2018A&A...609A.126S

Aims. We aim to determine individual distances to a small number of rather round, quite regularly shaped planetary nebulae by combining their angular expansion in the plane of the sky with a spectroscopically measured expansion along the line of sight.
Methods. We combined up to three epochs of Hubble Space Telescope imaging data and determined the angular proper motions of rim and shell edges and of other features. These results are combined with measured expansion speeds to determine individual distances by assuming that line of sight and sky-plane expansions are equal. We employed 1D radiation-hydrodynamics simulations of nebular evolution to correct for the difference between the spectroscopically measured expansion velocities of rim and shell and of their respective shock fronts.
Results. Rim and shell are two independently expanding entities, driven by different physical mechanisms, although their model-based expansion timescales are quite similar. We derive good individual distances for 15 objects, and the main results are as follows: (i) distances derived from rim and shell agree well; (ii) comparison with the statistical distances in the literature gives reasonable agreement; (iii) our distances disagree with those derived by spectroscopic methods; (iv) central-star "plateau" luminosities range from about 2000L_☉ to well below 10000L_☉, with a mean value at about 5000L_☉, in excellent agreement with other samples of known distance (Galactic bulge, Magellanic Clouds, and K648 in the globular cluster M 15); (v) the central-star mass range is rather restricted: from about 0.53 to about 0.56M_☉, with a mean value of 0.55M_☉.
Conclusions. The expansion measurements of nebular rim and shell edges confirm the predictions of radiation-hydrodynamics simulations and offer a reliable method for the evaluation of distances to suited objects.