Disc breaking and parametric instability in warped accretion discs driven by differential precession

Abstract: We present the first local simulations of accretion disc breaking (or disc tearing) with differential precession. Precession can occur due to a non-spherical potential (e.g. tilted circumbinary discs), or relativistic effects (e.g. tilted discs around spinning black holes). This tends to induce a twist in the disc, potentially causing it to break into rings. We extend earlier work on free (unforced) warps in Held+2026 [arXiv:2511.18655v1] to include differential precession in the shearing box, and carry out quasi-2D, isothermal, high-resolution ($N = 32$ cells per scale-height $H$) numerical simulations in which an imposed precession drives a warp in a tilted disc in either the wavelike ($α&lt; H/r$) or diffusive ($α&gt; H/r$) regime. Our key finding is that, at sufficiently large tilts and precession amplitudes, the disc breaks into multiple (4-5) mutually tilted rings exhibiting a rich morphology: from wide ($\sim 10H$), flat rings to compact tori of width $\sim H$. Interactions between rings occur as a result of oblique shocks that form in the gaps between them, leading to instances of disc rejoining. Smaller tilts and precession amplitudes lead instead to parametric instability of inertial waves in the disc. We develop a linear viscous theory of bending waves under the influence of an imposed precession. Finally, we present a systematic study of the effects of grid-based dissipation on tilted discs, and find that numerical dissipation damps the tilt and induces precession. This effect decreases with resolution as $\propto (1/N)<sup>β$, $2.3 \lesssim β\lesssim 3.9$.