  We identify a new secular instability of eccentric stellar disks around
supermassive black holes. We show that retrograde precession of the stellar
orbits, due to the presence of a stellar cusp, induces coherent torques that
amplify deviations of individual orbital eccentricities from the average, and
thus drive all eccentricities away from their initial value. We investigate the
instability using N-body simulations, and show that it can drive individual
orbital eccentricities to significantly higher or lower values on the order of
a precession time-scale. This physics is relevant for the Galactic center,
where massive stars are likely to form in eccentric disks around the SgrA*
black hole. We show that the observed bimodal eccentricity distribution of disk
stars in the Galactic center is in good agreement with the distribution
resulting from the eccentricity instability and demonstrate how the dynamical
evolution of such a disk results in several of its stars acquiring high (1-e <
0.1) orbital eccentricity. Binary stars on such highly eccentric orbits would
get tidally disrupted by the SgrA* black hole, possibly producing both S-stars
near the black hole and high-velocity stars in the Galactic halo.
