# Circumbinary disk inner radius as a diagnostic for disk--binary misalignment

## TL;DR

This paper uses hydrodynamical simulations and observational data to determine the inclination of a circumbinary disk around HD 98800 BaBb, confirming its polar alignment and proposing a new diagnostic method based on the disk's inner radius.

## Contribution

It demonstrates that the inner radius of a circumbinary disk can diagnose its misalignment, specifically confirming polar orientation in a highly eccentric binary system.

## Key findings

- The observed inner radius excludes a mild inclination, confirming polar alignment.
- Resonance theory predicts weaker torques and smaller cavities in polar disks.
- Hydrodynamical simulations support the observational inference of disk inclination.

## Abstract

We investigate the misalignment of the circumbinary disk around the binary HD 98800 BaBb with eccentricity $e\simeq 0.8$. \cite{Kennedy2019} observed the disk to be either at an inclination of $48^{\circ}$ or polar aligned to the binary orbital plane. Their simulations showed that alignment from $48^\circ$ to a polar configuration can take place on a shorter timescale than the age of this system. We perform hydrodynamical numerical simulations in order to estimate the cavity size carved by the eccentric binary for different disk inclinations as an independent check of polar alignment. Resonance theory suggests that torques on the inner parts of a polar disk around such a highly eccentric binary are much weaker than in the coplanar case, indicating a significantly smaller central cavity than in the coplanar case. We show that the inferred inner radius (from carbon monoxide measurements) of the accretion disk around BaBb can exclude the possibility of it being mildly inclined with respect to the binary orbital plane and therefore confirm the polar configuration. This study constitutes an important diagnostic for misaligned circumbinary disks, since it potentially allows us to infer the disk inclination from observed gas disk inner radii.