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

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 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.