Tidal Truncation of Inclined Circumstellar and Circumbinary Discs in Young Stellar Binaries

TL;DR

This paper investigates how tidal forces in young stellar binaries affect the size and shape of misaligned circumstellar and circumbinary discs, revealing complex dependencies on binary eccentricity, inclination, and other parameters.

Contribution

It provides a detailed analysis of tidal truncation for inclined discs, including new calculations of truncation radii considering arbitrary binary inclinations and eccentricities.

Findings

Misaligned circumstellar discs tend to have larger outer radii.

Discs inclined by more than 45-90 degrees may fill their Roche lobes.

Inner radii of circumbinary discs are generally smaller when misaligned.

Abstract

Recent observations have shown that circumstellar and circumbinary discs in young stellar binaries are often misaligned with respect to the binary orbital plane. We analyze the tidal truncation of such misaligned discs due to torques applied to the disc at the Lindblad resonances from the tidal forcings of the binary. We consider eccentric binaries with arbitrary binary-disc inclination angles. We determine the dependence of the tidal forcing strengths on the binary parameters and show that they are complicated non-monotonic functions of eccentricity and inclination. We adopt a truncation criterion determined by the balance between resonant torque and viscous torque, and use it to calculate the outer radii of circumstellar discs and the inner radii of circumbinary discs. Misaligned circumstellar discs have systematically larger outer radii than aligned discs, and are likely to fill their Roche lobes if inclined by more than $45^\circ - 90^\circ$, depending on the binary mass ratio and disc viscosity parameter. Misaligned circumbinary discs generally have smaller inner radii than aligned discs, but the details depend sensitively on the binary and disc parameters.