Despite the internal and external consistency exhibited in the PNLF method, the use of planetary nebulae for extragalactic distance determinations is still relatively new and the limitations on the technique are not fully known. One concern about PNLF distances arises from the observations of PN in the Virgo Cluster (Jacoby et al. 1990). In these galaxies, there is clearly a small population of overluminous objects which do not fit the 5007 luminosity function. Jacoby et al. arbitrarily excluded these objects from their analysis, stating that their inclusion would shorten the derived distance to Virgo, and degrade the quality of the fits. To date, however, the nature of these objects is not completely known. Observations in NGC 1023 performed in sub-arcsec seeing suggest that most of these objects are probably chance PN superpositions, compact H II regions, or faint supernova remnants (Ciardullo et al. 1991). However, it is also possible that the overluminous objects represent a low probability tail to the PNLF. If so, future fits to luminosity functions at larger distances must include this contribution.
A greater concern about the PNLF lies in the uncertain physics of the phenomenon. In every galaxy examined so far, the shape of the rapid cutoff at the bright end of the PNLF is the same. More importantly, the internal and external tests prove that the position of this magnitude cutoff is insensitive to the details of the stellar population. This implies that whatever is causing the abrupt magnitude truncation, it does not change much with metallicity or age.
The insensitivity of the PNLF to metallicity is fairly easy to understand. Both the ionizing flux from a PN's central star, and the process of forbidden line cooling in the surrounding nebula depend on metal abundance. In the nebula, the flux emitted at 5007 Å depends on the number of oxygen atoms. However, because oxygen is one of the principal coolants of the nebula, if the abundance of oxygen is decreased, the resulting increase in the electron temperature and collision rate produces an increase in the amount of emission per ion. The result is that the flux emitted at 5007 Å by [O III] is proportional to the square root of the nebula's oxygen abundance (Jacoby 1989). This dependence, however, is almost exactly opposite that calculated for the PN's central star. According to the post-asymptotic branch models of Lattanzio (1986) and Brocato et al. (1990), the maximum luminosity attained by a hydrogen-exhausted core varies inversely with metal abundance, with a factor of two decrease in Z resulting in a ~ 30% increase in total flux. The net result of these two effects is that distances derived from planetary nebulae should be remarkably independent of metallicity, with D(PNLF) Z0.06! The self-consistent post-asymptotic branch models of Dopita et al. (1992) support this analysis, as does the analysis of a metal-poor PNLF formed from observations in the SMC, M32, NGC 185, and NGC 205 (Ciardullo and Jacoby 1992).
The insensitivity of the PNLF to changes in population age and turnoff mass is more difficult to understand. By combining nebular models with post-asymptotic giant branch evolutionary tracks, Jacoby (1989) was able to reproduce the abrupt truncation of the PNLF by assuming a sharp cutoff in the distribution of PN central stars masses. These models show that the PNLF can be recovered if the masses of central stars fall off with a dispersion of = 0.02 M. Dispersions even as large as 0.05 M, however, clearly do not fit the data, and although observations of Galactic planetary nebulae (Schönberner 1981; Kaler 1983; Shaw and Kaler 1989) and white dwarfs (Weidemann and Koester 1984; McMahan 1989) do suggest that the distribution of remnant masses is sharply peaked, it is probably not as sharp as what is required. Moreover, most mass loss laws suggest that the mass of a PN central star depends on the initial mass of its progenitor, but in order to explain all the PNLF observations, this dependence must be virtually non-existent. Although the measurements of Weidemann and Koester (1983) suggest that for stars with initial mass less than M < 3 M this might be the case, the PN observations in the Magellanic Clouds and the NGC 1023 Group are clearly inconsistent with any PNLF dependence on turnoff mass.
One possible solution to this problem is suggested by the analysis of Magellanic Cloud planetaries by Kaler and Jacoby (1991). These authors have shown that, although the LMC and SMC do contain a number of planetaries with high mass central stars, when the sample of PN is restricted to those with large [O III] 5007 fluxes, the mass distribution for central stars does agree with the sharp mass cutoff models. The implication is that high mass remnants must evolve through their high-temperature, high-luminosity phase so quickly that their nebulae never achieve the low densities needed for efficient forbidden line cooling during this phase (Jacoby 1989).
Another possible way of producing a sharp PNLF cutoff which is independent of turnoff mass is through a dredge-up scenario, whereby PN above a certain critical mass have drastically different nebular abundances as a result of previous CNO burning in their envelopes. Such events can increase the emission line cooling of species such as [N II] 6548, 6584 at the expense of [O III] 5007 and C III] 1909 and thereby reduce the [O III] 5007 flux from high mass objects by ~ 0.4 mag. Kaler and Jacoby (1989, 1990) have presented evidence for just such an effect in Galactic and Magellanic Cloud planetaries, but their analysis only deals with nebular abundances, and does not address the question of how envelope CNO burning affects the luminosity and evolution of the ionizing central star.
Still a third mechanism for explaining the PNLF's independence of turnoff mass involves mass loss from post-asymptotic giant branch stars. The above analyses use as their point of departure the standard post-asymptotic branch evolutionary tracks of Paczynski (1971), Schönberner (1981; 1983), and Wood and Faulkner (1986). In these models, the maximum UV flux emitted by a PN central star depends very strongly on its mass (cf. Fig. 14). However, new self-consistent models by Vassiliadis and Wood (1992) which include mass loss at all stages along the evolutionary path suggest that it is possible for stars of widely different initial masses (1 M < M < 2.5 M) to converge in the log L-log Teff diagram and produce the same maximum UV flux. If this is true, then the invariance of the PNLF to population age is a natural consequence of this degeneracy.