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 \leq e \leq 0.9 , and mass ratio 0.1 \leq q \leq 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 .