A&A 473, 467-484 (2007)
DOI: 10.1051/0004-6361:20077437
The evolution of planetary nebulae
IV. On the physics of the luminosity function
D. Schönberner, R. Jacob, M. Steffen, and C. SandinAstrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
e-mail: [deschoenberner;msteffen]@aip.de
(Received 8 March 2007 / Accepted 16 July 2007)
Abstract
Context.The luminosity function of planetary nebulae, in use for about two
decades in extragalactic distance determinations, is still subject to
controversial interpretations.
Aims.The physical basis of the luminosity function is investigated by means
of several evolutionary sequences of model planetary nebulae computed with a 1D
radiation-hydrodynamics code.
Methods.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.
Results.Maximum line luminosities in H
and [O III] 5007 Å
are achieved at stellar effective temperatures of about 65 000 K and
95 000...100 000 K, 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
(
45 000 K) central stars are optically thin in the Lyman continuum,
and that their [O III] 5007 Å emission fails to explain the
bright end of the observed planetary nebulae luminosity function.
However, sequences with central stars of 0.6 
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.
Conclusions.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, A&A, 423, 995) according to which the maximum 5007 Å luminosity occurs during the recombination phase well
beyond 100 000 K 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 , to account
for the bright end of the luminosity function.
Key words: hydrodynamics -- radiative transfer -- planetary nebulae: general -- stars: AGB and post-AGB
© ESO 2007