© ESO 2021

1 Introduction

Planetary nebulae (PNe) are a brief but enigmatic stage in the evolution of low- and intermediate-mass stars towards the ends of their lives. Central stars of PNe (CSPNe) are some of the rarest objects observed by Gaia (Gaia Collaboration 2016), a European Space Agency (ESA) mission conducting precision astrometry and photometry for nearly two billion sources in the Milky Way and beyond. Gaia shows great potential for the study of PNe: parallaxes inform distance estimates and in turn CSPN absolute magnitudes and evolutionary phase; proper motions add more dimensions to dynamics and relate PNe to their parent stellar populations, constraining ages and masses; and repeated photometric observations enable the study of variability and binarity.

Unlocking Gaia’s potential requires a complete and accurate cross-match of Gaia sources with CSPNe. Chornay & Walton (2020; hereinafter CW20) used an automated approach to generate an extensive catalogue of candidate CSPNe in Gaia Data Release 2 (DR2, Gaia Collaboration 2018). The nature of Gaia’s iterative release process necessitates updates to catalogues based on Gaia data, as the set of sources and their identifications changes between releases (Torra et al. 2021). Moreover, when the Gaia data themselves are used for cross-matching, better data translates into improved accuracy. In this work, we present a new catalogue of candidate CSPNe and compact PNe in Gaia Early Data Release 3 (EDR3, Gaia Collaboration 2021) based on the same methodology as CW20. With a completely new Gaia catalogue not expected for some time, this will provide a valuable resource for the study of Galactic PNe for years to come.

2 Methods

2.1 Input catalogues

Our PN positions come from the Hong Kong/AAO/Strasbourg Hα (HASH) PN catalogue (Parker et al. 2016, as of 5 July 2021), which now contains 2670 ‘true’ PNe (those with spectroscopic confirmation; an 8% increase since CW20) and 3800 PNe in total (including likely and possible identifications). We saw in CW20 that three very extended PNe had CSPNe more than 60′′ away from the HASH positions, outside of our search radius. To address this we adopt positions for Sh 2-188 from Weidmann & Gamen (2011) and for FP J1824-0319 and FP J0905-3033 from Parker et al. (2006). Gaia EDR3 is likewise larger than DR2. The longer survey duration (12 more months, for 34 months in total), along with improved calibration, results in higher completeness (7% more sources overall) and greater astrometric precision. The set of sources in EDR3 is distinct from that ofDR2 not only in that more sources are present; some may have disappeared or changed identifiers (Torra et al. 2021). Gaia Data Release 3 (DR3) will include the same sources as EDR3 but with additional data products.

2.2 Cross-matching

We use the same method employed in CW20, and here provide a brief review, pointing the reader to this earlier work for a more detailed background. The aim is to automatically match CSPNe or compact and stellar-like nebulae to Gaia sources. The expectation is that these sources will be close to the catalogued position of the PN, but the possibility of non-detections, background interlopers, and positional inaccuracies necessitates a more nuanced approach than simple nearest-neighbour matching.

The likelihood ratio method of Sutherland & Saunders (1992) is well-suited to this aim. Given a candidate match at angular separation r, the approach compares the probability of finding a genuine match at r to finding a background object. Our implementation assumes a uniform background density in each field, and a radially symmetric positional distribution of genuine CSPNe parameterised by the radius of the PN (allowing larger PNe to have more offset CSPNe, albeit with lower probability). We also employ the colour distributions of true CSPNe and background sources, which are parameterised based on the photometric excess factor (Evans et al. 2018), with the effect of down-weighting colours for sources whose colour is potentially contaminated by nearby sources or background. Distributions are derived iteratively, using sources withsecure identifications based on colour to empirically determine the positional distribution of genuine CSPNe, and in turn using the positionally secure sources to update the colour distribution. This works because CSPNe are often much bluer than typical Gaia sources and can therefore be selected purely based on colour with relatively high confidence.

We made a few small changes to the algorithm’s treatment of the G_BP –G_RP colours. In deriving the initial and final colour distributions, we only considered sources with G brighter than 19, which have relatively precise colours. In computing the likelihood ratios for individual sources, we then convolved the densities with the photometric uncertainties after accounting for the smoothing already applied by the kernel density estimation. This lessens the impact of faint sources with extreme and likely spurious colours. We also adopted the prescription of Riello et al. (2021) for describing a locus of photometric excess values of well-behaved sources. The photometric excess is no longer used by Gaia as a filter for published photometry, though for large excess values the photometry is still not very discriminative, as it is likely dominated by the background.

