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A self-consistent stellar and 3D nebular model for Planetary Nebula IC418

We present a coherent stellar and nebular model reproducing the observations of the Planetary Nebula IC418. We want to test whether a stellar model obtained by fitting the stellar observations is able to satisfactory ionize the nebula and reproduce the nebular observations, which is by no mean evident. This allows us to determine all the physical parameters of both the star and the nebula, including the abundances and the distance. 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 done with Cloudy_3D, and is based on CTIO, Lick, SPM, IUE and ISO spectra as well as HST images. More than 140 nebular emission lines are compared to the observed intensities. 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 36.7kK. Its luminosity is 7700 solar luminosity. We describe an original method to determine the distance of the nebula using evolutionary tracks. No clumping factor is need to reproduce the age-luminosity relation. The distance of 1.25 kpc is found in very good agreement with recent determination using parallax method. The chemical composition of both the star and the nebula are determined. Both are Carbon-rich. The nebula presents evidence of depletion of elements Mg, Si, S, Cl (0.5 dex lower than solar) and Fe (2.9 dex lower than solar). This is the first self-consistent stellar and nebular model for a Planetary Nebula that reproduces all the available observations ranging from IR to UV, showing that the combined approach for the modeling process leads to more restrictive constraints and, in principle, more trustworthy results.