Hydrodynamics of warps in the local model of astrophysical discs

TL;DR

This paper demonstrates how the local shearing box model can be used to analyze the dynamics of warped astrophysical discs, deriving a conservation law for warp evolution and showing consistency with global models.

Contribution

It introduces a local framework for studying warped disc dynamics, including a conservation law for warp amplitude, aligning local and global descriptions.

Findings

Local model reproduces known warp regimes

Conservation law governs warp evolution

Consistency with global disc models

Abstract

We show how the local approximation of astrophysical discs, which is the basis for the well known model of the shearing box, can be used to study many aspects of the dynamics of warped discs. In the local model, inclination of the orbit of a test particle with respect to the reference orbit corresponds to a vertical oscillation of the particle at the orbital frequency. Warping of a disc corresponds to a locally axisymmetric corrugation of the midplane of the disc that oscillates vertically at the orbital frequency, while evolution of the warp corresponds to a modulation of the complex amplitude of the vertical oscillation. We derive a conservation law for this amplitude that is the local equivalent of the conservation of angular momentum and therefore governs the evolution of the warp. For lengthscales that are long compared to the vertical scaleheight of the disc, the known non-resonant and resonant regimes of warp dynamics, including the diffusive and wavelike regimes of Keplerian discs, occur in the local model in the same way as in a global view of warped discs.