# Planet formation and stability in polar circumbinary discs

## TL;DR

This study investigates the formation, alignment, and stability of polar circumbinary discs and planets, revealing a higher likelihood of polar configurations and their stability across various binary parameters, supported by hydrodynamical and N-body simulations.

## Contribution

It provides new insights into the symmetry breaking between prograde and retrograde configurations and demonstrates the stability of polar planets around eccentric binaries.

## Key findings

- Polar CBDs are more likely than previously thought due to symmetry breaking.
- Polar orbits of circumbinary planets are stable over a wide range of binary parameters.
- Planets with negligible mass have minimal impact on binary orbits.

## Abstract

Context. Dynamical studies suggest that most circumbinary discs (CBDs) should be coplanar. However, some theoretical works show that under certain conditions a CBD can become polar, which means that its rotation vector is orthogonal with respect to the binary orbital plane. Interestingly, very recent observations show that polar CBDs exist in nature (e.g. HD 98800). Aims. We test the predictions of CBD alignment around eccentric binaries based on linear theory. In particular, we compare prograde and retrograde CBD configurations. Then, assuming planets form in these systems, we thoroughly characterise the orbital behaviour and stability of misaligned (P-type) particles. This is done for massless and massive particles. Methods. The evolution of the CBD alignment for various configurations was modelled through three-dimensional hydrodynamical simulations. For the orbital characterisation and the analysis stability, we relied on long-term N-body integrations and structure and chaos indicators, such as $\Delta e$ and MEGNO. Results. We confirm previous analytical predictions on CBD alignment, but find an unexpected symmetry breaking between prograde and retrograde configurations. Therefore, the likelihood of becoming polar for a highly misaligned CBD is higher than previously thought. Regarding the stability of circumbinary P-type planets (also know as Tatooines), polar orbits are stable over a wide range of binary parameters. In particular, for binary eccentricities below 0.4 the orbits are stable for any value of the binary mass ratio. In the absence of gas, planets with masses below $10^{-5}\,M_{\odot}$ have negligible effects on the binary orbit. Finally, we suggest that mildly eccentric equal-mass binaries should be searched for polar Tatooines.