59,297 research outputs found

### The Structure of Close Binaries in Two Dimensions

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

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

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

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 ($P_{\rm turn} \simeq 70$ min) and the short-period cut-off
($P_{\rm min} \simeq 80$ 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

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