© The Authors 2025

1. Introduction

Planetary nebulae (PNe) are the ejected material associated with the final stages of evolution of low-to-intermediate stars (up to 8 M_⊙). Since these stars represent the vast majority of stars more massive than our Sun and dominate the chemical enrichment of our Galaxy, at least with respect to the light elements, their detailed study is of major importance for understanding how matter is distributed and recycled across the Galaxy.

One major problem in PN studies is the lack of reliable data for the mass of their main sequence (MS) progenitors. If known, this would allow a direct determination of the link between their initial and final masses. While such an estimation is an unreliable task for general PNe, this is not the case for PNe that are physically associated with star clusters. In these rare cases, the PN initial masses can be estimated with adequate precision from independent studies of the cluster turn-off mass via colour-magnitude diagrams (CMDs) and theoretical cluster isochrone fitting.

Unfortunately, the PN phase is very brief, typically just a few tens of thousands of years (Badenes et al. 2015), though the oldest PN known also resides in an open cluster (OC) with a kinematic age of 78 000 ± 25 000 years but is an extreme, unique outlier (Fragkou et al. 2022). OCs are relatively young, typically a few hundred million years old, and so only higher-mass progenitors can form PNe within such clusters (e.g. Fragkou et al. 2019b). PNe-open star cluster associations are consequently extremely rare. Indeed, up until now, only three PNe have very strong evidence to support their physical association with Galactic open star clusters (Parker et al. 2011; Fragkou et al. 2019a,b, 2022). These associations are based on several key agreements. The most important is the tight agreement, within the small errors of the radial velocities of the PN and host cluster. This is because cluster members have a very tight velocity spread to ∼1 km s⁻¹ (Mathieu 2000). Confirmation of membership is further supplemented by agreement of distance, reddening, proper motions, and even the PN physical size at the cluster distance being feasible so that taken together these measured parameters provide a compelling case for association.

It is valuable to establish more OC-PN associations and study them in detail because of their unique capability to allow for an independent determination of the properties of their progenitors. Our new, high-resolution, spectral data for PN NGC 2818 provide high precision radial velocity measures across the PN to within 1 km s⁻¹, which were then used to determine its systemic velocity which, together with updated Gaia distances, reddening estimates, and other properties, demonstrates the likely physical association of PN NGC 2818 with OC NGC 2818A. The current agreement of radial velocities to within 1 km s⁻¹ between the PN and the cluster should be interpreted cautiously, due to the uncertainties inherent to the nebula’s systemic radial velocity determination. The tight match may be coincidental and fortuitous, given the observed error margins, but it is worth noting that the derived systemic velocity aligns well with previously reported values using different methods. We believe this adds to the evidence for cluster membership. This work should finally bring to an end the long debate about the status of this OC-PN association.

The PN NGC 2818 was first detected by Herschel in the 19th century and has been studied in detail by numerous authors (e.g. Tifft et al. 1972; Dufour 1984; Vázquez 2012; Derlopa et al. 2024). Tifft et al. (1972) were the first to report a possible association of the PN with the OC given its line-of-sight angular proximity. This cluster, taking its official designation from the possibly associated PN, was also named NGC 2818A.

Dufour (1984) conducted an early, comprehensive study of PN NGC 2818. The author found that it is a high-excitation PN with a reddening of E(B − V) = 0.23 ± 0.02, a radial velocity of 18.5 ± 1.7 km s⁻¹, an ionised mass larger than 0.6 M_⊙, a radius of 1.1 pc, an expansion velocity of 52 ± 3 km s⁻¹, a kinematic age of 22 000 years, and enhanced N and He abundances, indicating it has type I PN chemistry (Peimbert & Torres-Peimbert 1983). Assuming that the PN is a physical member of the cluster, the author estimated a PN progenitor mass of 2.2 ± 0.3 M_⊙ Frew et al. (2016) estimated a nebular reddening of E(B − V) = 0.17 ± 0.08. We use this value throughout this analysis as it generally agrees with other estimates. Gómez-Muñoz et al. (2023) also provide the most recent reddening estimate of E(B − V) = 0.186 (with no error given) that agrees well with the value we have adopted and is in good agreement with other estimates.

