Differential deceleration of nebular shells and the displacement of central stars

The motions of nebulae through the interstellar medium would be expected to cause a shift of the central star towards the leading surface of the nebular shell, essentially a net deceleration of the shell with reference to the central star. On the assumption of a uniform-density interstellar medium, and using simple analytic formulae to describe the deceleration of the nebular shell, the development with time of the central star's offset has been examined. The argument of Bohuski et al (Astrophys. J.; 193:197 (1974)), that the observed small offsets of central stars of planetary nebulae demonstrate that they have not been appreciably decelerated, is not necessarily correct. However, with the relevant values of the parameters for planetary nebulae the argument is correct. A lower limit is found to the mass of a planetary nebula of approximately 0.01 mass of the sun for an assumed interstellar density of 10-25 g cm-3 from the crudely-measured offsets of four large planetaries. (author)