In some galaxies, the stars orbiting the supermassive black hole take the form of an eccentric nuclear disk, in which every star is on a coherent, apsidally-aligned orbit. The most famous example of an eccentric nuclear disk is the double nucleus of Andromeda, and there is strong evidence for many more in the local universe. Despite their apparent ubiquity however, a dynamical explanation for their longevity has remained a mystery: differential precession should wipe out large-scale apsidal-alignment on a short timescale. Here we identify a new dynamical mechanism which stabilizes eccentric nuclear disks, and explain for first time the negative eccentricity gradient seen in the Andromeda nucleus. The stabilizing mechanism drives oscillations of the eccentricity vectors of individual orbits, both in direction (about the mean body of the disk) and in magnitude. Combined with the negative eccentricity gradient, the eccentricity oscillations push some stars near the inner edge of the disk extremely close to the black hole, potentially leading to tidal disruption events. Order of magnitude calculations predict extremely high rates in recently-formed eccentric nuclear disks ($sim0.1 - 1$ ${rm yr}^{-1} {rm gal}^{-1}$). Unless the stellar disks are replenished, these rates should decrease with time as the disk depletes in mass. If eccentric nuclear disks form during gas-rich major mergers, this may explain the preferential occurrence of tidal disruption events in recently-merged and post-merger (E+A/K+A) galaxies.
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