| Summary: | It has been believed that spiral arms in pure stellar disks decay in several galactic rotations due to the heating by the spiral arms. However, it might be caused by a numerical heating. We performed a three-dimensional N-body simulations with a sufficiently large number of particles and found that stellar disks can maintain spiral arms for more than 10 Gyr without the help of cooling. Spiral arms are transient and recurrent and they heat disk with a heating rate, dQ/dt, correlated to the spiral amplitude |Am|. On the other hand, |Am| is suppressed by Toomre’s Q. Therefore, the dynamical heating becomes less effective in the later phase of the evolution. This mechanism maintain the spiral arms for more than 10 Gyr.
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