Circumstellar and Circumbinary Disks in Eccentric Stellar Binaries

We explore test particle orbits in the orbital plane of eccentric stellar binary systems, searching for ``invariant loops'': closed curves that change shape periodically as a function of binary orbital phase as the test particles in them move under the stars' gravity. Stable invariant loops play the same role in this periodically-varying potential as stable periodic orbits do in stationary potentials; in particular, when dissipation is weak, gas will most likely follow the non-intersecting loops, while nearby particle orbits librate around them. We use this method to set bounds on the sizes of disks around the stars, and on the gap between those and the inner edge of a possible circumbinary disk. Gas dynamics may impose further restrictions, but our study sets upper bounds for the size of circumstellar disks, and a lower bound for the inner radius of a circumbinary disk. We find that circumstellar disks are sharply reduced as the binary's eccentricity grows. Disks change in size and shape only marginally with the binary phase, with no strong preference to increase or decrease at any particular phase. The circumstellar disks in particular can be quite asymmetric. We compare our results with other numerical and theoretical results and with observations of the $\alpha$ Centauri and L1551 systems, finding very good agreement. The calculated changes in the shapes and crowding of the circumstellar orbits can be used to predict how the disk luminosity and mass inflow should vary with binary phase.