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

TL;DR

This paper models the evolution of planetary nebulae to understand the physics behind their luminosity function, emphasizing the roles of optical depth, stellar mass, and nebular properties in shaping observed brightness distributions.

Contribution

It provides detailed hydrodynamical models linking nebular evolution, optical depth, and luminosity, challenging previous assumptions about the maximum luminosity phase and the necessity of massive central stars.

Findings

Maximum line luminosities occur at specific stellar temperatures.

Most planetary nebulae with hot central stars are optically thin.

Bright end of luminosity function can be explained without very massive stars.

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.