In different studies, the PN distance estimates are varied between 2.50 kpc (van de Steene & Zijlstra 1995), 3.05 kpc (Zhang 1995), 1.79 kpc (Phillips 2002), 2.00 kpc (Stanghellini et al. 2008), 2.50 ± 0.50 kpc (Stanghellini & Haywood 2010), 3.0 ± 0.8 kpc (Frew et al. 2016), and 4.17 kpc (Bailer-Jones et al. 2021). Agreement between PN and cluster distance estimates is a key determinant of cluster membership, so the greater than factor of two spread in PN distances among these works is an issue that needs to be resolved. The PN distance estimates are generally unreliable when based on indirect methods, and Gaia data for the PN central star (CSPN) where some of the aforementioned literature studies rely, are inconclusive due to its faintness (see below). We consider the best available statistical surface brightness radius (SB-r) relation PN distance of 3.0 ± 0.8 kpc from Frew et al. (2016) as the most reliable PN distance determination due to the proven and relatively high accuracy (∼22%) for this well calibrated statistical distance scale.

Cahn et al. (1992) estimate a nebular electron temperature of 15 200 K and a He/H abundance of 0.11 supporting the type I chemistry suggested by Dufour (1984). Frew et al. (2013) estimate an absolute nebular Hα flux of log F(Hα) = − 10.73 ± 0.04 mW m⁻², while Bucciarelli & Stanghellini (2023) find an absolute nebular Hβ flux of log F(Hβ) = − 11.28 ± 0.07 mW m⁻², a N/H abundance of 8.4 ± 0.2 and a O/H abundance of 8.5 ± 0.2, also supporting the evidence that the PN is of Type I chemistry. Moreover, recent ultraviolet (UV) studies determine a nebular near-UV magnitude of 14.382 ± 0.009 and a far-UV magnitude of 14.387 ± 0.015 (Gómez-Muñoz et al. 2023).

The identified blue CSPN is located at the projected geometric centre of the PN with $\mathrm{RA}={09}^{\mathrm{h}}{16}^{\mathrm{m}}01\stackrel{\text{s}}{.}7$ and Dec = $-36°37\prime 38\stackrel{″}{.}8$, J2000 (Weidmann & Gamen 2011). Its Gaia DR3 magnitudes are G = 19.00 ± 0.01 mag, Bp = 17.34 ± 0.04 mag, and Rp = 17.11 ± 0.05 mag, which, if converted to the Johnson-Cousins system¹ are translated as B = 19.16 ± 0.10 mag, V = 19.04 ± 0.10 mag, and R = 18.94 ± 0.08 mag. As described below, these faint magnitudes are problematic for Gaia estimates of distance.

The CSPN has a Gaia DR2 parallax of 0.27 ± 0.32 mas (indicating a distance of 3.7 kpc) and a Gaia DR3 parallax of 0.03 ± 0.21 mas (indicating a distance of 31.3 kpc). The Gaia DR3 parallax implies a very large distance that is not supported by the evidence and is very different than the one quoted in Gaia DR2. Moreover, very low, as in this case, and negative Gaia DR3 parallaxes are considered problematic and cannot be trusted. Gaia data (Gaia Collaboration 2022) have large uncertainties for the very faint CSPN magnitudes of many PNe and indeed many are beyond Gaia limits² (G = 19.00 mag, see above) so they are not reliable, including for this case, so we did not take these data into account in the following analysis. In early studies the CSPN effective temperature has been estimated to be 149 kK (Bohigas 2008) and 160 kK (Mata et al. 2016), while its Zanstra H I and He II temperatures were estimated to be 175 kK and 215 kK, respectively (Gathier & Pottasch 1988).

Detailed morpho-kinematical PN studies with ShapeX (Steffen et al. 2011) by Vázquez (2012) and more recently by Derlopa et al. (2024) reveal that the nebula has a complex, non-uniform bipolar structure with multiple microstructures, bubbles, filaments, and cometary knots. Fabry-Perot data reveal a PN size of 120 × 50 arcsec² as measured in the Hα line and 160 × 60 arcsec² in the [N II]λ6584 Å line (Derlopa et al. 2024). The bipolar PN morphology, the same as found for all other confirmed OC-PN, is consistent with that associated with higher mass progenitors and those PNe emerging from common envelope binary evolution systems, including magnetic jet ejections misaligned to the axis of symmetry of the PN’s main bipolar structure (Derlopa et al. 2024). The inclination angle of the major axis of the PN, with respect to the line-of-sight, is estimated to be 60° by Vázquez (2012) and 70° ±3° by Derlopa et al. (2024).

