| Abstract | We have computed an extensive grid of optically thick model planetary nebulae (PN) in order to determine the extent to which the emission-line fluxes used in the planetary nebular distance scale are affected by the stellar effective temperature and the nebular and stellar metallicity. We conclude that the nebular flux in the Hβ line is closely related to the luminosity of the central star, but that the more commonly used flux in the [O III] line at 5007 A can also be calibrated to give a reliable estimate of this quantity. We also present a simple method for determining the stellar effective temperature and the luminosity, and the nebular metallicity using only the Balmer lines and the lines of [O III] in the optical. As an absolute calibration of the planetary nebular distance scale, we have derived the excitation, extinction, and metallicity-corrected cutoff in the luminosity function for the planetary nebulae in both the Small and Large Magellanic Clouds and have derived the true distance modulus to the LMC by a new hydrogen-reignition clump-fitting technique based on self-consistent helium-burning evolutionary models for the central stars. On this basis we estimate the distance to the LMC to be 47.2 +/- 3.3 kpc. Using the cutoffs in the observed luminosity functions of the Galactic Bulge PN, M31, and the Virgo Cluster, and correcting the absolute luminosities of the planetary nebulae nuclei (PNn) for both stellar age and metallicity effects, we have been able to derive relative distance modulii of these systems. We find the following true distance modulii (m - M)_0_; LMC 18.37 +/- 0.15, SMC 18.72 +/- 0.15, Galactic Center 14.4 +/- 0.2 M31 24.14 +/- 0.20 and Virgo Cluster 30.86 +/- 0.25. In all cases where Cepheid distances are known, we find a + 0.14 mag zero-point offset with respect of the PN cosmic distance scale. Correcting to the Cepheid scale, we infer that Virgo lies at a distance of 15.8 +/- 1.8 Mpc, which would imply a global Hubble constant of 84 +/- 11 km s^-1^ Mpc^-1^. We conclude that the principle uncertainty in the PN cosmic distance scale is in our knowledge of the intrinsic upper luminosity cutoff of the PN central stars, which is critically dependent upon the stellar age, and the treatment of mass loss in the stellar evolutionary models. |
