In the course of this work it was found that a precise value for the angular diameter of the nebula is important for accurately determining physical parameters. The diameter is often determined using a technique called `gaussian deconvolution'. It was found that this method was only weakly founded in theory. Therefore a theoretical investigation was conducted to determine accurate conversion factors for a variety of surface brightness distributions.
The method for modeling nebulae has been applied several times. First, the method was used to model the LMC PN SMP 58. In this research we could tentatively conclude that the nebulae around LMC [WR] central stars are more compact than their galactic counterparts, illustrating how modeling can give clues on the shaping of nebulae.
Second, the method has been used to model the ISO SWS spectra of NGC 7027 and NGC 6543. The SWS spectrum of NGC 7027 shows evidence for evolution, or at least variability, of the central star. The preliminary model is not successful in giving a full explanation of the observed changes in the spectrum, based on the assumption that they are only caused by an increase in the stellar temperature. Nevertheless, one can state that models of this type are needed to gain an understanding of the change in the physical conditions occuring in the central star. When this final analysis is combined with an interpretation of the reported decline of the radio flux, this could result in a unique measurement of the evolutionary speed of the central star of NGC 7027. Using the model of NGC 6543, a rather stringent upper limit could be placed on the He II Lyman continuum emanating from the central star. This is one of the first times that such a constraint could be derived for a stellar spectrum.
Cloudy has also been used to conduct a parameter study of the spectral evolution of a typical post-AGB star, with particular emphasis on the evolution of the infrared colors. Several assumptions have to be made in order to calculate evolutionary tracks for post-AGB stars. A study of the type presented here is important for understanding how these assumptions affect the infrared spectrum of the post-AGB stars. The results of this study may be helpful for understanding the observations made in e.g. the IRAS color-color diagram. This in turn may lead to an improved understanding of mass loss processes, hydrodynamic interactions and evolutionary rates of the central star. Eventually it may lead to better evolutionary calculations. However, we are still far from this goal and our study should only be viewed as a small step towards achieving this goal. Another benefit from this study is that it may help in identifying more efficient search criteria for post-AGB stars and young PN.
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Peter van Hoof
Royal Observatory of Belgium
Ringlaan 3
1180 Brussel
Belgium
email: p DOT vanhoof AT oma DOT be