Extreme scale height variations and nozzle shocks in warped disks

TL;DR

This paper investigates the dynamics of strongly warped accretion disks around black holes, revealing how extreme warps cause nozzle shocks that rapidly damp the warp and potentially lead to observable variability.

Contribution

It extends the ring theory to Kerr metrics and combines it with 3D GR hydrodynamic simulations to analyze warp-induced shocks and their effects on disk evolution.

Findings

Warp amplitude threshold $oldsymbol{oldsymbol{ ext{psi}}_c}$ depends on radius as $(r/r_g)^{-1/2}$.

Nozzle shocks form at warp minima, causing rapid warp damping within 10-20 orbits.

Warp damping timescales are much shorter than in unwarped disks, implying potential for rapid variability.

Abstract

Accretion disks around both stellar-mass and supermassive black holes are likely often warped. Whenever a disk is warped, its scale height varies with azimuth. Sufficiently strong warps cause extreme compressions of the scale height, which fluid parcels "bounce" off of twice per orbit to high latitudes. In this paper, we study the dynamics of such strong warps using two methods: (i) the nearly analytic "ring theory" of Fairbairn & Ogilvie (2021a), which we generalize to the Kerr metric; and (ii) 3D general-relativistic hydrodynamic simulations of tori ("rings") around black holes, using the H-AMR code. We initialize a ring with a warp and study the subsequent evolution on tens of orbital periods. The simulations agree excellently with the ring theory until the warp amplitude, $\psi$, reaches a critical value $\psi_{\rm c}$. When $\psi>\psi_{\rm c}$, the rings enter the bouncing regime. We analytically derive (and numerically validate) that $\psi_{\rm c}\approx (r/r_{\rm g})^{-1/2}$ in the non-Keplerian regime, where $r_{\rm g}=GM/c^2$ is the gravitational radius and $M$ is the mass of the central object. Whenever the scale height bounces, the vertical velocity becomes supersonic, which leads to a "nozzle shock" as the gas collides at the scale height minima. Nozzle shocks damp the warp within $\approx10-20$ orbits in the simulations; but, that damping is not captured by the ring theory. Nozzle shock dissipation leads to inflow timescales that are 1-2 orders of magnitude shorter than unwarped $\alpha$ disks which may result in rapid variability, such as in changing-look active galactic nuclei or in the soft state of X-ray binaries. We also propose that steady disks with strong enough warps may self-regulate to have amplitudes near $\psi_{\rm c}$.