© ESO 2020

1 Introduction

In a recent work (González-Santamaría et al. 2019, hereafter, Paper I), we used Gaia Data Release 2 (DR2) astrometry to build a catalogue of central stars of planetary nebulae (CSPNe), along with precise distances and luminosities, which we named the Golden Astrometry Planetary Nebulae (GAPN). The Gaia DR2 data was analysed together with literature values for the extinction, stellar temperatures, expansion velocities, and nebular radii to estimate other parameters such as physical sizes and kinematical ages. We were able to locate the CSPNe in a Hertzsprung-Russel (HR) diagram and to compare their distribution with that predicted by up-to-date evolutionary tracks. The scope of GAPN includes 211 CSPNe, which were selected by applying quality filters to the astrometric measurements (parallax relative errors as well as distance-derived errors below 30%).

Several previous works have taken advantage of the extraordinary quality of Gaia DR2 astrometry to search for wide binaries among the brightest Milky Way stars (Jiménez-Esteban et al. 2019), proving that it is possible to search for comoving objects by considering proper motions and parallaxes (and radial velocities, if they are available) based on Gaia or a combination of Gaia and Hipparcos data. In this work, we aim to carry out a systematic search for comoving systems in the field around each nebular central star (CS) in the GAPN sample. In this way, we intend to shed more light on the phenomenon of binarity in planetary nebulae, extending the search for binary companions close to the central stars to possible more distant binary partners, which likely have a less direct influence on the evolution of the CS but are equally interesting when it comes to constraining values such as the age and mass of the CS. Previous studies of wide binary companions to planetary nebulae (PNe), in particular, the Hubble Space Telescope (HST) snapshot programme from Ciardullo et al. (1999), were successful in providing accurate distances to PNe by measuring the photometry of nearby objects that were postulated to be probable binary partners. Gaia DR2 measurements will allow now to confirm some of these derivations.

A recent review by Boffin & Jones (2019) analyses the importance of binaries in the formation and evolution of PNe, asserting the idea that most of them could be ejected from binaries but also stressing the fact that providing a quantitative value about the incidence of binarity is not an easy task. Nevertheless, binarity is one of the most accepted theories for explaining asphericity in the nebular morphology, given that approximately 75% of the total of known PNe are aspherical (Manchado 2004; Jones & Boffin 2017). In addition, Soker (2001) discusses some morphological properties, such as a departure from axisymmetry and the formation of bipolar and multipolar lobes that support the binary model.

In the case of close binaries, with orbital separations on the order of a few AU, there can be a strong interaction between both stars. The interaction could involve the spin-up of the envelope by tidal forces, Roche lobe overflow, and common envelope (CE) evolution. In this phase, mass transfer between both stars is produced either by stellar winds or by Roche lobe overflow. According to Jones (2020) approximately 12–20% of PNe host a post-CE system, and in such systems, it has been hypothesised that the ingestion of the companion can lead to the bipolar ejection of the progenitor envelope, which strongly affects the PN morphology. Other authors propose that more distant binary companions may provide an alternative mechanism for the formation of highly aspherical morphologies by influencing the direction of collimated winds from the parent star, whose axis of rotation precesses due to the influence of a companion that is not necessarily close (Garcia-Segura 1997, see discussion in Sahai & Trauger 1998).

In wide binaries, the link is not so strong, but knowing some properties – such as the common age of the components or the orbital separation – can give us certain clues about the evolution of the CSPNe and about the possible influence of wide companions in the nebular morphology. Bear & Soker (2017) suggested that triple systems could shape the morphology of those PNe that depart from axial-symmetry or mirror-symmetry and hierarchical systems have been found in some PNe (for instance in NGC 246, Adam & Mugrauer 2014). In our work, we focus on wide binaries that can be detected as separate sources in Gaia DR2. Future Gaia archives, which will include the analysis of the astrometric solution for several tens of observational epochs, will hopefully lead us to find some astrometric binary companions at angular distances as short as 0.1 arcsecs among the brightest CSPNe.

