# Inclination Evolution of Protoplanetary Disks Around Eccentric Binaries

## TL;DR

This paper presents a theoretical analysis of how inclined protoplanetary disks around eccentric binaries can evolve to a polar alignment, challenging the traditional view of alignment with the binary's orbital plane.

## Contribution

The study derives an analytic criterion for polar alignment of disks around eccentric binaries and explores the long-term evolution considering disk warp and dissipation effects.

## Key findings

- Disks with larger aspect ratio than viscosity parameter precess as a quasi-rigid body.
- A simple criterion predicts when disks evolve toward polar alignment.
- Inclination evolution timescale is shorter than disk lifetime for typical parameters.

## Abstract

It is usually thought that viscous torque works to align a circumbinary disk with the binary's orbital plane. However, recent numerical simulations suggest that the disk may evolve to a configuration perpendicular to the binary orbit ("polar alignment") if the binary is eccentric and the initial disk-binary inclination is sufficiently large. We carry out a theoretical study on the long-term evolution of inclined disks around eccentric binaries, calculating the disk warp profile and dissipative torque acting on the disk. For disks with aspect ratio $H/r$ larger than the viscosity parameter $\alpha$, bending wave propagation effectively makes the disk precess as a quasi-rigid body, while viscosity acts on the disk warp and twist to drive secular evolution of the disk-binary inclination. We derive a simple analytic criterion (in terms of the binary eccentricity and initial disk orientation) for the disk to evolve toward polar alignment with the eccentric binary. When the disk has a non-negligible angular momentum compared to the binary, the final "polar alignment" inclination angle is reduced from $90^\circ$. For typical protoplanetary disk parameters, the timescale of the inclination evolution is shorter than the disk lifetime, suggesting that highly-inclined disks and planets may exist orbiting eccentric binaries.