  We consider the possibility that an infalling bulge core or stellar cluster
could form an eccentric disk, following tidal disruption by a massive black
hole in the center of a galaxy. As a function of central black hole mass, we
constrain the core radii and central densities of cluster progenitors capable
of becoming nearly Keplerian disks which can support lopsided slow modes. We
find that progenitor stellar clusters with core radii less than a pc and
densities above a few times 10^5 Msol/pc^3 are likely eccentric disk
progenitors near a massive black hole of mass 10^7 to 10^8 Msol. Lower density
and larger progenitor cores are capable of causing eccentric stellar disks near
more massive black holes. Our constraints on the progenitor cores are
consistent with existing N-body simulations, which in one case has produced an
eccentric disk. For M31 and NGC 4486B, the estimated progenitor cluster cores
are dense and compact compared to Galactic globular clusters, however the cores
of nearby galaxies such as M33, M32 and M31 itself are in the right regime. If
galaxy mergers can create eccentric disks, then they would be a natural
consequence of hierarchical galaxy formation.
