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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 thebright end of the region's [O III] $\lambda 5007$ planetary nebula luminosityfunction. We show that the most luminous PNe produce $\gtrsim 1{,}200 \,\rm{L}_{\odot}$ of power in their [O III] $\lambda 5007$ line, implying centralstar luminosities of at least $\sim 11{,}000 \, \rm{L}_{\odot}$. Even with themost recent accelerated-evolution post-AGB models, such luminosities requirecentral star masses in excess of $0.66 \, \rm{M}_{\odot}$, and main sequenceprogenitors of at least $\sim 2.5 \, \rm{M}_{\odot}$. Since M31's bulge hasvery few intermediate-age stars, we conclude that conventional single-starevolution cannot be responsible for these extremely luminous objects. We alsopresent the circumstellar extinctions for the region's bright PNe anddemonstrate that the distribution is similar to that found for PNe in the LargeMagellanic Cloud, with a median value of $A_{5007} = 0.71$. Finally, we compareour results to extinction measurements made for PNe in the E6 elliptical NGC4697 and the interacting lenticular NGC 5128. We show that such extinctions arenot unusual, and that the existence of very high-mass PN central stars is ageneral feature of old stellar populations. Our results suggest thatsingle-star population synthesis models significantly underestimate the maximumluminosities and total integrated light of AGB stars.

The True Luminosities of Planetary Nebulae in M31's Bulge: Massive Central Stars from an Old Stellar Population