| Abstract |
In a previous work, 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 <= e <= 0.9 and mass
ratio 0.1 <= q <= 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 ed < 0.15, but if the
mass ratio is unequal the disc is offset from the centre 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. |