Article

# The evolution of planetary nebulae IV. On the physics of the luminosity function

10/2007;
Source: arXiv

ABSTRACT 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.

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### Keywords

asymptotic-giant branch

dense initial envelopes

different initial envelope configurations

Individual luminosity functions

ionising photons

luminosity function

Lyman continuum

maximum 5007A luminosity

maximum line emission

Maximum line luminosities

nebular optical depth

observed luminosity function

observed planetary nebulae luminosity function

optically thick

optically thin case

relevant line emissions

stellar luminosity declines

thick/thin transition

various central-star models

white-dwarf domain