Vázquez (2012) find a PN polar expansion velocity of 105 km s⁻¹ and an equatorial expansion velocity of 20 km s⁻¹. Based on those, and a PN distance of 2.50 kpc (van de Steene & Zijlstra 1995), they estimate a PN kinematic age of 8400 ± 3400 yr, much lower than the value found by Dufour (1984), Derlopa et al. (2024) find a somewhat higher expansion velocity of 120 ± 20 km s⁻¹ for the bipolar nebular component and an expansion velocity of 70 ± 20 km s⁻¹ for its equatorial component, much larger than previous estimates and also atypically large for PNe. Distinct expansion velocities are also estimated for the different mictrostructures of the PN. Based on their findings and adopting a PN distance of 4.17 kpc (Bailer-Jones et al. 2021), Derlopa et al. (2024) derive a PN kinematic age of 9400 ± 2900 yr.

Such an association has been long debated across multiple studies. The PN radial velocity (a key parameter that could confirm its cluster membership when compared to that of the cluster) is estimated by different authors to range from −16 to +21 km s⁻¹ (Perek & Kohoutek 1967; Tifft et al. 1972; Dufour 1984; Meatheringham et al. 1988; Durand et al. 1998). Based on these values and the estimated cluster radial velocities from different studies, some authors claim that the PN is a cluster member (e.g. Tifft et al. 1972; Dufour 1984), while others claim that it is not (Mermilliod et al. 2001; Majaess et al. 2007; Bonatto et al. 2008). However, all these nebular radial velocity estimates are obtained from low-resolution spectral data and have large uncertainties. High-resolution spectral data and radial velocity precision of up to 1 km s⁻¹ are required for any reliable hypothesis regarding the status of this being a true PN-OC pair on this basis (see Parker et al. 2011; Zanstra 1931; Fragkou et al. 2019b, 2022). Vázquez (2012) estimate a nebular radial velocity of 26 ± 2 km s⁻¹ from their high-resolution spectra, the most reliable result until now. Using the same data Derlopa et al. (2024) estimate a nebular radial velocity of 23 ± 4 km s⁻¹, with a spectral resolution of 11.5 km s⁻¹, claiming that the PN is most probably a cluster member.

In a recent study, Rani et al. (2023) estimate a cluster membership probability of the CSPN of only 11%. Despite this, they still claim that the nebula is possibly a cluster member since the CSPN proper motion is only 3σ from the cluster’s mean and the space velocities of the two objects are very similar. Their claim is supported by the Gaia DR3 documentation, which cites that proper motion uncertainties are 0.07 mas yr⁻¹ at G = 17 and 0.50 mas yr⁻¹ at G = 20. Based on this assumption they estimate a CSPN progenitor mass of 2.10 M_⊙ and a CSPN final mass of 0.66 M_⊙. Spectral energy distribution (SED) fitting allowed Rani et al. (2023) to estimate the CSPN effective temperature equal to T_eff = 190 ± 8 kK or even higher. The CSPN radius is estimated to be 0.026 ± 0.002 R_⊙.

In this work, we intend to show that the OC NGC 2818A does indeed host the PN NGC 2818 using newly obtained Gemini High-resolution Optical SpecTrograph (GHOST) at Gemini high-resolution spectra that yield a precision in individual measures of ≃1 km s⁻¹. In Sect. 2 we explore the properties of the OC NGC 2818A. In Sect. 3 we describe the observations, while in Sect. 4 we present our results. Finally, in Sect. 5 we discuss our findings and in Sect. 6 we state our conclusions.

2. The open cluster NGC 2818A

The OC NGC 2818A is located along the line of sight of PN NGC 2818 (see Figure 1) and they share the same core identifier. The 2400 ± 300 M_⊙ (Bastian et al. 2018) cluster contains four blue stragglers and two yellow stragglers (essentially evolved blue stragglers; Rani et al. 2023), and presents an extended MS turn off (TO) point, due to stellar rotation, and low levels of differential extinction (Bastian et al. 2018). Its TO mass is estimated to be 2.1 M_⊙ (Dufour 1984).

Fig. 1. Open cluster NGC 2818A. A 450 × 450 arcsec2 colour-composite RGB image of the cluster NGC 2818A. Red is Hα, Green is short-red (SR) and Blue is broad-band blue as extracted from the UK Schmidt Telescope SuperCOSMOS Hα Survey (SHS; Parker et al. 2005) through the Hong Kong/AAO/Strasbourg Hα (HASH) planetary nebula database (Parker et al. 2016). The PN NGC 2818, can be clearly seen on the west side of the cluster’s apparent centre.

