Parametric study of polar configurations around binaries

Dynamical studies suggest that most of the circumbinary discs (CBDs) should be coplanar. However, under certain initial conditions, the CBD can evolve toward polar orientation. Here we extend the parametric study of polar configurations around detached close-in binaries through $N$-body simulations. For polar configurations around binaries with mass ratios $q$ below $0.7$, the nominal location of the mean motion resonance (MMR) $1~:~4$ predicts the limit of stability for $e_{B} > 0.1$. Alternatively, for $e_{B} < 0.1$ or $q \sim 1$, the nominal location of the MMR $1~:~3$ is the closest stable region. The presence of a} giant planet increases the region of forbidden polar configurations around low mass ratio binaries with eccentricities $e_B\sim0.4$ with respect to rocky earth-like planets. For equal mass stars, the eccentricity excitation $\Delta e$ of polar orbits smoothly increases with decreasing distance to the binary. For $q<1$, $\Delta e$ can reach values as high as $0.4$. Finally, we studied polar configurations around $HD~98800BaBb$ and show that the region of stability is strongly affected by the relative positions of the nodes. The most stable configurations in the system correspond to polar particles, which are not expected to survive on longer time-scales due to the presence of the external perturber HD~$98800AaAb$.