The Herschel Planetary Nebula Survey (HerPlaNS): A Comprehensive Dusty Photoionization Model of NGC6781.

We perform a comprehensive analysis of the planetary nebula (PN) NGC 6781 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 M _⊙ 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 indicates 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 M _⊙ ) corresponds to the mass ejected during the last AGB thermal pulse event predicted for a 2.5 M _⊙ initial-mass star. A significant fraction of the total mass (about 70%) 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.