The present paper is structured as follows: in Sect. 2, we describe the methodology chosen to search for comoving objects, which is partially based on the procedure presented by Jiménez-Esteban et al. (2019), and we discuss the reliability of the possible binary partners, and, finally, we propose our list of solid binary candidates. In Sect. 3, we present the astrometric and photometric properties of the binary pairs detected. We used three bands in Gaia DR2 photometry together with literature data about the interstellar extinctions towards the systems to locate the companions of the CSPNe in an HR diagram. When Gaia colours were not available, we used the Virtual Observatory SED Analyzer (VOSA 6.0) tool from the Spanish Virtual Observatory (SVO, Bayo et al. 2008) to construct the spectral energy distribution from the available literature spectrophotometric data. Evolutionary models could then be fitted to obtain effective temperatures, luminosities, and masses (and their uncertainty values) that are to be compared with those inferred for the CSPNe in the GAPN sample. Section 4 discusses the results obtained, which can clearly be expanded upon when the third Gaia archive is published at the end of 2020.

2 Searching for comoving binary pairs

In order to search for comoving objects within our GAPN sample, we have to analyse the density of stars and their astrometric properties in a field close to each nebula. We decided to limit the study of fields to stars with magnitudes G lower than 19, considering that weaker objects usually have significant errors in their DR2 astrometric measurements. Comoving objects are those that have values of their five astrometric parameters (position in the sky, parallax and proper motions in right ascension, and declination) plus radial velocities, consistent with spatial closeness and gravitational linkage between them. In this case, radial velocities are not available for the companion candidates and we had to constrain our search to compatibility of the other five parameters.

To ensure a physical relationship, it is important to exclude the possibility of similar astrometry occurrence by chance, as well as to take into account the errors of the astrometric measurements in DR2. In the following, we describe how we proceeded.

First, we retrieved the astrometric measurements and their errors for all stars brighter than G = 19 in a 120 arcsec-wide region around the coordinates of each of the GAPN CSs. This angular radius was chosen as a balance between achieving sufficient statistics to measure the density of stars and their astrometric parameters, while covering a region relatively close to each nebulae (corresponding to a projected radius of 0.58 pc for a nebula at a distance of 1 kpc). On average, we found approximately 250 objects around each of the considered CSPNe.

If we define σ as the largest value of the error in parallax (or in proper motions) for a given pair of a field object and a particular CSPN, we selected those objects whose parallax and proper motions differ less than 2.5 ⋅ σ from the CS ones, the same criteria as those used by Jiménez-Esteban et al. (2019). Furthermore, in order to pick up objects with enough reliable astrometry, we only considered objects with parallax and proper motions relative errors smaller than 30%. We note that both parallax and proper motions in Gaia DR2 need to be corrected (for a systematic zero point and rotation bias, respectively) and that to estimate the errors in the astrometric parameters, both the internal and systematic errors have to be considered, as prescribed in Lindegren et al. (2018).

For each of the 211 sources in the GAPN sample, we looked for companions with compatible parallax and proper motions values within errors (2.5 ⋅ σ, as mentioned). After applying these constraints, we found 44 objects distributed in 31 different systems, that is to say, 31 out of 211 CSPNe haveat least one object that is a candidate to be a comoving companion.

It is physical separation, not angular separation, that should be used as a general criterion to search for binary companions. In the case of wide binaries, what is generally accepted is a limiting maximum value of 20 000 AU in projected physical separation of binaries (Weinberg et al. 1987; Close et al. 1990), although this value has been questioned in the case of sparse halo field stars or very young clusters (see Jiménez-Esteban et al. 2019 for a discussion). A recent study by Zavada & Píška (2020) proposed a value of 0.1 pc (~ 20 000 AU) for the maximum projected physical separation between binary components. Our 44 comoving candidates are located at distances from the CSPNe ranging from 1.8 to 119.3 arcsecs, along with projected physical separation distances ranging from 1500 to 410 000 AU.

Planetary nebulae have physical sizes that range between less than 0.1 pc in the earlier 14 kyr of their evolution (González-Santamaría et al. 2019) to values of more than 1 pc when dealing with old diluted nebulae. Limiting the search of binary companions to comoving objects at projected separation distances not greater than 20 000 AU implies that in general, our search remains inside the nebular area. As a result of setting this limitation to our sample, only 8 out of the 31 systems remained as possible comoving systems (one of them as a triple system). Identification charts for the CSPNe and the comoving companions are provided in Fig. A.1.

