Three-Dimensional Photoionization Structure and Distances of Planetary Nebulae. I. NGC 6369

We present the results of mapping the planetary nebula NGC 6369 by using multiple long-slit spectra taken with the Cerro Tololo Inter-American Observatory 1.5 m telescope. We create two-dimensional emission-line images from our spectra and use these to derive fluxes for 17 lines, the Hα/Hβ extinction map, the [S II ] line ratio density map, and the [N II] temperature map of the nebula. We use our photoionization code constrained by these data to determine the distance and the ionizing star characteristics and to show that a clumpy hourglass shape is the most likely three-dimensional structure for NGC 6369. Note that our knowledge of the nebular structure eliminates all uncertainties associated with classical distance determinations, and our method can be applied to any spatially resolved emission-line nebula. We use the central star, nebular emission line, and optical+IR luminosities to show that NGC 6369 is matter bound, as about 70% of the Lyman continuum flux escapes. Using recent evolutionary tracks from Blöcker, we derive a central star mass of about 0.65 M☉.