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 semilatus 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 semilatera recta rather than periods or semimajor axes.

https://researchbank.swinburne.edu.au/file/ab4c7d3f-f3a0-4cb3-bb4f-9790d3f33b19/1/PDF (Accepted manuscript).pdf

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

Aims The complex physics of close binary stars is made even more challenging by the proximity effects that affect it Understanding the influence of these proximity effects is one of the most important tasks in theoretical stellar astrophysics It is crucial to know how the specific intensity is distributed over the stellar disk for a correct modelling of the light curves of eclipsing binaries and planetary transits To provide theoretical input for light curve modelling codes, we present new calculations of gravity- and limb-darkening coefficients for a wide range of effective temperatures, gravities, metallicities, and microturbulent velocities Methods We computed limb-darkening coefficients for several atmosphere models, which cover the transmission curves of the Kepler , CoRoT, and Spitzer space missions as well as more widely used passbands (Stromgren, Johnson-Cousins, Sloan) In addition to these computations, which were made adopting the least-square method, we also performed calculations for the bi-parametric approximations by adopting the flux conservation method to provide users with an additional tool to estimate the theoretical error bars To facilitate the modelling of the effects of tidal and rotational distortions, we computed the gravity-darkening coefficients y (λ ) using the same models of stellar atmospheres as for the limb-darkening Compared to previous work, a more general differential equation was used, which now takes into account local gravity variations and the effects of convection Results The limb-darkening coefficients were computed with a higher numerical resolution (100 μ points instead of 15 or 17, as is often used in the ATLAS models), and five equations were used to describe the specific intensities (linear, quadratic, root-square, logarithmic, and a 4-coefficient law) Concerning the gravity-darkening coefficients, the influence of the local gravity on y (λ ) is shown as well as the effects of convection, which turn out to be very significant for cool stars The results are tabulated for log g ′s ranging from 00 to 50, –50  ≤  log [M/H]  ≤  +1, 2000 K  ≤  T eff  ≤  50 000 K and for five values of the microturbulent velocity ATLAS and PHOENIX plane-parallel atmosphere models were used for all computations

/pdf/gravity-and-limb-darkening-coefficients-for-the-kepler-corot-5ft0zb8466.pdf

Gravity and limb-darkening coefficients for the Kepler, CoRoT, Spitzer, uvby, UBVRIJHK, and Sloan photometric systems

Formation and evolution of binary and millisecond radio pulsars

Neutron star observations: Prognosis for equation of state constraints

The structure and evolution of the stars constitute one of the main prob­ lems of modern astrophysics. Binary stars are so common that it is not pos­ sible to develop a comprehensive theory of stellar structure and evolution without taking into account the duplicity of so many objects. According to }aschek & Gomez (1970) 50% o f the main-sequence stars are binaries. Van Albada & Blaauw (1967) estimated that 60% of the early-type stars are double with mass ratio larger than 0.2. Some types of objects are found in binary systems only: metallic-line stars (Abt 1961, 1965, Abt & Bidelman 1969), U Germinorum variables and novae (Kraft 1962, 1963, 1964), a large fraction of Wolf-Rayet stars (Underhill 1968). Hoyle (1964) and McCrea (1964) suggested that "blue stragglers" in open and globular clusters are the products of mass exchange in close binaries. This idea found some observa­ tional support in the case of open clusters (Cannon 1968, Deutch 1969, Strom & Strom 1970). Blaauw (1961) suggested that the early-type "run­ away" stars had escaped from close binaries disrupted as a result of a super­ nova explosion of another component. Binaries are considered to be possible candidates for X-ray sources (Shklovsky 1967, Cameron & Mock 1967, Prendergast & Burbidge 1968). The general evolution of Population I objects is strongly affected by the commonness of binaries within this population. It should be emphasized that duplicity is not found among the Population II stars . I t is also remarkable that none of the 50 known pulsars is in a binary. The most fundamental physical parameter of a star , its mass, may be reliably measured for components of binary systems only. Eclipsing variables allow us to study in some detail the surface of their components. Distribution of mass in a stellar envelope affects the orbital motion and leads to apsidal motion. This phenomenon makes it possible to check the structure of stellar models. It is generally accepted now that mass transfer in a binary from one component to another is the most basic phenomenon in the evolution of such a system. Therefore matteJ1 with a chemical composition modified by nuclear reactions may be expected to be lifted up to the stellar surface. The two out­ standing examples are the binaries HD 30353 and v Sgr (Wallerstein 1968), deficient in hydrogen and overabundant in nitrogen. The matter that is visi-

