# Parametric study of polar configurations around binaries

## TL;DR

This study investigates the stability and dynamics of polar circumbinary disks around binary stars using N-body simulations, revealing how resonance locations, planetary presence, and system specifics influence stability.

## Contribution

It extends parametric analysis of polar configurations around binaries, identifying stability limits related to mass ratio, eccentricity, and resonance locations, with application to real systems.

## Key findings

- Stability limits depend on mass ratio and eccentricity.
- Giant planets affect the stability regions of polar orbits.
- Polar configurations around HD 98800BaBb are influenced by nodal positions.

## Abstract

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~$98800AaAb$.