We carried out a test to assess the degree of chance coincidences of the astrometric values for each of our eight detected comoving pairs. We calculated the probability density distribution of the three astrometric measurements (parallax and proper motions) around each of the nebulae. In order to have enough statistics to draw the probability distribution, we considered spherical regions around the CSPNe with radii that vary from 1 to 4 pc depending on the obtained population, which was always above 400 objects. We limited our search to stars with magnitude G < 19 and we did not impose any constraint on the relative errors of the astrometric measurements. In fact, each of the astrometric quantities in DR2 is affected by errors, which in some cases can get quite large, including negative parallaxes (Lindegren et al. 2018). A Gaussian error distribution for every measurement was assumed and we sampled every measurement 100 times in order to properly take into account the errors. Then, to build the distributions, we chose a sampling interval equal to 2.5 ⋅ σ, being σ the error in the astrometric quantity previously used to search for comoving objects. This way, we were able to calculate the probability for every astrometric measurement in the region close to the CSPNe and, by combining the probabilities for the parallax and both proper motion parameters, we obtained a probability value for the specific triplet (p, μ_α, μ_δ). Such total probabilities always resulted in very low values, namely, below 0.2%. To illustrate this procedure, Fig. 1 shows the probability density distributions for parallax (p), proper motion in RA (μ_α) and proper motion in Dec (μ_δ) around Abell 24 and PN SB 36, which are two of the PNe with binary candidates.

Consequently, our search and selection procedure led us to propose a sample of eight comoving systems that we interpret as wide binary systems associated to the CSPNe in GAPN. The rest of the present work is focused on that sample.

3 Results

Table 1 contains the astrometric data for the eight central stars and their detected binary companions. CSs distances are obtained from Paper I, while companion stars distances are obtained from Gaia DR2 archive by the same method used in that work. Other parameters, such as projected physical separations between binaries or nebular sizes, are derived from these distances. As can be seen, angular separations range from 1.8 to 13.7 arcsecs and projected separations are between 1542 and 14 880 AU. As these are typical separation distances for wide binaries, they are expected to be large enough to discard the phenomenon of mass transfer. It should be noted that we used a 30% uncertainty threshold for the astrometry, the same threshold that we used in González-Santamaría et al. (2019) where we defined the GAPN sample. In spite of this, the relative errors of parallax in the measurements of the CS and its companions that are listed in Table 1 are always below 22%, with only four measurements that exceed 15%.

We present the photometric properties in Table 2, along with the parameters that are derived from them. Gaia DR2 photometry in bands G, G_BP, and G_RP, together with interstellar extinctions for the CSPNe from the literature can be used to derive extinction in the G band as well as colour excess E(G_BP-G_RP). We assumedthat interstellar extinction is the same for the CSPN and the binary companion and we used Danielski et al. (2018) relations to transform the global extinction A₀ into the Gaia passbands ones, taking into account the extinction coefficients dependency on colour. It has to be pointed out that circumstellar extinction is only important for compact PNe, which is not the case for any star in our sample. PHR J1129-6012 and PN SB 36 lack extinction information and, therefore, these two objects have been excluded from our evolutive analysis. The next step was to use PARSEC isochrones in Gaia DR2 passbands (Evans et al. 2018) to derive the effective temperature and luminosity values for the companion stars that are listed in Table 2.

We note that Abell 33-B and NGC 6853-C do not have colour data in DR2. For these stars, we retrieved the available photometricinformation via the Virtual Observatory SED Analyzer (VOSA) from the Spanish Virtual Observatory (SVO)¹ platform, and we built their spectral energy distribution (SED). Using the VOSA tool, we fitted the SED to NextGen (AGSS2009) models (Allard et al. 2012) and the result is shown in Fig. 2. The values obtained for the temperatures and luminosities for these two stars are also listed in Table 2.