Evolutionary Processes in Close Binary Systems

Close binary systems

I. Binary Stars in the Sky.- 1. Binary-Star Population in our Galaxy.- Bibliographical Notes.- II. Figures of Equilibrium.- 1. Equipotential Surfaces.- 2. Rotational Distortion.- 3. Tidal Distortion.- 4. Interaction between Rotation and Tides.- 5. Effects of Internal Structure.- 6. Gravity, Density Distribution, and Moments of Inertia.- Bibliographical Notes.- III. Dynamical Tides.- 1. Equations of the Problem.- A. Dissipative Systems.- B. Radiating Systems.- 2. Linearized Equations.- A. Viscous Spheroidal Deformations.- B. Boundary Conditions.- C. Homogeneous Model.- 3. Forced Oscillations: Dynamical Tides.- A. Mass-Point Model.- B. Centrally-Condensed Model.- C. Disturbing Potential.- 4. Dissipation of Energy by Dynamical Tides.- A. Viscous Friction.- B. Application to Binary Systems.- Bibliographical Notes.- IV. Generalized Rotation.- 1. Equations of Motion for Deformable Bodies.- A. Eulerian Equations.- 2. Rotation of Deformable Bodies.- A. Effects of Deformation.- B. Moments and Products of Inertia.- C. Coefficients of Deformation.- 3. Effects of Viscosity.- A. Equations of the Problem.- B. Tidal Friction: Spherical Configurations.- C. Tidal Friction: Spheroidal Configurations.- D. Dissipation of Energy by Tidal Friction.- 4. Nonuniform Rotation.- A. Steady-State Rotation Gravity-Darkening.- B. Non-Steady Rotation.- Bibliographical Notes.- V. Dynamics of Close Binaries.- 1. Equations of the Problem.- A. Perturbation Equations.- B. Evaluation of the Coefficients Tidal Lag.- 2. Perturbations of the Orbital Plane Precession and Nutation.- A. Effects of Viscosity.- B. Linearized Case.- C. Secular and Long-Periodic Motion.- D. Solution of Equations.- 3. Perturbations in the Orbital Plane.- A. Secular Perturbations: Rotational Distortion.- B. Secular Perturbations: Tidal Distortion.- C. Apsidal Motions: Comparison with Observations.- 4. Period Changes in Eclipsing Binary Systems.- A. Generalized Law of Areas.- B. Orbital Period: a Definition.- C. Relation between Orbital Period and Times of the Minima.- 5. Effects of Variable Mass.- A. Generalized Equations of Motion.- B. Isotropic Mass Loss.- C. Non-Isotropic Mass Loss.- 6. Perturbations by a Third Body.- A. Equations of the Problem.- B. Short-Range Perturbations.- C. Long-Range Perturbations.- D. Effects of the Light Equation.- Bibliographical Notes.- VI. The Roche Model.- 1. Roche Equipotentials.- A. Surfaces of Zero Velocity.- 2. Geometry of Roche Surfaces.- A. Radius and Volume.- B. Roche Limit.- C. Geometry of the Eclipses.- D. External Envelopes.- 3. The Roche Coordinates.- A. Rotational Problem.- B. Tidal Problem.- C. Double-Star Problem.- Bibliographical Notes.- VII. Stability of the Components of Close Binary Systems.- 1. Criteria of Stability.- 2. Secular Stability.- A. Rotational Problem.- B. Double-Star Problem.- 3. Dynamical Stability.- A. Vibrations of the Roche Model.- 4. Concluding Remarks.- Bibliographical Notes.- VIII. Origin and Evolution of Binary Systems.- 1. Evolution of the Stars.- 2. Classification of Close Binary Systems.- A. Characteristic Parameters.- 3. Nuclear Evolution of Close Binary Systems.- A. Detached Systems.- B. Semi-Detached Systems.- C. Contact Systems.- 4. Tidal Evolution of Close Binary Systems.- A. Energy and Momentum.- B. Evolution with Constant Momentum.- C. Comparison with Observations.- D. Tidal Evolution.- 5. Beginnings and Ends.- A. Origin of Close Binaries.- B. Terminal Stages: Subdwarf Binaries.- C. X-Ray Binaries and Black Holes.- Bibliographical Notes.- References.- Index of Names.- Index of Subjects.

Zdeněk Kopal

Papers

Close binary systems

Dynamics of Close Binary Systems

Physics and astronomy of the moon

The Measure of the Moon

Language of the stars