Multiple studies, listed below for convenience, have attempted to estimate the cluster physical parameters and these have been used here to estimate our reported mean cluster values from these literature determinations (Tifft et al. 1972; Pedreros 1989; Tylenda et al. 1992; Zhang 1995; Dutra & Bica 2000; Mermilliod et al. 2001; Tadross et al. 2002; Lata et al. 2002; van den Bergh 2006; Pandey et al. 2010; Kharchenko et al. 2013; Cantat-Gaudin et al. 2018; Soubiran et al. 2018; Liu & Pang 2019; Bossini et al. 2019; Jaehnig et al. 2021; Tarricq et al. 2021; Hao et al. 2021; Dias et al. 2021; Sun et al. 2021; Li et al. 2022; Liu et al. 2023; Cordoni et al. 2023; Hunt & Reffert 2024; Cavallo et al. 2024). Based on all these previously published values and estimating their error weighted average³, we found a cluster systemic radial velocity of 22.0 ± 2.6 km s⁻¹, cluster proper motions pmRA = −4.4 ± 0.3 mas yr⁻¹ and pmDec = 4.5 ± 0.3 mas yr⁻¹, a cluster mean parallax of 0.28 ± 0.03 mas (this parallax, when converted, implies a distance of $3.6_{-0.4}^{+0.5}$ kpc), a distance (as quoted in literature studies) of 3.5 ± 0.2 kpc, a reddening E(B − V) = 0.18 ± 0.02 (implying an extinction of A_v = 0.59 ± 0.07), an age of 1077 ± 64 Myr, and an iron abundance of [Fe/H] = −0.3 ± 0.1, which implies a metallicity of Z = 0.008 ± 0.002 for Z_⊙ = 0.0152 (Bressan et al. 2012). The Cardelli et al. (1989) extinction law with Rv = 3.1 was used where relevant.

In recent work, van Groeningen et al. (2023) conduct a comprehensive cluster study using Gaia DR2 data (Gaia Collaboration 2016), to identify the stars that have a high probability to be cluster members. Following their findings and using only stars that have a probability ≥90% to be physical members of NGC 2818A (244 stars) and Gaia DR3 data (Gaia Collaboration 2022), we found a systemic cluster radial velocity of 22.0 ± 1.3 km s⁻¹ (the quoted error was derived by standard error propagation of the Gaia measurement errors) with cluster member’s radial velocities having a standard deviation of σ = 5.4 km s⁻¹, a mean cluster parallax of 0.303 ± 0.003 mas (implying a cluster distance of 3.30 ± 0.03 kpc), and cluster proper motions pmRA = −4.421 ± 0.003 mas yr⁻¹ and pmDec = 4.548 ± 0.003 mas yr⁻¹. The derived parameters are in excellent agreement with the error-weighted mean of those reported by previous authors and since their estimation relies on reliable Gaia data and highly probable cluster members, we consider them as a better representation of the cluster true values and use these for the subsequent analysis.

We used, uncorrected for extinction, Gaia DR3 data for all stars within the cluster’s tidal radius of 225 arcsec from the cluster apparent centre, to construct a Gaia (B_p − R_p vs B_p) cluster colour-magnitude diagram (CMD, Figure 2). High probability (≥90%; van Groeningen et al. 2023) cluster members were overplotted in orange dots. Subsequently, we fitted in green a theoretical Padova isochrone (Bressan et al. 2012; Marigo et al. 2013; Chen et al. 2014, 2015; Marigo et al. 2017; Pastorelli et al. 2019, 2020), based on the cluster parameters derived above. We note that the isochrone does not fit very well to the data. Keeping the, highly reliable, Gaia OC distance (3.30 ± 0.03 kpc) and the consistent literature reddening E(B − V) = 0.18 ± 0.02, and using the Cardelli et al. (1989) extinction law with Rv = 3.1, we performed additional fits of multiple isochrones varying the cluster age and metallicity. Applying a χ² minimisation to our ≥90% membership probability data and the different models we found that the isochrone that best fits our data is for an age of 955 ± 70 Myr and an iron abundance of [Fe/H] = −0.024 ± 0.015 (metallicity Z = 0.0144 ± 0.0005 for Z_⊙ = 0.0152). The quoted errors reflect the best fit model if accounting for all Gaia DR3 data, within 225 arcsec from the cluster’s apparent centre, and the distance and reddening uncertainties.