The information in Table 2 can be used to explore the evolutionary properties of the companion stars. All companions with DR2 photometry show positions close to the zero-age main sequence (ZAMS), except for Abell 34-B, which has already evolved into the subgiant branch. We used the PARSEC evolutionary tracks and interpolated them to derive the mass values that are listed in the last column of Table 2. Taking into account the low errors in DR2 photometry (which have a complex dependence on the number of visits of the satellite and on the brightness of the sources, among other variables), we estimate that our masses have uncertainties below 20%. By assuming the values obtained for the masses and the positions of the objects on the main sequence, we can also infer the spectral types of these stars.

The next step was to compare the mass values obtained for the companion stars with those of the CSPNe. In the case of the central starsof Abell 33, Abell 34, and NGC 6853, we adopted the temperature and luminosity values published in Paper I. We have not found a reliable effective temperature measurement published for the NGC 3699 central star and so, this system was excluded from the evolutionary analysis. In Kaler & Jacoby (1989), they estimated that such temperature must be high, namely, on the order of 260 kK. However, the application of this value for the bolometric correction would lead to an unrealistically high luminosity for this object. The evolutionary parameters of Abell 24 CS are also subject to a high level of uncertainty. Its location in the HR diagram, as calculated in Paper I, places it at a rather high temperaturefor its luminosity and by interpolating Miller Bertolami (2016) evolutionary tracks, only a lower limit of 3 M_⊙ for the progenitor star could be obtained. We would like to call attention to the fact that by using a lower extinction value for this object, of A_V = 0.055, as obtained using the DR2 distance and Bayestar19 3D Dust Maps (Green et al. 2019), the position in the HR diagram that is obtained is compatible with the Miller Bertolami (2016) evolutionary track for a progenitor star of 3 M_⊙.

NGC 246 central star is a H-deficient CSPN, Heap (1975). It is an extremely hot member of the PG1159 spectroscopic subtype, within which it is the brightest (m_V = 11.78) star. Werner et al. (2006) fitted NLTE stellar atmosphere models to FUSE and HST/STIS spectra obtaining T_eff = 130 kK and log g = 5.7. Using post-AGB evolutionary models calculated under a born-again scenario from a very late thermal pulse (VLTP) by Miller Bertolami & Althaus (2006), they derived a stellar mass of M = 0.74 M_⊙ which would be the remnant of a Main Sequence star of approximately 3.75 M_⊙ (Althaus et al. 2009).

Evolutionary masses for H-rich post-AGB stars can be derived by fitting evolutionary tracks by Miller Bertolami (2016) and the progenitor mass obtained from their self-consistent models that include all previous evolutionary stages from the ZAMS to the white dwarf phase. Table 2 shows the progenitor masses derived for the CSPNe together with low and high uncertainty values. These uncertainties are estimated from the luminosity and temperature errors in the HR diagram derived in Paper I. In the following sections, we comment on the results obtained for the individual binary pairs.

Fig. 1 Probability distributions for parallax and proper motions of objects in the neighbourhood of Abell 24 (left) and PN SB 36 (right). The black arrow indicates the interval corresponding to the CS parameters values.

Fig. 2 Fits to NextGen (AGSS2009) models of Abell 33 - B and NGC 6853 - C spectral energy distributions obtained with VOSA tool from the Spanish Virtual Observatory.

3.1 Abell 24

Abell 24 (Fig. A.1) is an elliptical PN located 691 pc away from the Sun. It is a large nebula with a mean radius of 0.633 pc (~130 000 AU). We found a wide binary companion, Abell 24-B, with a projected separation of 9912 AU from the CS. By fitting its photometry to PARSEC evolutionary tracks, we obtained a mass of 0.76 M_⊙, which corresponds to an early K-type star. Meanwhile, a lower limit mass of 3 M_⊙ can be derived for Abell 24 CS from comparison with Miller Bertolami (2016) post-AGB evolutionary tracks.

Ciardullo et al. (1999) commented on the presence of a possible binary pair in this PN, but they identified a different companion closer to the CSPN that finally was classified as a “doubtful association”. If we analyse this other candidate in Gaia DR2, we find that neither parallax, nor proper motions are compatible with those from the CS, thus, we can discard a binary bound in this case.

