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 binarys 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.
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