IFU spectroscopy of Southern Planetary Nebulae IV: A Physical Model for
  IC 418
  We describe high spectral resolution, high dynamic range integral field
spectroscopy of IC418 covering the spectral range 3300-8950{\AA} and compare
with earlier data. We determine line fluxes, derive chemical abundances,
provide a spectrum of the central star, and determine the shape of the nebular
continuum. Using photoionisation models, we derive the reddening function from
the nebular continuum and recombination lines. The nebula has a very high inner
ionisation parameter. Consequently, radiation pressure dominates the gas
pressure and dust absorbs a large fraction of ionising photons. Radiation
pressure induces increasing density with radius. From a photoionisation
analysis we derive central star parameters; $\log T_{\mathrm eff} = 4.525$K,
$\log L_*/L_{\odot} = 4.029$, $\log g = 3.5$ and using stellar evolutionary
models we estimate an initial mass of $2.5 < M/M_{\odot} < 3.0$. The inner
filamentary shell is shocked by the rapidly increasing stellar wind ram
pressure, and we model this as an externally photoionised shock. In addition, a
shock is driven into the pre-existing Asymptotic Giant Branch stellar wind by
the strong D-Type ionisation front developed at the outer boundary of the
nebula. From the dynamics of the inner mass-loss bubble, and from stellar
evolutionary models we infer that the nebula became ionised in the last
$100-200$\,yr, but evolved structurally during the $\sim 2000$ yr since the
central star evolved off the AGB. The estimated current mass loss rate ($\dot M
= 3.8\times 10^{-8} M_{\odot}$yr$^{-1}$) and terminal velocity ($v_{\infty}
\sim 450$ km/s) is sufficient to excite the inner mass-loss bubble. While on
the AGB, the central star lost mass at $\dot M = 2.1\times 10^{-5}
M_{\odot}$yr$^{-1}$ with outflow velocity $\sim 14$ km/s.
