A&A 625, A137 (2019) https://doi.org/10.1051/0004-6361/201935184 Astronomy & © ESO 2019 Astrophysics Confronting expansion distances of planetary nebulae with Gaia DR2 measurements? D. Schönberner and M. Steffen Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany e-mail: [email protected]; [email protected] Received 31 January 2019 / Accepted 25 March 2019 ABSTRACT Context. Individual distances to planetary nebulae are of the utmost relevance for our understanding of post-asymptotic giant-branch evolution because they allow a precise determination of stellar and nebular properties. Also, objects with individual distances serve as calibrators for the so-called statistical distances based on secondary nebular properties. Aims. With independently known distances, it is possible to check empirically our understanding of the formation and evolution of planetary nebulae as suggested by existing hydrodynamical simulations. Methods. We compared the expansion parallaxes that have recently been determined for a number of planetary nebulae with the trigonometric parallaxes provided by the Gaia Data Release 2. Results. Except for two out of 11 nebulae, we found good agreement between the expansion and the Gaia trigonometric parallaxes without any systematic trend with distance. Therefore, the Gaia measurements also prove that the correction factors necessary to convert proper motions of shocks into Doppler velocities cannot be ignored. Rather, the size of these correction factors and their evolution with time as predicted by 1D hydrodynamical models of planetary nebulae is basically validated. These correction factors are generally greater than unity and are different for the outer shell and the inner bright rim of a planetary nebula. The Gaia measurements also confirm earlier findings that spectroscopic methods often lead to an overestimation of the distance. They also show that even modelling of the entire system of star and nebula by means of sophisticated photoionisation modelling may not always provide reliable results. Conclusions. The Gaia measurements confirm the basic correctness of the present radiation-hydrodynamics models, which predict that both the shell and the rim of a planetary nebula are two independently expanding entities, created and driven by different physical processes, namely thermal pressure (shell) or wind interaction (rim), both of which vary differently with time. Key words. planetary nebulae: general – stars: AGB and post-AGB – stars: distances 1. Introduction techniques and their comparison with evolutionary tracks in the (distant-independent) log g-Teff plane (see e.g. Méndez et al. Individual distances to planetary nebulae (PNe) are of great rel- 1992, and references therein). evance for our understanding of post-asymptotic giant-branch The so-called “gravity distances” of Méndez et al.(1992) (post-AGB) evolution provided they are of sufficient accuracy to and Kudritzki et al.(2006) are based on model atmospheres of allow a trustworthy determination of stellar and nebular proper- different degrees of sophistication: static atmospheres with lim- ties that can be compared with theoretical predictions. Moreover, ited consideration of line blanketing in the former, and “unified” objects with known individual distances serve as calibrators for model atmospheres that also include the wind envelope in the the so-called statistical distances based on secondary nebular latter work. To get the distance, the stellar gravity is combined properties. Prior to the Gaia era, direct trigonometric distances with the stellar mass that is read off from post-AGB tracks in were only available for a rather limited number of close-by PNe a Teff=log g plane, the visual absolute brightness, and the model through long-term measurements of the US Naval Observatory flux for the given Teff (see Eq. (4) in Méndez et al. 1992). (USNO, Harris et al. 2007) and the Hubble Space Telescope The distances of Méndez et al.(1992) and Kudritzki et al. (HST, Benedict et al. 2009). (2006) are based on the old post-AGB evolutionary tracks of Much effort was thus invested in getting individual dis- Schönberner(1979, 1981, 1983). The new evolutionary cal- tances for more distant objects using other methods, for exam- culations of Miller Bertolami(2016) give somewhat higher ple detailed spectroscopic determinations of the central-star post-AGB luminosities (and lower gravities) for a given remnant parameters by non-local thermal equilibrium model-atmosphere mass. In short, the gravity distances are now smaller by about 5%, and these adjusted distances are used here for comparison1. ? This work has made use of data from the European Space Pauldrach et al.(2004) analysed the UV spectra of a number Agency (ESA) mission Gaia (https://www.cosmos.esa.int/ of PN central stars using a very sophisticated, hydrodynam- gaia), processed by the Gaia Data Processing and Analysis Con- ically consistent model, which includes the expanding stellar sortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/ consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia 1 For more details, the reader is referred to Sect. 5.2 in Schönberner Multilateral Agreement. et al.