3.2 Abell 33

This PN (Fig. A.1) has a round shape and it is located 932 pc away from the Sun. It has a medium radius of 0.516 pc (~106 000 AU). We detected a wide binary companion with a projected separation of 1542 AU from the CS. This star was already mentioned as a possible binary companion by Ciardullo et al. (1999) and this is now confirmed by DR2 astrometry. Using the VOSA tool, we fit the SED of Abell 33-B to NextGen (AGSS2009) models to and we obtained a value of 0.76 M_⊙, which corresponds to an early K-type star, while a value of 1.13 M_⊙ was derived for Abell 33 CS from postAGB tracks in Miller Bertolami (2016).

3.3 Abell 34

This PN (Fig. A.1) is located 1118 pc away from the Sun. It has a round shape and a large radius of 0.778 pc (~160 000 AU). We found a comoving star with a projected separation of 10 472 AU from the CS. Ciardullo et al. (1999) already mentioned the existence of this possible binary companion, although they calculated a probability of 28% for it to correspond to a chance alignment. Gaia DR2 astrometry allows us to confirm that this star is a true wide binary companion of the CSPN.

Abell 34-B, a subgiant star, has already evolved from the MS. By fitting its photometry to PARSEC evolutionary tracks, we obtained a mass of 0.91M_⊙, a spectral type G2-5IV and an evolutionary age of 9200 Myrs. If we fit the models for postAGB stars from Miller Bertolami (2016), we obtain a MS mass of 1.02 M_⊙ and an age of 9244 Myrs for Abell 34 CS. These values allow us to confirm a common binary scenario for the evolution of these stars. An HR diagram showing the position of both Abell 34 CS and its comoving companion star is shown in Fig. 3.

Fig. 3 HR diagram showing the positions of both Abell 34 CS and its comoving companion star (rhomboid symbols). The CS is plotted together with the 0.532 M⊙ evolutionary track from Miller Bertolami (2016), that corresponds to a mass of 1.0 M⊙ in the MS.Ages shown on the track refer to the post-AGB phase. In order to obtain the age from the MS, a value of 9244 Myr must be added. The companion star is plotted together with the 9200 Myr isochrone and ZAMS from PARSEC models in Gaia passbands (Evans et al. 2018). Masses are expressed in units of solar mass (M⊙).

3.4 NGC246

This PN (Fig. A.1), also known as the Skull nebula, is located at a distance of 506 pc from the Sun. It is characterised by an elliptical morphology and a medium size, with a mean radius of 0.298 pc (~61 000 AU). We detected a comoving star with a projected separation of 2,118 AU from the CSPN. According to Adam & Mugrauer (2014), this PN has associated a triple system of stars, with two companions with separations around 500 AU and2000 AU. In this context, we detected the farthest one, while the closest one cannot be resolved in the light of Gaia DR2 data. From the photometry fit to PARSEC models, NGC 246-B has a mass of 0.85 M_⊙ and a spectral type G8-5, while we assume a progenitor mass for NGC 246 CS of 3.75 M_⊙, as previously discussed. An optical spectrum that was recently obtained at the INT telescope using the IDS spectrograph allows us to confirm an intermediate spectral type for NGC 246-B, as well as to obtain a radial velocity value of − 13 ± 8 km s⁻¹, compatible with the known value for thecentral star of −16 km s⁻¹.

3.5 NGC3699

NGC 3699 (Fig. A.1) is located at a distance of 1506 pc from the Sun. It has a bipolar morphology, a small mean radius of 0.153 pc (~32 000 AU), and it presents a quite high extinction in the G passband. We have identified a binary companion with a projected separation of 5036 AU from the CS. By fitting DR2 photometry to PARSEC models, we obtained a mass of 1.16 M_⊙ and a late-F spectral type for this star.

