Warps and breaks in circumbinary discs

Disc warping, and possibly disc breaking, has been observed in protoplanetary discs around both single and multiple stars. Large warps can break the disc, producing multiple observational signatures. In this work, we use comparisons of disc time-scales to derive updated formulae for disc breaking, with better predictions as to when and where a disc is expected to break and how many breaks could occur. Disc breaking is more likely for discs with small inner cavities, cooler temperatures, and steeper power-law profiles, such that thin, polar-aligning discs are more likely to break. We test our analytical formulae using three-dimensional grid-based simulations of protoplanetary discs warped by the gravitational torque of an inner binary. We reproduce the expected warp behaviours in different viscosity regimes and observe disc breaking at locations in agreement with our derived equations. As our simulations only show disc breaking when disc viscosity is low, we also consider a viscous criterion for disc breaking, where rapid alignment to the precession vector can prevent a break by reducing the maximum misalignment between neighbouring rings. We apply these results to the GW Orionis circumtriple disc and find that the precession induced from the central stars can break the disc if it is relatively thin. We expect repeated or multiple disc breaking to occur for discs with sufficiently steep power-law profiles. We simulate a polar-aligning disc around an eccentric binary with steep power-law profiles and observe two separate breaking events at locations in rough agreement with our analytical predictions.