Astrophysics, abstract
astro-ph/0612508

From: Jeremy Sepinsky [view email]

Date: Mon, 18 Dec 2006 21:09:31 GMT (165kb)

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

Authors: J. F. Sepinsky, B. Willems, V. Kalogera

Comments: 12 pages, 10 figures, 2 Tables, Submitted to the Astrophysical Journal

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 a generalized semi-analytical fitting formula for the volume-equivalent Roche lobe radius appropriate for non-synchronous, eccentric binary star and planetary systems.

http://arxiv.org/abs/astro-ph/0612508