A&A 609, A126 (2018) Astronomy DOI: 10.1051/0004-6361/201731788 & c ESO 2018 Astrophysics Expansion patterns and parallaxes for planetary nebulae? D. Schönberner1, B. Balick2, and R. Jacob1 1 Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany e-mail: [email protected] 2 Astronomy Department, University of Washington, Seattle, WA 98195, USA e-mail: [email protected] Received 17 August 2017 / Accepted 25 September 2017 ABSTRACT 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 2000 L to well below 10 000 L , with a mean value at about 5000 L , 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 0.56 M , with a mean value of 0.55 M . Conclusions. The expansion measurements of nebular rim and shell edges confirm the predictions of radiation-hydrodynamics simu- lations and offer a reliable method for the evaluation of distances to suited objects. Key words. planetary nebulae: general – stars: fundamental parameters – techniques: image processing – techniques: spectroscopic 1. Introduction A comprehensive discussion of commonly used methods to obtain individual distances for PNe can be found in Frew (2008). For many years long-slit Doppler studies of planetary nebulae Based on individual distances of about 120 calibrating sources, a (PNe) have shown that structures in PNe expand at mildly su- −1 new distance scale was devised which is based on the Hα-surface personic speeds of order 10−30 km s or more (see compila- brightness evolution with nebular radius. The reliability of this tions by Hajian et al. 2007; López et al. 2012; Schönberner et al. distance calibration has been supported recently by Jacob et al. 2014). Their speeds and sharp leading edges argue that the ex- (2013) by employing radiation-hydrodynamics models. An up- pansions are actually pressure-driven. In general, these veloc- 00 00 date of Frew’s 2008 calibration is given in Frew et al.(2016). ities correspond to proper motions of 0:02 to over 0:06 in a Individual distances of higher accuracy are urgently needed decade at a distance of 1 kpc. Therefore the expansion patterns of since they enable estimates of masses via the (core) mass- PNe with simple, sharp-edged features can discerned in repeated luminosity relation for post-asymptotic-giant-branch (post- high-spatial-resolution images that span a decade using geomet- AGB) stars. This mass can be compared with the mass that rically stable cameras (Liller 1965; Liller et al. 1966; Osterbrock follows from distance-independent methods, for example, from 1966; Hajian et al. 1995). As these papers highlight, the Doppler detailed spectroscopic determinations of the photospheric pa- expansion speeds divided by the corresponding angular expan- rameters by non-LTE model atmospheres and comparison with sion rates can, in principle, be combined to derive distances evolutionary tracks in the log g-Teff plane or from sophisticated to PNe using the “expansion parallax method”. Once their dis- radiation-hydrodynamical wind models which provide stellar tances are known, many intrinsic properties of the PNe and their mass, radius, and luminosity without referring to any stellar central stars (mass, luminosity, death rates, Galactic distribution) model calculations. are derivable. For the bulk of objects one has, however, to rely on statistical distance scales that depend on poorly justified as- However, radiation-hydrodynamical models of Pauldrach sumptions. Accordingly, objects with known parallax serve as et al. (2004) argued that (i) the dependence of stellar luminos- excellent calibrators. ity with mass is smaller than expected and (ii) the central stars of some well-studied PN had luminosities 4:2 < log(L=L ) < 4:5 ? Results of this paper are based on observations made with the and masses right at the Chandrasaekhar limit. The reliability of NASA/ESA Hubble Space Telescope in Cycle 16 (GO11122) and older their wind models have been reinforced by Kaschinski et al. data obtained from the Data Archive at the Space Telescope Science (2012) and Hoffmann et al.(2016). Because of this quite disturb- Institute, which is operated by the Association of Universities for Re- ing finding any independent determination of the distance to the search in Astronomy, Inc., under NASA contract NAS 5-26555. objects in question would be of utmost relevance not only for Article published by EDP Sciences A126, page 1 of 24 A&A 609, A126 (2018) accurate determinations of stellar properties but also for check- and 2002 with the same camera, the F658N and F502N filters, ing the complicated physics underlying stellar wind models. and similar exposure times. Table1 contains the archive log of The Hubble Space Telescope (HST) and large radio inter- all observations. ferometers with subarcsecond resolution have revolutionized ex- Only one orbit was allocated to each target. Owing to the pansion studies. Expansions and proper motions are best de- likely secular drifts of guide stars we did not endeavor to match rived from geometrically simple PNe with bright, sharp-edged the pointing direction and orientation of the telescope in both features with angular diameters of 3000 or less. Systematic ra- epochs. No dithering was used to save time. After pipeline data dial expansion patterns have been monitored from multi-epoch calibration, there are no epoch-to-epoch changes of the fluxes of HST images for NGC 6543 (Reed et al. 1999; Balick & Hajian bright field stars, and their displacements in the two epochs were 2004), BD + 30◦3639 (Akras & Steffen 2012; Li et al. 2002) and consistent with normal random proper motions. a few other PNe (Palen et al. 2002; Hajian et al. 1995). Similar Geometric corrections of both epochs are extremely impor- expansions have also been found from radio images using the tant to suppress false positive results. We applied the best avail- Very Large Array (VLA) for NGC 7027 (Zijlstra et al. 2008), able corrections appropriate for each epoch. The geometric dis- M2-42 Guzmán et al.(2006), IC 418 (Guzmán et al. 2009), and tortion of each of the cameras within WFPC2 is correctable to NGC 6881 (Guzmán-Ramírez et al. 2011). much less than a pixel except at the corners of the field of view.1 In this paper, we present HST/WFPC2 images of a dozen Most targets fitted comfortably within the PC camera. additional bright PNe with simple geometries in the emission IC 4593, NGC 3132, and NGC 7009 were too large to fit well lines of Hα, [O iii], and [N iii] to: (1) more generally characterize in the PC and, so were observed in one of the wide-field cam- the rates and patterns of the expansions of PNe, and (2) extend eras (000:10 pixel−1). NGC 3242, which marginally overfills the the measurements of expansion distances to another dozen bright PC, was reobserved in the PC since that camera was the only targets with relatively simple shapes and sharp-edged features. one available for earlier images. We did not observe IC 4593; in- The application of radiation-hydrodynamical models to stead, we used archival images from April 1999 and February high-quality multi-epoch HST images for the derivation of ac- 2007. The earlier data came from the WF camera whereas the curate distances is the primary contribution of this paper. As we PC was used for the newer images. These cameras have differ- shall see, the outer edge of a smooth shell is the simplest means ent point-spread functions (PSF). Although this complicates our to measure expansion distances. However, it is much fainter then analysis, the final results for IC 4593 (i.e. no discernible change the bright rim of the cavity inside, so its position is more poorly in size or shape) appear to be robust. defined. On the other hand, the bright rim is generally a bubble- The F502N and F658N HST images of the objects used for driven shock, a pattern that moves through the gas at a speed that our studies have all been published previously (mostly in Hajian may not represent that of the gas inside it. Where possible we et al. 2007) along with long-slit échelle observations along sev- measure the expansion rates of both features and use our models eral cuts through the nebula and simple models of their shapes. to convert the shock pattern motions into true gas motions. The images are also found in AppendixB. This paper is organised as follows: in Sect.