The evolution of planetary nebulae*
IV. On the physics of the luminosity function
Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany e-mail: [deschoenberner;msteffen]@aip.de
Received:
8
March
2007
Accepted:
16
July
2007
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 Hβ 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
Based in parts on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Science Institute, which is operated by the Association of the Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. The data are retrieved from the ESO/ST-ECF Science Archive Facility.
© ESO, 2007