The fraction of polar aligned circumbinary disks

TL;DR

This paper investigates the likelihood of circumbinary disks aligning in a polar configuration, considering factors like disk mass, binary eccentricity, and initial inclination, to predict disk orientations in binary star systems.

Contribution

It extends previous models to include non-zero mass disks and quantifies the fraction of systems with polar disks based on binary eccentricity and disk properties.

Findings

Polar fraction increases with binary eccentricity for low-mass disks.

Massive disks have a polar fraction of approximately 37%, independent of eccentricity.

Initial mutual inclination influences the likelihood of polar alignment.

Abstract

Circumbinary gas disks that are misaligned to the binary orbital plane evolve toward either a coplanar or a polar-aligned configuration with respect to the binary host. The preferred alignment depends on the dynamics of the disk: whether it undergoes librating or circulating nodal precession, with librating disks evolving to polar inclinations and circulating disks evolving to coplanar. We quantify the fraction of binary star systems whose disks are expected to have polar orbits $f_\text{polar}$, extending previous work to include disks with non-zero mass. Our results suggest that, for low mass disks, the polar fraction is highly sensitive to the distribution of binary eccentricity with a higher fraction expected for higher binary eccentricities, $f_{\rm polar}\sim e_{\rm b}$. However, for massive discs, the fraction is independent of the binary eccentricity and $f_{\rm polar}\approx 0.37$. The value of $f_\text{polar}$ is always reduced in a population with a greater preference for low initial mutual inclination. We also explore the consequences of the finite lifetime and non-zero radial extent of a real disk, both of which affect a disk's ability to complete its evolution to a stationary configuration. Our findings can be used to make predictions given populations with well-understood distributions of binary eccentricity, initial mutual inclination, and disk angular momentum.