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Image intensifier detections of PNe in M31 and its dwarf companions (NGC 147, NGC 185, NGC 205, and M32) with the Lick 3-m telescope (Ford, Jenner, & Epps 1973; Ford & Jenner 1975; Ford, Jacoby, & Jenner 1977; Ford & Jacoby 1978) and subsequent Image Tube Scanner spectrophotometry showed that the brightest nebulae had approximately the same [OIII] lambda5007 flux. We reasoned that if we compared similar old stellar populations, the main sequence turn-off masses would be similar. Consequently, there would be a maximum number of ionizing photons that could be produced by a planetary's central star, and a maximum [OIII] lambda5007 flux. Using this reasoning, we proposed that planetary nebulae might be used as standard candles (Ford & Jenner, 1978). Although the utility of the planetary nebula luminosity function (PNLF) has been controversial (Sandage & Tammann 1990; Bottinelli et al. 1991; Tammann 1993), a great deal of observational work (e.g. Ciardullo et al. 1989a; Ciardullo et al. 1989b; Jacoby et al. 1989) showed that the PNLF in the bulges of spiral galaxies and in early type galaxies is an excellent standard candle with little or no dependence on Hubble type. Analytical, theoretical, and numerical models (Jacoby, 1989; Dopita, Jacoby, & Vassiliadis 1992; Mendez et al. 1993) established the theoretical basis for the observational fact that the PNLF is a good standard candle. These studies showed that the PNLF has only a modest dependence on the ages and metallicities of the parent population, and the number of PNe observed. However, the observed dependencies appear to be much smaller than those predicted by the models. Jacoby, Walker, and Ciardullo (1990) found that the observed PNLF distance to the LMC is in excellent agreement with the LMC Cepheid distance.

Ciardullo et al. (1989a; C89a) developed the model for the PNLF that has been used so successfully for deriving distances to galaxies that do not have cepheids. Their representation of the PNLF is given in equation 1.

Equation 1 (1)

M* in equation 1 cuts off the luminosity function and serves as a "standard candle". Based on a distance of 770 Kpc to M31, the calibration of the PNLF was given by M* = - 4.48 (C89a). Using Madore & Freedman's (1991) Cepheid distance to M31, Ciardullo et al. (1998) derived M* = - 4.54. More recently Ferrarese et al. (2000) derived M* = - 4.58 by comparing PNLF distances with HST Cepheid distances to the same galaxies, or to galaxies in the same group or cluster. They found a very tight linear relationship between the PNLF and Cepheid distances. The PNLF distances to the Virgo and Fornax clusters appear to be systematically smaller than the Cepheid distances. This may be due to intracluster PNe; in a magnitude-limited sample, these will be preferentially on the nearside of the cluster (see Section 6).

The relationship between the apparent monochromatic magnitude m5007 and the observed monochromatic flux F5007 is given by

Equation 2 (2)

The [OIII] lambda5007 flux from an M* planetary at 10 parsecs is 1.977 × 10-4 ergs cm-2 s-1.

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