We retrieved all Gaia EDR3 sources within a 60′′ radius of the PN positions from HASH. All of these were used in calculating the background density and colour distribution (the latter only for G < 19), while only the subset of sources within half each PN angular size (taken from HASH) plus 2′′ were considered as candidates. For each PN, the set of candidate likelihood ratios were used to calculate reliabilities (the probability that a given candidate is the correct match).

3 Catalogue

The improved method applied to EDR3 produces a bimodal distribution of top match reliabilities similar to that from CW20 for Gaia DR2 (Fig. 1, lower left; for clarity only ‘true’ PNe are shown). Most sources have reliabilities close to their values from CW20; these are near the diagonal (region C) in the upper left plot of Fig. 1. Points in regions A and E represent the most significant changes, typically due to removed or new sources respectively. Counts of PNe in these regions are in Table 1, including ‘likely’ and ‘possible’ PNe. In addition, there are 207 new PNe in HASH since CW20 (included in Fig. 1; lower left); of these, 107 have candidates with reliability >0.2. There are also 22 objects published in CW20 that are no longer listed as PNe in HASH (not shown).

As with the previous iteration, the method retrieves blue CSPNe even out to large separations (Fig. 1, right; the largest PN in the cluster at the upper left has an angular radius of nearly 600′′). The few sources with unphysically blue colours are scored lower due to their large photometric uncertainties.

The complete catalogue of the 2117 highest ranked candidates with reliability >0.2 is in Table A.1. The catalogue includes the Gaia source identifier corresponding to the best match for each PN, the reliability of that match, and its angular separation from the PN position from HASH. Copied into the catalogue are relevant data from HASH (name, PN G identifier, PN coordinates, angular size,and confirmation status) and Gaia EDR3 (source coordinates, photometry, and astrometry). We additionally include the image parameter determination (IPD, Lindegren et al. 2021b) goodness-of-fit harmonic amplitude from Gaia (see Sect. 3.3) and the combined statistical and parallax distance derived in this work (see Sect. 4.2).

Fig. 1 Matching results for ‘true’ PNe. Top left panel: reliability of the CW20 Gaia DR2 matches versus the EDR3 matches from this work for PNe present in both. Red points are PNe where the location of the best candidate match has changed by more than 0′′.1. All of thesepoints are contained in the histogram in the lower left panel, which also includes PNe that were not in CW20. Upper right panel: separation versus colour distribution of highest-ranked candidates, colour-coded by reliability with the non-linear scale shown in the bottom right corner. Rings around markers indicate PN angular sizes.

3.1 Individual objects

Figure 2 shows wide- and narrow-band imagery from the VPHAS+ survey (Drew et al. 2014) overlayed with Gaia EDR3 (and DR2) sources for four PNe chosen to exemplify significant changes encountered in Gaia EDR3. Data from VPHAS+ were not used as part of the matching, but the images, which capture stellar colours and nebula emission, provide good examples of some of the changes encountered in the updated Gaia data.

KFL 16 and BMP J0713-0432 both have new detections in EDR3. The CSPN of KFL 16 has no Gaia colour but is sufficiently central that it is selected; its blue colour is evident in the VPHAS+ imagery. The CSPN of BMP J0713-0432 exhibits a blue G_BP –G_RP colour and as such is correctly identified despite not being the closest source to the PN position from HASH.

NGC 2440 had a clear CSPN detection in DR2. In EDR3 the central region of the PN now contains many nebula detections. The true CSPN is still selected based on its position (it is overwhelmed by the bright nebula in VPHAS+ but clear in space-based imagery), but with reduced confidence on account of the many new nearby sources. In the case of MaC 1–12, the lone detection from DR2 has disappeared, and no matching EDR3 source is found.

Fig. 2 VPHAS+ images of select PNe centred on their coordinates from HASH. North is up and east is to the left. The left two columns are colour images in different sets of filters, while the right two columns are quotient (r′ – Hα) images overlayed with Gaia sources coloured according to their GBP–GRP colours, with the best match highlighted.

