  The triple nucleus of M31 consists of a population of old red stars in an
eccentric disk (P1 and P2) and another population of younger A stars in a
circular disk (P3) around M31's central supermassive black hole (SMBH). We
argue that P1 and P2 determine the maximal radial extent of the younger A star
population and provide the gas that fueled the starburst that generated P3. The
eccentric stellar disk creates an $m=1$ non-axisymmetric perturbation to the
potential. This perturbed potential drives gas into the inner parsec around the
SMBH, if the pattern speed of the eccentric stellar disk is $\Omega_p \lesssim
3-10 {\rm km s^{-1} pc^{-1}}$. We show that stellar mass loss from P1 and P2 is
sufficient to create a gravitationally unstable gaseous disk of $\sim
10^5\Msun$ every $0.1-1$ Gyrs, consistent with the 200 Myr age of P3. Similar
processes may act in other systems to produce very compact nuclear starbursts.