Fig. 2. NGC 2818A CMD. Padova theoretical isochrones overplotted to our cluster Gaia DR3 CMD for stars within 225 arcsec from the cluster apparent centre. The orange points represent the stars with a cluster membership probability of ≥90% (van Groeningen et al. 2023). The green isochrone reflects the error weighted average of literature values and Gaia DR3 distance (age = 1077 Myr, E(B − V) = 0.18, distance = 3.30 kpc, iron abundance [Fe/H] = −0.29), while the blue isochrone is the model that best fits to our high probability membership data (age = 955 Myr, E(B − V) = 0.18, distance = 3.30 kpc, iron abundance [Fe/H] = −0.024). The red dot shows the position of the identified CSPN, located well within the white dwarf region of the cluster as expected.

To specify, the age and metallicity of the cluster were determined using a χ² minimisation. The χ² is defined as

$$\begin{array}{c}\hfill {\chi }^2=\frac{1}{\nu }{\displaystyle \sum _{i=1}^n}{\left(\frac{{\mathrm{colour}}_{\mathrm{DR}3}-{\mathrm{colour}}_{\mathrm{mod}}}{{\sigma }_{\mathrm{DR}3}}\right)}^2,\end{array}$$(1)

where colour_DR3 and colour_mod are the Gaia DR3 and Padova models colours respectively, σ_DR3 is the uncertainty of colour_DR3 and ν = n − 1 are the degrees of freedom. The value of n is the total number of stars in Gaia DR3 that have a cluster membership probability of ≥90%. We performed Monte Carlo simulations adding Gaussian noise along with their associated uncertainties into the Gaia DR3 data. A Gaussian distribution of ages for the best fit models, where the mean of the distribution represents the age of the cluster and its uncertainty, is given by the standard deviation of the age distribution. The metallicity of the cluster corresponds to the metallicity of the model that provides the best fit. We use these cluster values for the remainder of our study. From the best fitted isochrone we estimated a cluster TO mass of 1.88 M_⊙.

3. Observations

Confirming an OC-PN physical association requires the estimation of their systemic radial velocities with very high precision (≤1 km s⁻¹) due to the very low 1 km s⁻¹ cluster velocity dispersions seen in OCs. The OC radial velocity is well determined with Gaia, but there are only few similar studies about the PN. Vázquez (2012) analysed high-resolution PN spectra and find a PN systemic radial velocity close to that of the cluster, but not precise enough to confirm cluster membership. We acquired new, highly precise, high-resolution GHOST at Gemini 8.2 m spectra (Program: GS-2023B-FT212) for 11 different pointings across the PN to provide a more robust estimate for this study.

Uncertainties for individual pointings reflect the spread in radial velocities calculated from different PN emission lines. Aperture positions were carefully selected to be representative across this quite extended and evolved PN and so for reflecting the gas movements through the full extent of the nebula permitting an estimation of the systemic velocity through the average. The PN has a complex structure and different velocity components. Thus, the gas is moving in multiple directions with different speeds. For calculating the overall systemic PN velocity we had to take into account the movement of these nebular components at some level, given we have been using small integral field unit (IFU)-fibre samples and not a large IFU that can sample the full PN to provide an integrated value. Radial velocities computed from such symmetrically selected apertures counterbalance the gas’s internal movement allowing for a more precise determination of the systemic radial velocity. The observed spread of radial velocities at each pointing across the PN is because they reflect the internal gas movement and not just the systemic radial velocity, which for most compact PNe is seen in the integrated spectra determined values. Recall that typical PN expansion velocities are around 25–35 km s⁻¹ about the systemic value calculated -whereas this PN has a much higher expansion velocity. Here, the issue is resolved by selecting geometrically symmetric apertures throughout the PN that should largely ‘neutralise’ the internal gas movement. The aperture that is most representative of the PN’s systemic radial velocity is pointing f that is centred on the PN’s apparent centre and central star, and thus does not reflect internal gas movements in different directions and may be considered a reasonable proxy for the systemic velocity and agrees well with the cluster value. Unfortunately, due to the faintness of the CSPN, it would be very difficult to obtain deep CSPN spectral data of high resolution in order to compute an accurate CSPN radial velocity even with today’s best ground based facilities. For this we have to wait for the next class of telescopes and surveys.

