| Abstract |
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 α
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. |