3.2 Visual binaries

Visual binaries are astrophysically interesting because, among other reasons, characterisation of the companion can provide an estimate of the distance to the pair and thus to the PN. However, close companions – whether genuine or merely a chance alignment – can provide a challenge for our matching. Of the 53 PNe with two potential matches (two candidates with reliability > 0.2), about half are pairs with a separation of less than 1′′. These likely include some genuine binary systems, though their blended colour photometry and degraded astrometry makes it difficult to characterise the companion star and secure its relation through astrometry (e.g. González-Santamaría et al. 2020).

Some CSPNe are visual binaries in Hubble Space Telescope (HST) imagery: ten are presented in Ciardullo et al. (1999) (‘probable associations’) as well as additional pairs in Benetti et al. (2003) and Liebert et al. (2013). Typical separations of known pairs are fractions of an arcsecond; these appear blended from the ground. With the improved resolution of Gaia EDR3, we expect that more of these will be resolved: the source separation limit has decreased to 0′′.18 from 0′′.4 in DR2, but incompleteness starts to set in below 1′′.5 and is quite severe below 0′′.7 (Fabricius et al. 2021).

The detections for these PNe are listed in Table 2. Even sources not separated by Gaia can show signs of binarity if they have a non-zero IPD multipeak fraction, which indicates that some detections show multiple peaks. These can indicate a close visual binary, though depending on the separation it may only be resolved in some scan directions.

Abell 33 and NGC 3132 have companions at wide separations detectable from the ground (though the catalogue position of NGC 3132 is actually closer to that of the companion star, leading to ambiguity in our matching results). Of the closer pairs, only K 1–22 is resolved into separate sources by Gaia, possibly on account of their similar magnitudes. Another four PNe have a notable fraction of multi-peak detections, while the remaining PNe seem to have companions that are either too faint (e.g. Abell 31 and K 1–27) or too close (e.g. NGC 6818). The re-normalised unit weight error (RUWE, indicative of excess astrometric error; Lindegren 2018) values range from normal to significant, and none are labelled as duplicated sources.

3.3 Nebula detections

It is expected that for compact PNe, Gaia may not detect the CSPN but rather the bright central region of the nebula. Gaia can also detect features in extended PNe; this was seen early on in Gaia’s mission for NGC 6543 (Fabricius et al. 2016)¹. These detections were filtered out in the first two data releases, leaving only the eleventh-magnitude CSPN. Now in EDR3, some have returned (Fig. 3, upper left; cf. Fig. 14 in Fabricius et al. 2016).

A strong indicator that these sources are non-stellar is the large values of IPD goodness-of-fit harmonic amplitude (which we abbreviate to HA). This is newly included in Gaia EDR3, and measures how the astrometric goodness-of-fit varies with scan angle. A large HA suggests an elongated source, such as a galaxy or a partially resolved binary².

The lower left panel of Fig. 3 shows the HA distribution for all of our high-confidence matches (‘true’ PN with reliability >0.8), parameterised by the angular size of the PN. Many compact PNe have larger HA values indicating likely nebular detections (compared to the values for extended PNe, whose detections we expect to be stellar). The lower right panel shows the distribution of all candidate matches for a few select objects. There is a clear separation between the stellar CSPN, nearby nebula detections (sources within the radius of the PN that have high HA), and (usually more distant) field stars.

Nebula detections of extended PN appear rare, and to keep our approach simple, we do not use the HA in our matching. We nevertheless include it in our catalogue as an approximate way to check how stellar-like a source is. Large values should be treated with caution, particularly in conjunction with a high photometric excess factor, but do not necessarily indicate a nebula detection.

We note that, so far, these detections are not useful for studies of nebular evolution. NGC 6543 for example has a measured expansion rate of 3.13 ± 0.16 mas yr⁻¹ (similar to other PNe; Schönberner et al. 2018), large enough for Gaia to detect as proper motion. However, the nebula detections have only two-parameter solutions (positions only) with uncertainties much larger than any change due to expansion over Gaia’s mission duration.

Fig. 3 Nebula detections for bright PNe. The upper images are HST narrowband images of NGC 6543 (left) and the central region of NGC 5189 (right) overlayed with Gaia EDR3 sources (coloured points and crosses). Error bars have been rotated to reflect the direction of the principle component of the error covariance matrices, and scaled by a factor of 100 for visibility. The lower plots show the distribution of IPD goodness-of-fit harmonic amplitudes.The left plot shows the distribution for the best matches versus PN angular radius on a linear colour map for all best matches in our catalogue, with locations of the CSPNe of the PNe above (and NGC 2440 from Fig. 2) highlighted. The right plot shows all sources in the vicinity of these PNe, plotted against angular separation on a log scale. Vertical lines indicate the PN radii; the lack of points past 60′′ is a result of our selection cutoff. (Images credit: Hubble Legacy Archive/ESA/NASA.)

