59,297 research outputs found

    The Structure of Close Binaries in Two Dimensions

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    The structure and evolution of close binary stars has been studied using the two-dimensional (2D) stellar structure algorithm developed by Deupree (1995). We have calculated a series of solar composition stellar evolution sequences of binary models, where the mass of the 2D model is 8Msun with a point-mass 5Msun companion. We have also studied the structure of the companion in 2D, by considering the zero-age main-sequence (ZAMS) structure of a 5Msun model with an 8Msun point-mass companion. In all cases the binary orbit was assumed to be circular and co-rotating with the rotation rate of the stars. We considered binary models with three different initial separations, a = 10, 14 and 20Rsun. These models were evolved through central hydrogen burning or until the more massive star expanded to fill its critical potential surface or Roche lobe. The calculations show that evolution of the deep interior quantities is only slightly modified from those of single star evolution. Describing the model surface as a Roche equipotential is also satisfactory until very close to the time of Roche lobe overflow, when the self gravity of the model about to lose mass develops a noticeable aspherical component and the surface time scale becomes sufficiently short that it is conceivable that the actual surface is not an equipotential.Comment: 22 pages, 10 figures, accepted by Ap

    Equipotential Surfaces and Lagrangian points in Non-synchronous, Eccentric Binary and Planetary Systems

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    We investigate the existence and properties of equipotential surfaces and Lagrangian points in non-synchronous, eccentric binary star and planetary systems under the assumption of quasi-static equilibrium. We adopt a binary potential that accounts for non-synchronous rotation and eccentric orbits, and calculate the positions of the Lagrangian points as functions of the mass ratio, the degree of asynchronism, the orbital eccentricity, and the position of the stars or planets in their relative orbit. We find that the geometry of the equipotential surfaces may facilitate non-conservative mass transfer in non-synchronous, eccentric binary star and planetary systems, especially if the component stars or planets are rotating super-synchronously at the periastron of their relative orbit. We also calculate the volume-equivalent radius of the Roche lobe as a function of the four parameters mentioned above. Contrary to common practice, we find that replacing the radius of a circular orbit in the fitting formula of Eggleton (1983) with the instantaneous distance between the components of eccentric binary or planetary systems does not always lead to a good approximation to the volume-equivalent radius of the Roche-lobe. We therefore provide generalized analytic fitting formulae for the volume-equivalent Roche lobe radius appropriate for non-synchronous, eccentric binary star and planetary systems. These formulae are accurate to better than 1% throughout the relevant 2-dimensional parameter space that covers a dynamic range of 16 and 6 orders of magnitude in the two dimensions.Comment: 12 pages, 10 figures, 2 Tables, Accepted by the Astrophysical Journa

    The Roche problem: some analytics

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    Some exact analytical formulas are derived for the potential and mass ratio as a function of Lagrangian points position, in the classical Roche model of the close binary stars.Comment: aastex, 4 pp. ApJ accepte

    Gravitational Wave Emission by Cataclysmic Variables: numerical models of semi-detached binaries

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    Gravitational wave emission is considered to be the driving force for the evolution of short-period cataclysmic binary stars, making them a potential test for the validity of General Relativity. In spite of continuous refinements of the physical description, a 10% mismatch exists between the theoretical minimum period (Pturn≃70P_{\rm turn} \simeq 70 min) and the short-period cut-off (Pmin≃80P_{\rm min} \simeq 80 min) observed in the period distribution for cataclysmic variable binaries. A possible explanation for this mismatch was associated with the use of the Roche model. We here present a systematic comparison between self-consistent, numerically constructed sequences of hydrostatic models of binary stars and Roche models of semi-detached binaries. On the basis of our approach, we also derive a value for the minimum period of cataclysmic variable binaries. The results obtained through the comparison indicate that the Roche model is indeed very good, with deviations from the numerical solution which are of a few percent at most. Our results therefore suggest that additional sources of angular momentum loss or alternative explanations need to be considered in order to justify the mismatch.Comment: 7pages, 4figures. To appear in MNRA