The GHOST spectrograph was configured in the dual-IFU standard-resolution mode, which can observe two targets simultaneously by using two small and independent 1.2 × 1.2 arcsec² IFUs. GHOST’s range (383–1000 nm), is ideal for PN spectral studies since it contains their strongest optical emission lines. It consists of two separate detectors, one for the blue and one for the red arm, which collect light simultaneously. Its resolution in the standard resolution mode is normally R = 56 000, more than enough for our purpose of measuring the PN’s radial velocity at each selected point to individual precisions down to 1 km s⁻¹, but for our specific observations, this precision was a little lower than this (see below).

With ten 300-second exposures, we obtained spectra for 11 nebular pointings (labelled a-k), plus ten reference pointings in the adjacent sky for sky-subtraction (Figure 3). PN pointings a and k have been observed simultaneously and for their sky-subtraction the respective sky of the c pointing was used. For our pointings we intentionally carefully selected areas free from stars to avoid any stellar contamination in our data. Pointing f is centred on the CSPN, but it is too faint to be detected in our relatively short exposures, even with the 8 m Gemini telescope.

Fig. 3. Planetary nebula NGC 2818. A continuum subtracted Hα-SR SHS PN image indicating the position of the 11 GHOST 1.2 × 1.2 arcsec2 IFU PN (a-f) and their respective sky pointings. The pointing sizes represent the size of the GHOST IFUs.

We used a binning of 1 × 1, a slow readout, an up-looking port and silver mirror coating (the only available option at the time of the observations). The spatial binning of one of the GHOST data is a noticeable improvement in relation to the Vázquez (2012) data that have a spatial binning of two. The pixel size in the spatial direction is 0.4 arcsec. The airmass of our targets was better than 1.5 for all exposures.

The data were acquired on December 09 and 10, 2023 in a shared-risk GHOST run. This was affected by some problems with the focus (3% offset from the nominal value). The effects of this issue are minimal for observations in the dual target mode, where one of the IFUs is pointed on the sky, as in this work for most of our pointings. This is not the case for our exposure for pointings a and k, but since we used a separate sky IFU for their sky subtraction the effect is the same. A few adjustments were made in the reduction process for these out-of-focus data. These included i) setting the full-width-half-maximum (FWHM) of the Gaussian smoothing kernel to 6 pixels when reducing the flats, to account for the spatial smoothing of the slit profile caused by the poor focus and ii) extracting the spectra with uniform weighting. These steps improved the quality of the final data products despite a 10–20% reduction in the resolution (R ≈ 40 000), still more than enough for our purposes (see Sect. 4). The reduced data are free of artefacts down to the 1% level and for our analysis we do not use lines in the blue end of the spectrograph, where the dispersed orders are close enough to each other on the detector to cause possible cross-talk.

For the reduction of our data we used a combination of the DRAGONS 3.20 pipeline, as optimised for GHOST data acquired during the December 2023 shared risk run (see above), and standard Image Reduction and Analysis Facility (IRAF) techniques. For the wavelength calibration we used Thorium-Argon arc wavelength calibration lamps obtained before and after our science exposures. As our PN data have no continuum it was not possible for DRAGONS to estimate the seeing from the slit viewing camera images and fit an appropriate model to the individual fibre fluxes that is required for the extraction of the spectra. For this reason, we constructed a synthetic slit viewing camera image, as a Moffat profile of FWHM = 5″ to mimic uniform brightness, and used that instead. Since GHOST is primarily designed for point-sources (where the spatial profile is the same in all wavelengths) and because of the way that DRAGONS detects cosmic rays (based on deviations from the standard spatial profile), extended emission line sources may present some problems with cosmic-ray flagging when using a fairly uniform profile as in our case (if an emission line exists in only some of the fibres, it may get flagged as a cosmic ray and be removed from the final spectrum). Inspecting pixels flagged as cosmic rays in our data did not identify any significant issue. Barycentric correction has also been applied to our data and flux calibration was turned off, since it is not required for our science case.

The DRAGONS’s final products (i.e. the 1D spectral data of all of our PN and sky pointings, part of which are presented in Figure 4) have been transformed to the non-standard format that IRAF uses for log-linear wavelength axes. For the sky subtraction, we used the IRAF, IMAGES package task IMARITH, their respective sky pointings for pointings b-j and the respective sky pointing of pointing c for pointings a and k.