4 Distances

Distances to Galactic PNe have long been a key challenge in the study of PNe, with most distances reliant on statistical relations such as the Hα surface brightness to physical radius relation of Frew et al. (2016; hereinafter FPB16). The precision of the parallaxes in Gaia EDR3 should translate into improved precision in distance determinations, but leveraging these parallaxes is not entirely straightforward.

4.1 Parallaxes compared to statistical distances

Following Smith (2015), parallaxes can be used to evaluate the accuracy of a statistical distance scale using distance ratios, that is, the per-object product of statistical distance and parallax. An accurate statistical relation should yield a distance ratio distribution centred on unity. We use this method to compare Gaia parallaxes to the statistical distance scale of FPB16. Parallaxes are corrected for the zero point bias following Lindegren et al. (2021a). We use the sub-trend relations where applicable, and the same quality cuts as in CW20, with the aim of selecting high-quality measurements without biasing the sample (‘true’ PNe, reliability > 0.98, visibility_periods_used > 8, RUWE < 1.4, parallax error < 0.2 mas).

We find a median ratio of 1.03 ± 0.02 and a mean ratio of 1.11 ± 0.04 (uncertainties calculated via bootstrap). The overall distance scale is matched well (with some suggestion of the distances being slightly high), now with nearly twice as many objects being considered (294 compared to 160 in CW20). There is no statistically significant trend versus the PN surface brightness, implying the slope of the relation is reasonably accurate.

The effect of the parallax zero point correction (typically on the order of the median quasar parallax, −0.017 mas) is to make most parallaxes larger (implying smaller distances). Without the correction, the distance ratios would have a smaller median value of 0.97, and exhibit a small but significant trend with surface brightness, even after accounting for outliers. This demonstrates the need for caution when interpreting parallaxes, particularly for a population in which systematic errors can have noticeable effects.

4.2 Statistical distances as a prior

Estimating distances from parallaxes is well known to require a proper prior (Luri et al. 2018). Bailer-Jones et al. (2021; hereinafter BJ21) adopted two different priors for their catalogue covering most of Gaia EDR3: one based on a galaxy model and another that additionally incorporates Gaia photometry. Naturally, the effect of the adopted prior is greatest for stars with relatively large parallax uncertainties, which tends to result in distant, faint stars with underestimated distances. The photometry prior aims to mitigate such effects. The rapid evolution of CSPNe makes such photometric distances less useful. However, the relation between Hα surface brightness and physical size of the PN used in FPB16 can perform a similar function.

For each PN, we use the statistical distance of FPB16 and its uncertainty as a prior P(d), having shown in the previous section that the FPB16 scale remains broadly consistent with the Gaia parallaxes. The Gaia parallax ω and its uncertainty σ_ω provide the likelihood P(ω|d, σ_ω). We compute the posterior distance distribution on a fixed grid with 1 pc steps between 0 and 60 kpc (twice the largest prior distance), by simply applying Bayes’ theorem, that is, taking at each distance d the posterior probability to be the product P(d)P(ω|d, σ_ω), normalised by the sum of these values over the domain of the prior.

Following the catalogue format adopted by BJ21, we summarise the posterior by its median and 16th and 84th percentiles. We publish these values in our catalogue for all 733 sources with both parallaxes and statistical distances, regardless of reliability or excess astrometric noise; both of these latter should be considered when adopting the distances. There are an additional 131 sources in our catalogue that lack statistical distances but have relative parallax errors of better than 20%; we do not publish distances for these but expect the distances from BJ21 to not be overly influenced by their choice of prior.

Treating the width of the distributions as the difference between the 16th and 84th percentiles, the median precision improvement (relative to the median distance) over the statistical distance prior is 1.4, with one-third of the sample having its relative uncertainties improved by a factor of two or more (Fig. 4, left). A small fraction of sources have less concentrated posteriors, typically in the case where the prior and posterior modes have a large separation. The parallaxes dominate the uncertainties below relative errors of about 0.15 (Fig. 4, right).

