Relaxation of Warped Disks: the Case of Pure Hydrodynamics

TL;DR

This study investigates how nonlinear warps in hydrodynamic disks relax through fluid motions, revealing that warp decay depends on warp rate and width, with dynamics differing from traditional linear models.

Contribution

It provides the first systematic simulation analysis of nonlinear warp relaxation in pure hydrodynamics, highlighting key differences from linear theories.

Findings

Warp decay rate increases with warp rate and width.

Radial pressure gradients induce transonic motions that mix angular momentum.

Warp relaxation dynamics differ from assumptions in linear models.

Abstract

Orbiting disks may exhibit bends due to a misalignment between the angular momentum of the inner and outer regions of the disk. We begin a systematic simulational inquiry into the physics of warped disks with the simplest case: the relaxation of an unforced warp under pure fluid dynamics, i.e. with no internal stresses other than Reynolds stress. We focus on the nonlinear regime in which the bend rate is large compared to the disk aspect ratio. When warps are nonlinear, strong radial pressure gradients drive transonic radial motions along the disk's top and bottom surfaces that efficiently mix angular momentum. The resulting nonlinear decay rate of the warp increases with the warp rate and the warp width, but, at least in the parameter regime studied here, is independent of the sound speed. The characteristic magnitude of the associated angular momentum fluxes likewise increases with both the local warp rate and the radial range over which the warp extends; it also increases with increasing sound speed, but more slowly than linearly. The angular momentum fluxes respond to the warp rate after a delay that scales with the square-root of the time for sound waves to cross the radial extent of the warp. These behaviors are at variance with a number of the assumptions commonly used in analytic models to describe linear warp dynamics.