The Herschel Planetary Nebula Survey (HerPlaNS) - a comprehensive dusty
  photoionization model of NGC6781
  We perform a comprehensive analysis of the planetary nebula (PN) NGC6781 to
investigate the physical conditions of each of its ionized, atomic, and
molecular gas and dust components and the object's evolution, based on
panchromatic observational data ranging from UV to radio. Empirical nebular
elemental abundances, compared with theoretical predictions via nucleosynthesis
models of asymptotic giant branch (AGB) stars, indicate that the progenitor is
a solar-metallicity, 2.25-3.0 Msun initial-mass star. We derive the best-fit
distance of 0.46 kpc by fitting the stellar luminosity (as a function of the
distance and effective temperature of the central star) with the adopted
post-AGB evolutionary tracks. Our excitation energy diagram analysis indicate
high excitation temperatures in the photodissociation region (PDR) beyond the
ionized part of the nebula, suggesting extra heating by shock interactions
between the slow AGB wind and the fast PN wind. Through iterative fitting using
the Cloudy code with empirically-derived constraints, we find the best-fit
dusty photoionization model of the object that would inclusively reproduce all
of the adopted panchromatic observational data. The estimated total gas mass
(0.41 Msun) corresponds to the mass ejected during the last AGB thermal pulse
event predicted for a 2.5 Msun initial-mass star. A significant fraction of the
total mass (about 70 percent) is found to exist in the PDR, demonstrating the
critical importance of the PDR in PNe that are generally recognized as the
hallmark of ionized/H+ regions.
