On expansion parallax distances for planetary nebulae

The distances to individual wind-driven bubbles such as Planetary Nebulae (PNe) can be determined using expansion parallaxes: the angular expansion velocity in the sky is compared to the radial velocity of gas measured spectroscopically. Since the one is a pattern velocity, and the other a matter velocity, these are not necessarily the same. Using the jump conditions for both shocks and ionization fronts, I show that for typical PNe the pattern velocity is 20 to 30% larger than the material velocity, and the derived distances are therefore typically 20 to 30% too low. I present some corrected distances and suggest approaches to be used when deriving distances using expansion parallaxes.