Three-dimensional morphologies of planetary nebulae

The largest hurdle to understanding the physics of planetary nebulae is knowledge of their distances. Though measuring distances is normally a difficult problem in astronomy, measuring the distances to planetary nebulae is especially tough. The most commonly used techniques use sweeping assumptions about the population of planetary nebulae, yielding typical distance errors to these objects that are usually larger than the distances themselves. To solve this problem, we have been directly measuring accurate expansion parallax distances to PNe. This technique requires dividing the line-of-sight Doppler expansion velocity by the angular expansion rate of the nebula, which is measured by comparing two images separated by a time baseline of a few years. The only problem with this method is that the geometry of the PN needs to be determined—otherwise it would be impossible to reliably compare the observed tangential angular motions with measured line-of-sight velocities. Therefore, we present a new method to solve for the nebular geometry with a minimum of assumptions. The model is not limited by taking into account only geometry: ionization equilibrium has been imposed in order to inject realistic physics contraints into the modeling process. Using this technique, we analyze new images of PNe obtained as part of the Expansion Parallax Project from the Hubble Space Telescope within the past two years.