A self-consistent stellar and 3D nebular model of planetary nebula IC 418

Aims: We present a coherent stellar and nebular model that reproduces observations of the planetary nebula IC 418. We aim to test whether a stellar model found to provide an optimal description of the stellar observations is able to satisfactory ionize the nebula and reproduce the nebular observations, a finding that is by no mean evident. This allows us to determine all the physical parameters of both the star and the nebula, including chemical abundances and the distance.
Methods: We used all the observational material available (FUSE, IUE, STIS and optical spectra) to constrain the stellar atmosphere model performed using the CMFGEN code. The photoionization model is developed by comparing solutions provided by Cloudy_3D, with results from CTIO, Lick, SPM, IUE, and ISO spectra as well as HST images. The aperture sizes and positions of the different observations are taken into account. More than 140 model nebular emission lines are compared to the observed intensities. The distance is determined using evolutionary tracks.
Results: We reproduce all the observations for the star and the nebula. The 3D morphology of the gas distribution is determined. The effective temperature of the star is 36.7±0.5 kK. Its luminosity is 7700 L_⊙. No clumping factor is needed to reproduce the age-luminosity relation. We describe an original method for determining the distance of the nebula using evolutionary tracks. The distance of 1.25 kpc is found to be in very good agreement with recent determination using parallax method, and the age of the nebula is estimated to be 1400 years. The chemical composition of both the star and the nebula are determined. Both are carbon-rich. The nebula exhibits evidence of the depletion of elements Mg, Si, S, Cl (0.5 dex lower than solar), and Fe (2.9 dex lower than solar), which is indicative of a depletion of these elements onto grains.
Conclusions: We develop the first self-consistent stellar and nebular model of a planetary nebula that reproduces all the available observations ranging from IR to UV, showing that the combined approach to the modeling process leads to more restrictive constraints and, in principle, more trustworthy results.

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