2006/12/31 by J. F. Sepinsky, B. Willems, V. Kalogera · 1 citation
Mathematics · Physics and Astronomy · #Astro and Planetary Science #Astrophysics #Astrophysics and Star Formation Studies #Binary number #Binary star #Classical mechanics #Eccentricity (behavior) #Equipotential #Equipotential surface #Geometry #Lagrangian point #Mathematics #Orbit (dynamics) #Orbital eccentricity #Physics #RADIUS #Roche lobe #Stars #Stellar, planetary, and galactic studies #astro-ph
paper · pdf · doi:10.1086/513736
published as Astrophys.J.660:1624-1635,2007 · 12 pages, 10 figures, 2 Tables, Accepted by the Astrophysical Journal
arxiv created 2007/02/09 · openalex publication_date 2007/05/04 · arxiv updated 2011/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the existence and properties of equipotential surfaces and Lagrangian points in nonsynchronous, eccentric binary star and planetary systems under the assumption of quasi-static equilibrium. We adopt a binary potential that accounts for nonsynchronous 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 nonconservative mass transfer in nonsynchronous, eccentric binary star and planetary systems, especially if the component stars or planets are rotating supersynchronously 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 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 nonsynchronous, eccentric binary star and planetary systems. These formulae are accurate to better than 1% throughout the relevant two-dimensional parameter space that covers a dynamic range of 16 and 6 orders of magnitude in the two dimensions.