  The nebular evolution is followed from the vicinity of the asymptotic-giant
branch across the Hertzsprung-Russell diagram until the white-dwarf domain is
reached, using various central-star models coupled to different initial
envelope configurations. Along each sequence the relevant line emissions of the
nebulae are computed and analysed. Maximum line luminosities in Hbeta and
[OIII] 5007A are achieved at stellar effective temperatures of about 65000K and
95000-100000K, respectively, provided the nebula remains optically thick for
ionising photons. In the optically thin case, the maximum line emission occurs
at or shortly after the thick/thin transition. Our models suggest that most
planetary nebulae with hotter (>~ 45000K) central stars are optically thin in
the Lyman continuum, and that their [OIII] 5007A emission fails to explain the
bright end of the observed planetary nebulae luminosity function. However,
sequences with central stars of >~ 0.6 Msun and rather dense initial envelopes
remain virtually optically thick and are able to populate the bright end of the
luminosity function. Individual luminosity functions depend strongly on the
central-star mass and on the variation of the nebular optical depth with time.
Hydrodynamical simulations of planetary nebulae are essential for any
understanding of the basic physics behind their observed luminosity function.
In particular, our models do not support the claim of Marigo et.al (2004)
according to which the maximum 5007A luminosity occurs during the recombination
phase well beyond 100 000K when the stellar luminosity declines and the nebular
models become, at least partially, optically thick. Consequently, there is no
need to invoke relatively massive central stars of, say > 0.7 Msun, to account
for the bright end of the luminosity function.

Astrophysics