Disc breaking and parametric instability in warped accretion discs

TL;DR

This study probes how warped accretion discs evolve and under what conditions they tear into rings. Using high-resolution local shearing-box simulations with free, long-wavelength warps, the authors identify two distinct regimes: large warp amplitudes (ψ_max ≳ 1) trigger shock-mediated dissipation that breaks the disc into four rings, whereas small warp amplitudes (ψ_max ≲ 1) drive a hydrodynamic parametric instability (PI) without breaking. A linear bending-wave theory in the inviscid limit provides quantitative predictions for beat frequencies, surface-density changes, and Reynolds stresses, which agree with simulations at small amplitudes; viscosity dampens PI at small ψ_max and partially fills gaps at large ψ_max. The results illuminate a shock-driven tearing mechanism distinct from precession-based or pure anti-diffusion models, with implications for interpreting ringed structures in circumbinary and tilted-disc systems. Overall, the work highlights the critical role of warp amplitude and viscosity in determining whether warped discs break or become PI-dominated, offering a clearer physical picture of disc tearing in astrophysical contexts.

Abstract

We present the first local simulations of disc breaking/tearing in a warped accretion disc. Warps can arise due to a misalignment between the disc and the rotation axis of the central object, or a misalignment with the orbital plane of a binary (or planetary) companion. Warped discs can break into rings, as found in observations of circumbinary protoplanetary discs and global simulations of tilted discs around spinning black holes. In this work we isolate the mechanism of disc breaking in high-resolution, quasi-2D, local (shearing box), hydrodynamic simulations of a Keplerian disc. We consider the evolution of a free (unforced) warp in the wavelike ($α< H/r$) regime. At large warp amplitudes ($ψ_{\text{max}} \gtrsim 1$) the disc breaks into four rings on timescales of around 20 orbits which are separated by gaps of around $\sim 10H_0$. The warp exhibits a rich tapestry of small-scale dynamics, including horizontal sloshing motions, vertical oscillations or bouncing, warp steepening, and shocks. The shocks act as a source of enhanced dissipation which facilitates gap opening and thus disc breaking. At smaller warp amplitudes $ψ_{\text{max}} \lesssim 1$, for which we also develop a quasi-linear theory, the disc does not break, but instead exhibits hydrodynamic parametric instability. We also investigate the effect of viscosity: at small warp amplitudes the parametric instability is damped and the warp propagates as a pure bending wave, while at large warp amplitudes the emerging gaps are partially filled by viscous diffusion.

Figures (15)

• Figure 1: Left: schematic of a tilted disc annulus viewed from a global (inertial) reference frame and a shearing box (red) moving along an untilted circular orbit (the box should be tall enough to intersect the tilted disc, but we have reduced its size for visual clarity). The orange line denotes a single radius inside that annulus. Right: view of the tilted disc from the rotating reference frame of the shearing box. In general, a warped disc will appear in the shearing box as a set of fluid columns oscillating at the local orbital frequency.
• Figure 2: Theoretical prediction of time-evolution of vertically-integrated radial kinetic energy density (top panel) and vertical kinetic energy (bottom panel) for three different different viscosities: inviscid (black curve: wavelike regime), $\alpha = 0.003$ (gold curve), $\alpha = 0.03$ (blue curve).
• Figure 3: Density snapshots in the $xz$-plane in the fiducial simulation with a large warp amplitude ($A=28H_0, \psi \sim 1.95$). Top-left: the initial condition (orbit 0) is a free warp in the shape of a sinusoid. Top-middle (orbit 1.1): growing horizontal sloshing motions converge near the peaks of the warp leading to shocks that dampen the tilt. Top-right (orbit 4.1): after four orbits the warp has been noticeably flattened around the peaks of the sine curve. Bottom-left: by orbit 13.7 the disc appears to have broken into two rings. Bottom-middle (orbit 21.2): the disc begins to break into two more rings. Bottom-right (orbit 23.1): the disc has broken into four flat rings (the two rings at the radial boundaries are actually the same ring). The dashed vertical white lines show the approximate locations at which gaps open in the left-hand part of the disc.
• Figure 4: Top: $\rho u_x$ (in units of $\rho_0 c_{\text{s}0}^2$) in $xz$-plane shortly after initialization (orbit 0.1), showing the development of the horizontal sloshing motions. The vertical black dotted line through $x/H_0 = 0$ marks the radial location of the vertical slice of $u_x$ (bottom panel). The dotted red vertical lines at $z=-2H_0$ and $z=2H_0$ in the bottom panel show the approximate location of the bulk of the disc.
• Figure 5: Radial profile of the real part of the orbit-averaged vertical oscillation amplitude ( Equation \ref{['EQUATION_ComplexTilt']}). Different colors correspond to orbit-averages taken over different intervals. Over the first few orbits, there is clear evidence of warp steepening where the warp amplitude was initially greatest. The dashed blue lines mark the edges of the gaps that will form at later times (in the left-hand part of the domain), while the dashed red line marks the location of the peak of the sine curve.