Planetary Nebulae as Standard Candles. II. The Calibration in M31 and Its Companions

We present the results of a planetary nebula survey of M31's bulge performed with the Kitt Peak No. 1 0.9 m telescope and on-band off-band λ5007 filters. We detected a total of 429 planetary nebulae (PNs), of which 104 are members of a statistically complete and homogeneous sample covering the top 2.5 mag of the planetary nebula luminosity function (PNLF). We show that the PNLF is clearly not a power law, but instead has a sharp turnover beginning at an equivalent V-magnitude of M_5007_ ~ -3.8 and going to zero at M^*^_5007_ = -4.48. This behavior is most easily explained as arising from a sharp cutoff in the upper mass limit of PN central stars in combination with extremely rapid evolutionary time scales for more massive candidate progenitors. In addition, our analysis of the PN spatial distribution shows that the density of planetary nebulae per unit luminosity is approximately the same in M31's bulge and disk, and the implied stellar death rate is in good agreement with theoretical estimates. Both the distinctive shape of the PNLF and the invariance of the luminosity-specific PN number density demonstrate that bright planetary nebulae make excellent standard candles. We therefore lay the foundation for extragalactic distance estimates by deriving two maximum-likelihood equations: one which takes advantage of theoretical constraints on the luminosity-specific PN density, and one which is solely dependent on the shape of the PNLF. We explore this technique using new CCD [O III] λ5007 photometry of planetaries observed in the M31 companion galaxies M32, NGC 205, and NGC 185.