  In a previous work (Pichardo et al. 2005), we studied stable configurations
for circumstellar discs in eccentric binary systems. We searched for "invariant
loops": closed curves (analogous to stable periodic orbits in time-independent
potentials) that change shape with the binary orbital phase, as test particles
in them move under the influence of the binary potential. This approach allows
us to identify stable configurations when pressure forces are unimportant, and
dissipation acts only to prevent gas clouds from colliding with one another. We
now extend this work to study the main geometrical properties of circumbinary
discs. We have studied more than 100 cases with a range in eccentricity 0 .le.
e .le. 0.9, and mass ratio 0.1 .le. q .le. 0.9. Although gas dynamics may
impose further restrictions, our study sets lower stable bounds for the size of
the central hole in a simple and computationally cheap way, with a relation
that depends on the eccentricity and mass ratio of the central binary. We
extend our previous studies and focus on an important component of these
systems: circumbinary discs. The radii for stable orbits that can host gas in
circumbinary discs are sharply constrained as a function of the binary's
eccentricity. The circumbinary disc configurations are almost circular, with
eccentricity e_d < 0.15, but if the mass ratio is unequal the disk is offset
from the center of mass of the system. We compare our results with other
models, and with observations of specific systems like GG Tauri A, UY Aurigae,
HD 98800 B, and Fomalhaut, restricting the plausible parameters for the binary.

Astrophysics