2006ApJ...648..430S

Continuing our series of papers on the three-dimensional (3D) structures of and accurate distances to planetary nebulae (PNe), we present our study of the planetary nebula NGC 6781. For this object, we construct a 3D photoionization model and, using the constraints provided by observational data from the literature, we determine the detailed 3D structure of the nebula, the physical parameters of the ionizing source, and the first precise distance. The procedure consists of simultaneously fitting all the observed emission-line morphologies, integrated intensities, and the two-dimensional (2D) density map from the [S II] line ratios to the parameters generated by the model, and in an iterative way obtaining the best fit for the central star parameters and the distance to NGC 6781, obtaining values of 950±143 pc and 385 L_☉ for the distance and luminosity of the central star, respectively. Using theoretical evolutionary tracks of intermediate and low-mass stars, we derive the mass of the central star of NGC 6781 and its progenitor to be 0.60±0.03 M_☉ and 1.5±0.5 M_☉, respectively.