JournalThe Stability of Disks in Sharp Potentials 1

We connrm that a high circular velocity at the center is able to stabilize an entire stellar disk against bar-forming (m = 2) modes, irrespective of the dark halo density. Our simulations of unstable power-law disks also yield the growth rate and pattern speed of the dominant lop-sided (m = 1) mode in close agreement with that predicted by linear theory in our cleanest case. We show that these one-armed modes, which dominate models with extensive disks, can be controlled by tapering the outer disk. Two-armed instabilities of hard-centered disks are more diicult to identify because they are easily overwhelmed by particle noise. Nevertheless, we have detected the predicted modes in simulations with very large numbers of particles. Bisymmetric instabilities in these disks are provoked only by sharp edges and are therefore easily eliminated. We have constructed a cool disk model with an almost at rotation curve and a quasi-exponential density proole that is unambiguously stable. The halo in this stable model has a large core radius, with the disk and bulge providing almost all the rotational support in the inner parts.