Disc breaking and parametric instability in warped accretion discs

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 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 ($\alpha \lt H/r$) regime. At large warp amplitudes ($\psi _{\text{max}} \gtrsim 1$) the disc breaks into four rings on time-scales 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 $\psi _{\text{max}} \lesssim 1$, 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 explicit viscosity ($\alpha \sim 0.03$): 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.