Fig. 4. GHOST spectral data. The 1D spectra showing the Hα and [N II]λ6548,6584 Å doublet for each pointing a-k are provided. In the spectra of pointings b, d, e, f, and i we can see a prominent split of the [N II]λ6548,6584 Å lines and in the pointings b, d, and f a less clear split of the Hα line.

4. Results

Using the IRAF task SPLOT, we applied Gaussian fits to the stronger nebular emission lines, the [N II]λ6548,6584 Å doublet and the Hα line, determining their peak wavelength, their Doppler shifts and hence radial velocities. We did the same for the [S II]λ6716,6731 Å doublet for estimating the nebular electron density. Pointing f is centred on the location of the CSPN but, as expected, it is too faint for any relevant absorption lines to be detected in our short exposure spectral data.

In the spectra of pointings b, d, e, f, and i, we found that the [N II]λ6548,6584 Å lines are split indicating significant nebula expansion at these sampled locations. The same applies for the Hα line for pointings b, d and f, but the split is less significant (see Figure 4). The high-excitation structure found by Vázquez (2012) in the central part of the nebula is also reflected in our data with the detection of the [He II]λ4686 Å and [He II]λ6560 Å lines in the spectra of pointings d, f and i.

From the λ6300 Å sky line of our sky exposures, which are not contaminated from nebular emission, we can measure the resolution of the instrument and the precision of the measured radial velocities. Since this line is a sky line, its radial velocity should be zero. Any deviation from this value indicates the instrumental resolution. Using all our sky pointings, we found that our data have a mean resolution of 0.08 with σ = 0.03 km s⁻¹. It is clear that the instrumentation provides more than enough precision to better than 1 km s⁻¹ in any one measurement, confirming a much better radial velocity precision than the one required for our study. The issue then is how we can use our observations to determine the best systemic velocity estimate for the PN as a whole given our distributed pointings across this resolved source and the internal velocity structure and expansion velocity differences depending on the axis used and corruption for inclination angle.

The radial velocity for each pointing was measured from the Doppler shifts of the brightest nebula emission lines: the Hα and the [N II]λ6548,6584 Å doublet. High-resolution spectra allow the peaks of the individual components of the split spectral lines to be resolved and thus, measured separately. This give us a more precise determination of the radial velocity. In lower resolution data the peak of the lines would be biased towards the brightest component giving a false estimate (Vázquez 2012). Three of our pointings (b, d, and f) present splits in all three Hα and [N II] lines, while pointings e and i, present splits only in the case of the [N II] lines. The spectra of the rest of our pointings exhibit no split lines. In the case of pointings where all the lines present a split, we calculated the average radial velocity from both components and then estimated the mean radial velocity from all lines. In the case of pointings where only the [N II] lines are split, we estimated their radial velocity from their average, omitting the Hα line, since its single peak is biased to its brightest component inducing large errors. In the case of pointings where no lines present a split, we estimated their radial velocities, as the average of the Doppler shifts of each Hα and [N II] line, based on their single peaks. Table 1 shows our radial velocity estimates for each pointing.

By taking the average of the estimated radial velocities for each pointing, we found the systemic nebular radial velocity to be equal to 23.7 ± 5.5 km s⁻¹, matching, within the errors, the cluster’s well determined radial velocity. This provides key support to PN cluster membership. No matter which emission lines are chosen for measuring the radial velocity of each pointing, the final result of the systemic nebular radial velocity remains between 22 to 24 km s⁻¹ but with different induced measurement errors. If we only take into account the more accurate split emission line results (completely omitting pointings with only single peaks), the systemic nebular radial velocity was found to be 24.5 ± 4.1 km s⁻¹. Radial velocity uncertainties for individual pointings, reflect the radial velocities calculated from different PN emission lines. Moreover, and as described in Sect. 3, the spread of radial velocities, as calculated from different pointings (see Table 1), reflects the nebular internal gas movement. Our data are not flux calibrated, plus the blue arm Hγ and Hδ lines are too faint to be detected so it is not possible to estimate the nebular reddening from our blue arm spectra using Hβ with these lines. However, recent independent estimates of the PN reddening (e.g. Frew et al. 2016; Gómez-Muñoz et al. 2023), agree very well with the determined cluster reddening of E(B − V) = 0.18 adding further evidence to the case of a true PN-OC association. The reddening estimates, in conjunction to the Frew et al. (2016) surface-brightness radius relation PN statistical distance of 3 kpc also agrees to the Gaia DR3 cluster distance, providing further support of PN cluster membership.

