Instability of a protoplanetary disk in its main accretion phase

We present three-dimensional numerical simulations for the formation and evolution of an accreting protoplanetary disk. The disk was assumed to be formed by the gravitational collapse of a rotating gas cloud. It was assumed to be nearly axisymmetric but to have a nonaxisymmetric perturbation. We constructed 11 models, changing the angular momentum distribution and initial perturbation. In a typical model, the growth of the bar mode (m = 2) begins 300 yr after the formation of the protoplanetary disk. The growth is exponential in the linear regime and has an e-folding timescale of 100 yr. The bar mode changes the protoplanetary disk into a fast-rotating bar. The angular momentum is transferred from the bar to the outer infalling envelope, and spiral density waves are emitted outward. The bar shrinks into a smaller round disk after the angular momentum transfer. This increases the accretion rate temporarily. The disk grows through accretion and becomes unstable against the bar mode again. The recurrence period was about 800 yr. Our simulations indicate that accretion is dynamical and that its rate is highly variable in the early protoplanetary disk.