Circumstellar and circumbinary discs 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 gravity of the stars. 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 discs around the stars, and on the gap between those and the inner edge of a possible circumbinary disc. Gas dynamics may impose further restrictions, but our study sets upper bounds for the size of circumstellar discs, and a lower bound for the inner radius of a circumbinary disc. We find that circumstellar discs are sharply reduced as the eccentricity of the binary grows. For the disc around the secondary star, the tidal (Jacobi) radius calculated for circular orbits at the periastron radius gives a good estimate of the maximum size. Discs 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 discs 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 disc luminosity and mass inflow should vary with binary phase.