Numerical Simulations of Secular Instabilities

Abstract

The work presented in this chapter investigates nonlinear evolution of secular GI. Understanding nonlinear evolution of secular GI is important to understand subsequent planetesimal formation. Because of the slow growth of the instability, one has to use numerical methods that are less diffusive and avoid numerical errors as much as possible. Motivated by this, we first formulate Lagrange-cell method for long-term hydrodynamic simulations. Our method utilizes symplectic integrator, which avoids diffusive errors. Numerical simulations with the formulated methods show that nonlinear evolution is understood as self-gravitational collapse of a dust ring. We also conducted simulations considering radially extended disks. The results show that secular GI creates multiple dust rings that move inward at the so-called drift velocity. Since dust grains become larger via nonlinear secular GI, the resulting multiple rings will be observed a single dark gap. Secular GI creates insignificant substructures in a gas disk, with which we can distinguish secular GI from other ring formation mechanisms that create substructures in both gas and dust disks. Most of the contents in this chapter are based on our papers published in the journals: Tominaga et al. [31, 33].