3.6 NGC 6853

The NGC 6853 nebula (Fig. A.1), also known as the Dumbbell Nebula, is located at only 372 pc from the Sun. It has a bipolar shape and a medium mean radius of 0.368 pc (~76 000 AU). In this case, we detected two wide binary companions, one of them with a projected separation of 2453 AU from the CS and the other with a projected separation of 3322 AU. For the former, DR2 photometry allowed to derive a mass of 0.59 M_⊙ and a late-K spectral type. The latter comoving star, is faint (G = 18.99) and Gaia colour (G_BP − G_RP) is not available for it. By fitting the SED available at the SVO with the VOSA tool, we find that it is a late M-type star with a mass value of 0.2 M_⊙.

NGC 6853 is included in the David Jones catalogue² of binary PNe. The existence of a binary in NGC 6853 was first suggested by Cudworth (1973), who identified a companion with V = 17 located at 6.5 arcsecs from the central star, which is coincidental with the brightest of our wide companions. In 1977, astrometric measurements by Cudworth confirmed that the proper motions agree with those of the CS. These results are further confirmed by Gaia DR2 astrometry. Regarding NGC 6853-C, it is the faintest star in our sample, with the highest errors in the astrometric parameters, namely, 22% in parallax, but with overall values that meet our selection criteria. Forthcoming EDR3 astrometry will help to clarify if B and C stars form a bound pair orbiting NGC 6853 CS.

3.7 PHR J1129-6012

PHR J1129-6012 (Fig. A.1) is an elliptical PN located quite far from the Sun, at 2159 pc. It is a small nebula, with a mean radius of 0.099 pc (~20 000 AU). We detected a comoving object with a projected separation of 9551 AU from the CS. Both stars in the system have similar brightness (mag G ≈ 17) and similar Gaia colour (G_BP − G_RP ≈ 1) which appears interesting and warrants further study of this object. We note that a high interstellar extinction is expected for this nebula, as itis located at a very low galactic latitude; this fact perhaps explains the red colour observed for the CS.

Very recently, Chornay & Walton (2020) highlighted the fact that CSPN identifications in commonly used PN catalogues are highly uncertain and so, they published a new catalogue of CSPN using DR2 astrometry and colours (G_BP − G_RP) to more accurately identify the bluest and more centred star within a nebula. In their catalogue, they assign a probability of only 40% to PHR J1129-6012 CS being the CSPN. In fact, The Hong Kong/AAO/Strasbourg H_α (HASH) database provides a spectrum of this source, which allows us to derive an extinction value E(B − V) close to 1. In that case, it would imply that the absolute brightness of this pair of stars would not correspond to that of a CSPN and, therefore, the identification would not be correct.

3.8 PN SB 36

PN SB 36 (Fig. A.1) is also a very small PN, with a mean radius of 0.029 pc (~6000 AU). It is located 1610 pc away from the Sun, close to the galactic plane. We identified a comoving object with a projected separation of 14 880 AU from the CS. Although PN SB 36 is included in our GAPN sample (concretely from Kerber et al. 2003), there are lingering doubts as to whether it really is a PN since its spectrum in the HASH database shows only H_α emission.

4 Conclusions

Using Gaia DR2 astrometry (parallaxes and proper motions), we found nine wide binary companions associated to eight CSPNe in the GAPN sample (Golden Astrometry Planetary Nebulae, González-Santamaría et al. 2019), with projected separations of less than 15 000 AU in all cases. When we searched for comoving objects to these CSPNe, we applied quite strict selection criteria in order to avoid any false comoving object detection. Furthermore, we did a thorough analysis to estimate the probability of any of the companion stars having been detected by chance and we obtained very low values.

Some of the binary pairs were already listed as possible binaries in the literature, and Gaia DR2 astrometry has allowed us to confirm them as such. We also found two of the CS identifications as doubtful, although the binary pairs are potentially related. Our procedure allows us to identify a limited number of systems due to the errors present in DR2 astrometry, but it is also a useful introductory methodology that could potentially allow us to identify larger numbers of binary systems in the future when Gaia DR3 and later archives become available. By using appropriate evolutionary models, we were able to estimate masses for both the CS and the binary companions that are compatible with a joint evolution scenario. Furthermore, the companion of Abell 34 CS has already evolved out of the MS and we were able to obtain a value for its age, which is in satisfactory agreement with the age obtained for the nebula central star.

