologies suitable for marking shoe materials with computer generated patterns follows. It is concluded that an electrographic printer has the best combination of characteristics. There follows a description of experiments demonstrating xerography on shoe upper materials, and the design of a system integrating a low-cost laser printer to the recognition system which proved the concept of continuous automatic stitchmarking. With this performing satisfactorily, the system was converted to use a high speed printer requiring the use of an advanced graphics processor for handling the data transformations and interfacing with the printer. Modifications to the printer for operation with shoe materials are described, together with the need for a special toner. A full description of the resulting stitchmarking system is given, followed by details of analyses of its performance. Individual chapters are devoted to the accuracy, recognition efficiency, and the timing of the system. A potential bottleneck in determining the orientation of certain difficult shapes is identified, and faster methods for dealing with these are specially investigated. This concludes that the best approach is to optimise the present method and accelerate the calculations by using a more advanced microprocessor. A discussion of the general running of the machine includes details of problems which occurred with the modified printer mechanism and how these were overcome. Finally, suggestions are made for incorporation in an improved system capable of handling larger shapes with a tenfold speed increase

A Complete N-body Model of the Old Open Cluster M67

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 12000 single stars and 12000 binaries 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 by 90% 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 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 is lost, both from the current luminosity function and from the current mass fraction in white dwarfs. The model contains 20 blue stragglers 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 blue stragglers in M67.Comment: 32 pages, 17 figures, submitted to MNRA

Direct N-body Modelling of Stellar Populations: Blue Stragglers in M67

We present a state-of-the-art N-body code which includes a detailed treatment of stellar and binary evolution as well as the cluster dynamics. This code is ideal for investigating all aspects relating to the evolution of star clusters and their stellar populations. It is applicable to open and globular clusters of any age. We use the N-body code to model the blue straggler population of the old open cluster M67. Preliminary calculations with our binary population synthesis code show that binary evolution alone cannot explain the observed numbers or properties of the blue stragglers. On the other hand, our N-body model of M67 generates the required number of blue stragglers and provides formation paths for all the various types found in M67. This demonstrates the effectiveness of the cluster environment in modifying the nature of the stars it contains and highlights the importance of combining dynamics with stellar evolution. We also perform a series of N = 10000 simulations in order to quantify the rate of escape of stars from a cluster subject to the Galactic tidal field.Comment: 26 pages, 18 figures, accepted for publication in MNRA

Approximate input physics for stellar modelling

We present a simple and efficient, 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 briefly discuss a few results obtained with the updated stellar evolution code.Comment: uuencoded compressed postscript. The preprint are also available at http://www.ast.cam.ac.uk/preprint/PrePrint.htm

The C-flash and the ignition conditions of type Ia supernovae

Thanks to a stellar evolution code able to compute through the C-flash we link the binary population synthesis of single degenerate progenitors of type Ia supernovae (SNe Ia) to their physical condition at the time of ignition. We show that there is a large range of possible ignition densities and we detail how their probability distribution depends on the accretion properties. The low density peak of this distribution qualitatively reminds of the clustering of the luminosities of Branch-normal SNe Ia. We tighten the possible range of initial physical conditions for explosion models: they form a one-parameter family, independent of the metallicity. We discuss how these results may be modified if we were to relax our hypothesis of a permanent Hachisu wind or if we were to include electron captures.Comment: 10 pages, 14 figures, MNRAS accepte

Opaque or transparent? A link between neutrino optical depths and the characteristic duration of short gamma-ray bursts

Cosmological gamma ray bursts (GRBs) are thought to occur from violent hypercritical accretion onto stellar mass black holes, either following core collapse in massive stars or compact binary mergers. This dichotomy may be reflected in the two classes of bursts having different durations. Dynamical calculations of the evolution of these systems are essential if one is to establish characteristic, relevant timescales. We show here for the first time the result of dynamical simulations, lasting approximately one second, of post--merger accretion disks around black holes, using a realistic equation of state and considering neutrino emission processes. We find that the inclusion of neutrino optical depth effects produces important qualitative temporal and spatial transitions in the evolution and structure of the disk, which may directly reflect upon the duration and variability of short GRBs.Comment: Accepted for publication in ApJ Letter