  Spiral structure in disk galaxies is modeled with nine collisionless N-body
simulations including live disks, halos, and bulges with a range of masses. Two
of these simulations make long-lasting and strong two-arm spiral wave modes
that last for $\sim5$ Gyr with constant pattern speed. These two had a light
stellar disk and the largest values of the Toomre $Q$ parameter in the inner
region at the time the spirals formed, suggesting the presence of a Q-barrier
to wave propagation resulting from the bulge. The relative bulge mass in these
cases is about 10\%. Models with weak two-arm spirals had pattern speeds that
followed the radial dependence of the Inner Lindblad Resonance.