In this work, we limit ourselves to the search for distant binary partners. In a recent study, Bear & Soker (2017) proposed that hierarchical triple systems can explain the morphologies of PNe, in displaying large departures from axisymmetrical and point-symmetrical structures, and, in some cases, from mirror-symmetry. Among our eight listed nebulae, we find a variety of morphologies, such as round (Abell 33, Abell 34 and PN SB 36), elliptical (Abell 24, NGC 246 and PHR J1129-6012), and bipolar (NGC 3699 and NGC 6853), so there is no correlation between our wide binaries sample and the nebular morphology. However, multi-band, highly sensitive, and high spatial resolution images would be needed to distinguish morphological structures that could give us clues on the possible influence such wide companions might have had.

Bear & Soker (2017) pointed out that very wide tertiary stars, or even higher-order hierarchical systems at hundreds of AU, cannot play a significant role in shaping the morphologies. All our wide binary companions are too far from the central star to influence their nebula morphology under the mechanisms proposed by these authors. Nevertheless, one of our objects, NGC 3699, is included in their catalogue under the category of objects “shaped by a triple system”. We will have to wait for the forthcoming Gaia DR3 release to expand the search for binaries to include objects located closer to the CS so that we might be able to contribute agreater volume of statistics to the study of the influence of binary systems – hierarchical or otherwise – in the shaping of PNe.

Acknowledgements

This work has made use of data from the European Space Agency (ESA) Gaia mission and processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and the ALADIN applet. The authors have also made use of VOSA, developed under the Spanish Virtual Observatory project supported by the Spanish MINECO through grant AYA2017-84 089, and partially updated thanks to the EU Horizon 2020 Research and Innovation Programme, under grant 776 403 (EXOPLANETS-A). The INT is operated on the island of La Palma by the Isaac Newton Group of Telescopes in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. Funding from Spanish Ministry projects ESP2016-80 079-C2-2-R, RTI2018-095076-B-C22, Xunta de Galicia ED431B 2018/42, and AYA-2017-88 254-P is acknowledged by the authors. I.G.S. acknowledges financial support from the Spanish National Programme for the Promotion of Talent and its Employability grant BES-2017-083126 cofunded by the European Social Fund. We also wish to acknowledge the support received from the CITIC, funded by Xunta de Galicia and the European Union (FEDER Galicia 2014-2020 Program) by grant ED431G 2019/01.

Appendix A Images

Fig. A.1 Identification images of Abell 24, Abell 33, Abell 34, NGC 246, NGC 3699, NGC 6853, PHR J1129-6012, and PN SB 36 nebulae (from left to right and from up to down), showing the location of both the CSPN (arrow) and the comoving companions. Images from ALADIN applet.

References

All Tables

All Figures

	Fig. 1 Probability distributions for parallax and proper motions of objects in the neighbourhood of Abell 24 (left) and PN SB 36 (right). The black arrow indicates the interval corresponding to the CS parameters values.
In the text

	Fig. 2 Fits to NextGen (AGSS2009) models of Abell 33 - B and NGC 6853 - C spectral energy distributions obtained with VOSA tool from the Spanish Virtual Observatory.
In the text

Fig. 3 HR diagram showing the positions of both Abell 34 CS and its comoving companion star (rhomboid symbols). The CS is plotted together with the 0.532 M⊙ evolutionary track from Miller Bertolami (2016), that corresponds to a mass of 1.0 M⊙ in the MS.Ages shown on the track refer to the post-AGB phase. In order to obtain the age from the MS, a value of 9244 Myr must be added. The companion star is plotted together with the 9200 Myr isochrone and ZAMS from PARSEC models in Gaia passbands (Evans et al. 2018). Masses are expressed in units of solar mass (M⊙).

In the text

	Fig. A.1 Identification images of Abell 24, Abell 33, Abell 34, NGC 246, NGC 3699, NGC 6853, PHR J1129-6012, and PN SB 36 nebulae (from left to right and from up to down), showing the location of both the CSPN (arrow) and the comoving companions. Images from ALADIN applet.
In the text