The True Luminosities of Planetary Nebulae in M31's Bulge: Massive
  Central Stars from an Old Stellar Population
  We measure the Balmer decrements of 23 of the brightest planetary nebulae
(PNe) in the inner bulge ($r \lesssim 3$ arcmin) of M31 and de-redden the
bright end of the region's [O III] $\lambda 5007$ planetary nebula luminosity
function. We show that the most luminous PNe produce $\gtrsim 1{,}200 \,
\rm{L}_{\odot}$ of power in their [O III] $\lambda 5007$ line, implying central
star luminosities of at least $\sim 11{,}000 \, \rm{L}_{\odot}$. Even with the
most recent accelerated-evolution post-AGB models, such luminosities require
central star masses in excess of $0.66 \, \rm{M}_{\odot}$, and main sequence
progenitors of at least $\sim 2.5 \, \rm{M}_{\odot}$. Since M31's bulge has
very few intermediate-age stars, we conclude that conventional single-star
evolution cannot be responsible for these extremely luminous objects. We also
present the circumstellar extinctions for the region's bright PNe and
demonstrate that the distribution is similar to that found for PNe in the Large
Magellanic Cloud, with a median value of $A_{5007} = 0.71$. Finally, we compare
our results to extinction measurements made for PNe in the E6 elliptical NGC
4697 and the interacting lenticular NGC 5128. We show that such extinctions are
not unusual, and that the existence of very high-mass PN central stars is a
general feature of old stellar populations. Our results suggest that
single-star population synthesis models significantly underestimate the maximum
luminosities and total integrated light of AGB stars.
