The dynamics of stellar disks in live dark-matter halos

Recent developments in computer hardware and software enable researchers to simulate the self-gravitating evolution of galaxies at a resolution comparable to the actual number of stars. Here we present the results of a series of such simulations. We performed $N$-body simulations of disk galaxies with between 100 and 500 million particles over a wide range of initial conditions. Our calculations include a live bulge, disk, and dark matter halo, each of which is represented by self-gravitating particles in the $N$-body code. The simulations are performed using the gravitational $N$-body tree-code Bonsai running on the Piz Daint supercomputer. We find that the time scale over which the bar forms increases exponentially with decreasing disk-mass fraction and that the bar formation epoch exceeds a Hubble time when the disk-mass fraction is $\sim0.35$. These results can be explained with the swing-amplification theory. The condition for the formation of $m=2$ spirals is consistent with that for the formation of the bar, which is also an $m=2$ phenomenon. We further argue that the non-barred grand-design spiral galaxies are transitional, and that they evolve to barred galaxies on a dynamical timescale. We also confirm that the disk-mass fraction and shear rate are important parameters for the morphology of disk galaxies. The former affects the number of spiral arms and the bar formation epoch, and the latter determines the pitch angle of the spiral arms.