Disk Tearing: Numerical Investigation of Warped Disk Instability

We present numerical simulations of misaligned disks around a spinning black hole covering a range of parameters. Previous simulations have shown that disks that are strongly warped by a forced precession—in this case, the Lense–Thirring effect from the spinning black hole—can break apart into discrete disks or rings that can behave quasi-independently for short timescales. With the simulations we present here, we confirm that thin and highly inclined disks are more susceptible to disk tearing than thicker disks or those with lower inclination, and we show that lower values of the disk viscosity parameter lead to instability at lower warp amplitudes. This is consistent with detailed stability analysis of the warped disk equations. We find that the growth rates of the instability seen in the numerical simulations are similar across a broad range of parameters, and are of the same order as the predicted growth rates. However, we did not find the expected trend of growth rates with viscosity parameter. This may indicate that the growth rates are affected by numerical resolution, or that the wavelength of the fastest-growing mode is a function of local disk parameters. Finally, we also find that disk tearing can occur for disks with a viscosity parameter that is higher than predicted by a local stability analysis of the warped disk equations. In this case, the instability manifests differently, producing large changes in the disk tilt locally in the disk, rather than the large changes in disk twist that typically occur in lower-viscosity disks.