  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.