The advantage of our adopted distances is that they leverage the Gaia parallaxes while smoothly transitioning to statistical distances in cases where parallaxes are unavailable or extremely uncertain. For simplicity we have only considered the mean relation of FPB16; a similar approach could be taken incorporating the sub-trends in FPB16 or even the Galactic model of BJ21. The most appropriate prior will of course depend on the application.

Fig. 4 Improvement over statistical distances of combined distances for ‘true’ PNe with high-reliability matches. Left panel: distribution of statistical and combined distances and relative uncertainties, with lines connecting pairs of points corresponding to the same object. Right panel: cumulative distribution of relative uncertainties for parallaxes, statistical distances, and combined distances. The dotted lines for parallaxes and statistical distances are counts including objects with only parallaxes (not in FPB16) and all ‘true’ PNe from FPB16 (not necessarily having parallaxes or Gaia matches) respectively.

5 Conclusions

In this work, we present a new version of our catalogue of candidate CSPNe and compact nebula detections, updated for Gaia EDR3 and including newly identified PNe from HASH. While we have made small improvements to the matching algorithm, the minimal changes required demonstrate the robustness of our original method. We have also discussed the effects of close companions and nebula detections, and introduced a novel approach to combining PN statistical distances and Gaia parallaxes.

The next Gaia data release, Gaia DR3, is expected in 2022. It is based on the exact same astrometric and photometric data as Gaia EDR3. Therefore, the astrometry from this Gaia EDR3 release will remain the best available for studying PNe based on their distances and kinematics until the full nominal mission Gaia data release in several years to come³.

Acknowledgements

We would like to thank the referee, W.A. Weidmann, for his comments, which have helped improve the contents and clarity of this paper. This research has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (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 Multilateral Agreement. This research has also made use of the HASH PN database (http://hashpn.space), and of Astropy (http://www.astropy.org), a community-developed core Python package for Astronomy (Astropy Collaboration 2013, 2018). Parts of this research were based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 177.D-3023, as part of the VST Photometric Hα Survey of the southern Galactic plane and bulge (VPHAS+, http://www.vphasplus.org). This research was supported through the Cancer Research UK grant A24042.

References

All Tables

All Figures

Fig. 1 Matching results for ‘true’ PNe. Top left panel: reliability of the CW20 Gaia DR2 matches versus the EDR3 matches from this work for PNe present in both. Red points are PNe where the location of the best candidate match has changed by more than 0′′.1. All of thesepoints are contained in the histogram in the lower left panel, which also includes PNe that were not in CW20. Upper right panel: separation versus colour distribution of highest-ranked candidates, colour-coded by reliability with the non-linear scale shown in the bottom right corner. Rings around markers indicate PN angular sizes.

In the text

	Fig. 2 VPHAS+ images of select PNe centred on their coordinates from HASH. North is up and east is to the left. The left two columns are colour images in different sets of filters, while the right two columns are quotient (r′ – Hα) images overlayed with Gaia sources coloured according to their GBP–GRP colours, with the best match highlighted.
In the text

Fig. 3 Nebula detections for bright PNe. The upper images are HST narrowband images of NGC 6543 (left) and the central region of NGC 5189 (right) overlayed with Gaia EDR3 sources (coloured points and crosses). Error bars have been rotated to reflect the direction of the principle component of the error covariance matrices, and scaled by a factor of 100 for visibility. The lower plots show the distribution of IPD goodness-of-fit harmonic amplitudes.The left plot shows the distribution for the best matches versus PN angular radius on a linear colour map for all best matches in our catalogue, with locations of the CSPNe of the PNe above (and NGC 2440 from Fig. 2) highlighted. The right plot shows all sources in the vicinity of these PNe, plotted against angular separation on a log scale. Vertical lines indicate the PN radii; the lack of points past 60′′ is a result of our selection cutoff. (Images credit: Hubble Legacy Archive/ESA/NASA.)

In the text

Fig. 4 Improvement over statistical distances of combined distances for ‘true’ PNe with high-reliability matches. Left panel: distribution of statistical and combined distances and relative uncertainties, with lines connecting pairs of points corresponding to the same object. Right panel: cumulative distribution of relative uncertainties for parallaxes, statistical distances, and combined distances. The dotted lines for parallaxes and statistical distances are counts including objects with only parallaxes (not in FPB16) and all ‘true’ PNe from FPB16 (not necessarily having parallaxes or Gaia matches) respectively.

In the text