Hubble Space Telescope Spectroscopy of a Planetary Nebula in an M31 Open
  Cluster: Hot-Bottom Burning at $3.4 \, M_{\odot}$
  We use imaging and spectroscopy from the Hubble Space Telescope (HST) to
examine the properties of a bright planetary nebula (PN) projected within M31's
young open cluster B477-D075. We show that the probability of a chance
superposition of the PN on the cluster is small, ${\lesssim}2\%$. Moreover, the
radial velocity of the PN is the same as that of the cluster within the
measurement error of ${\sim}10$ km s$^{-1}$. Given the expected ${\sim}70$ km
s$^{-1}$ velocity dispersion in this region, ${\sim}$8 kpc from M31's nucleus,
the velocity data again make it extremely likely that the PN belongs to the
cluster. Applying isochrone fitting to archival color-magnitude photometric
data from the HST Advanced Camera for Surveys, we determine the cluster age and
metallicity to be 290 Myr and $Z = 0.0071$, respectively, implying an initial
mass of $3.38^{+0.03}_{-0.02} \, M_{\odot}$ for any PN produced by the cluster.
From HST's Space Telescope Imaging Spectrograph observations and Cloudy
photoionization modeling, we find that the PN is likely a Type I planetary,
with a nitrogen abundance that is enhanced by ${\sim}$5-6 times over the solar
value scaled to the cluster metallicity. If the PN is indeed a cluster member,
these data present strong empirical evidence that hot-bottom burning occurs in
AGB stars with initial masses as low as $3.4 \, M_{\odot}$.
