On the distances of planetary nebulæ

Reconsidering calibration of statistical distance scales for planetary nebulæ leads naturally to examining precision and especially the systematic errors of other methods. Here we present a different calibration strategy based on the precise trigonometric parallaxes for sixteen central stars published by Harris et al. (2007) of USNO, with four improved by Benedict et al. using the Hubble Space Telescope. We tested various other methods against those and each other. The statistical scales tested – Cahn et al. (1992), Zhang (1995), Frew (2008), and Stanghellini et al. (2008) – all show signs of radius dependence (i.e. distance ratio [scale/true] depends on nebular radius). Almost all have overall systematic error; Frew’s mean statistical scale seems free of that and also perhaps a scale of Zhang’s based on brightness temperature. Systematic errors were introduced by choices of data sets for calibration, by methodologies used, and by assumptions made about the nebulæ. Some spectroscopic parallaxes published by Ciardullo et al. (1999) seem consistent with the trigonometric ones where the objects overlap in nebular radius. Pottasch’s (1996) earlier spectroscopic parallaxes, on the other hand, underestimate distance consistently by a factor of two, probably because of a calibration difference. ‘Gravity’ distances seem to be overestimated by 40-50 per cent for nearby objects but may be underestimated for distant objects. Angular expansion distances appear to be suitable for calibration after correction for astrophysical effects (e.g. Mellema 2004). In particular the measurements by Hajian and collaborators using the VLA seem to yield fairly accurate distances after correction by Frew. Extinction distances appear to be often unreliable individually though sometimes approximately correct overall. Comparison of the Hipparcos parallaxes (van Leeuwen 2007) for large planetaries with our ‘best estimate’ distances confirms that those parallaxes are overestimated by a factor 2.5, as suggested by Harris et al.’s result for PHL 932. The ultimate goal is an accurate and internally consistent set of distances for planetaries. However, some of our tools and analysis can also be applied in distance scale comparisons utilizing parallaxes and/or distances for other objects as well.