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Spiral structure in disk galaxies is modeled with nine collisionless N-bodysimulations including live disks, halos, and bulges with a range of masses. Twoof these simulations make long-lasting and strong two-arm spiral wave modesthat last for $\sim5$ Gyr with constant pattern speed. These two had a lightstellar disk and the largest values of the Toomre $Q$ parameter in the innerregion at the time the spirals formed, suggesting the presence of a Q-barrierto wave propagation resulting from the bulge. The relative bulge mass in thesecases is about 10\%. Models with weak two-arm spirals had pattern speeds thatfollowed the radial dependence of the Inner Lindblad Resonance.

Long-Lived Spiral Structure for Galaxies with Intermediate Size Bulges