(2018). Article published by EDP Sciences A137, page 1 of8 A&A 625, A137 (2019) atmosphere with the supersonic wind region. This model, origi- Frew et al.(2016). The agreements are very satisfying: nally developed for mass-losing massive stars, provides the stel- – the USNO parallaxes are confirmed by the Gaia DR2, lar parameters (effective temperature, radius, luminosity, mass) although the USNO errors are comparatively high for objects independently of any stellar evolutionary tracks, and hence also further away than 0.5 kpc. The HST distances slowly deviate the distance. with increasing distance from the 1:1 relation for unknown Another important approach to get an individual distance reasons, until they are about 30% higher at 0.50 pc (cf. Fig. 1 is to model the whole system, central star and nebular enve- in Kimeswenger & Barría 2018). lope, by employing for instance the well-known photoionisation – The comparison with the two statistical distance scales code “Cloudy”2. Since many parameters determine the nebu- reveals only insignificant deviations from the 1:1 relation – lar emission, a consistent solution that also includes the stellar though the individual distance differences can be very high, parameters is rather complex and prone to degeneracy, which up to about a factor of two to either side (cf. Figs. 2 and 3 in must be resolved by additional constraints. An interesting vari- Kimeswenger & Barría 2018). ant is the combination of a full spectroscopic analysis of the The purpose of the present paper is a comparison of the most stellar atmosphere including the stellar wind with a consis- recent expansion distances determined by SBJ with the trigono- tent nebular photoionisation model, as has been performed for metric distances provided by the Gaia DR2. As an aside, we instance by Morisset & Georgiev(2009) for the IC 418 sys- also discuss briefly the quality of spectroscopic (or gravity) tem. These authors also provide an illuminating discussion of methods and/or the use of photoionisation models for distance the degeneracy problem and a possible way to solve it. determinations for the objects in common. A further powerful method of deriving individual distances The paper is organised as follows. Firstly, we present a brief to planetary nebulae is the expansion-parallax method. In the lat- introduction to the method of determining expansion distances est study of this kind (Schönberner et al. 2018, hereafter SBJ), (Sect.2). Then, in Sect.3, we introduce our sample of PNe two- or three-epoch HST images were employed. From these that have expansion and Gaia trigonometric parallaxes and com- images, angular proper motions of for instance the nebular rim pare the distances in detail. In particular, we demonstrate the and shell edges were determined and combined with measured importance of the correction factors. The following Sect.4 deals expansion (Doppler) velocities to derive directly the distances with an empirical determination of individual correction factors, by assuming that the expansions along the line of sight and in both for nebular shell and rim. This article closes with a short the plane of sky are equal. summary and the conclusion (Sect.5). It turned out that the (corrected) expansion distances as derived by SBJ are in general smaller than the distances based on the spectroscopic methods. However, both the gravity and 2. Essence of the expansion method the expansion distances are subject to uncertainties that are dif- We follow here the notation used in SBJ. Approximating the ficult to control. In the case of the former, the distances rely on a main structure of a PN as a system of (spherical) expanding precise determination of the stellar gravity (Méndez et al. 1992, shock waves, the so-called “shell” followed by the “rim” with Eq. (4) therein), which is a difficult task for very hot stars and internal velocity and density gradients (cf. Fig.1), the distance is the main source for the distance uncertainties. usually determined by the relation The situation is even more complicated for the expansion 0 ˙ parallaxes because we are dealing in this case with expanding Dexp = 211 VDoppler = θ; (1) gaseous shells led by shocks. The problem, usually ignored in 0 1 the past, lies in the conversion of pattern expansions (the leading where Dexp is the distance in parsec (pc), VDoppler (in km s− ) is shocks) into flow velocities (Doppler line split). The correc- half the Doppler split of a suitable emission line observed in the tion factor (see Sect.2) to be applied for the distance is always direction to the nebular centre, θ (in milli-arcseconds, or mas) the larger than unity, but its size fully relies on a proper description angle between the centre of the nebula and the feature (or nebu- of the formation and expansion of PNe and their shock fronts.