The nebular expansion velocity (see Table 1), was measured in each pointing from both the FWHM of the Hα line (taking into account for the thermal broadening using the λ6300 Å night sky line) and the split of the [N II] lines where present. The measured values were then de-projected based on the average (65°) of the nebular inclination angles found by Vázquez (2012) and Derlopa et al. (2024). The mean nebular polar expansion velocity was found to be equal to 91 km s⁻¹ with σ = 12 km s⁻¹, close but somewhat lower than the values found by Vázquez (2012) and Derlopa et al. (2024) (105 km s⁻¹ and 120 ± 20 km s⁻¹ respectively) by ShapeX morpho-kinematical modelling, while its equatorial expansion velocity was found to be 42 km s⁻¹, presenting a standard deviation of σ = 6 km s⁻¹. The higher expansion velocity estimates found in previous studies, are possibly a result of their employed models. The expansion velocity is interestingly atypically high for PNe.

The average [N II]/Hα line ratio was found to be 3.34 – which is typical for Type-I PNe (see Kingsburgh & Barlow 1994). Such PNe are also mostly bipolar, as in the present case, and indeed all PNe so far confirmed to lie in OCs are bipolar. The average [S II]λ6731/6716 Å ratio is used for determining electron densities (see Figure 5). For pointings b, d and i, the [S II] lines present a split, and each component has been measured separately and then added. We obtain [S II]λ6731/6716 Å= 0.72 ± 0.19 (see Table 1).

Fig. 5. 1D GHOST spectrum of pointing f (centred on the CSPN) showing the [S II]λ 6716,6731 Å doublet used to estimate Ne. Note the mild line splitting as seen in other species for other pointings.

Considering that [N II] as well as [S II] are low-ionisation lines, whose ionisation potentials are close if compared, for instance, with that of [O III], T_e[N II] is the appropriate T_e to derive N_e[S II]. The T_e[N II] = 11500 ± 800K, found by Dufour (1984) and the above [S II]λ6731/6716 Å are then adopted to obtain N_e. By using the Temden task in PyNeb (Luridiana et al. 2015), we estimated a mean nebular electron density of N_e < 100 cm⁻³ though it is clear from Table 1 that for several pointings, such as c and f in particular, that the N_e is well determined at the level of a few hundred electrons revealing real point dependent variation. The derived electron density for some pointings is an upper limit because in these cases the [S II] line ratio is close to the low density limit, as shown by Osterbrock & Ferland (2006), and therefore the [S II] lines are not sensitive enough for calculating with precision a N_e.

Even though in the spectra of pointings f and i the [O III]λ4363 Å line is detected, which would allow the direct derivation of T_e[O III], our spectra are neither flux-calibrated nor corrected for interstellar extinction, therefore only diagnostic emission-line ratios based on close enough lines, such as [S II]λ6731/6716Å, can be safely used for deriving the nebular physical parameters. The large spread of electron densities in different pointings (see Table 1) reflects the low signal-to-noise of the [S II] lines in some of our pointings and real density variations of different nebular components. The mean [S II]λ6731/6716 Å ratio was used for the determination of the mean nebular electron density as the optimal representation of the true nebular physical conditions for the calculation of the nebular ionised mass below. Density variations in individual nebular components are not expected to affect these general conditions especially since many components exceed or approach the low density limit. For these reasons, we used the mean nebular electron density N_e < 100 cm⁻³ where relevant.

5. Analysis and discussion

We adopt a PN apparent size of 140 × 55 arcsec² as the mean of its major and minor axis in Hα and [N II]λ6584 Å imaging (Derlopa et al. 2024). Using the adopted Gaia cluster distance of 3.30 ± 0.03 kpc we estimated a PN physical size of 2.24(±0.02)×0.88(±0.01) pc.

From the estimated nebular physical sizes (major and minor axes) and measured polar and equatorial expansion velocities we can determine the nebular kinematic age. We calculated separately the nebular age from its major axis and polar expansion velocity and from its minor axis and equatorial expansion velocity and then found their mean. Assuming that the expansion velocity has not changed with time, we estimated a PN kinematic age τ_k = 11 000 ± 2000 yr, slightly higher, but agreeing within the errors with age estimates from previous studies (Vázquez 2012; Derlopa et al. 2024) that assume different PN distances. Using the effective recombination coefficient of Hβ from Osterbrock & Ferland (2006), the absolute nebular Hβ flux of log F(Hβ) = − 11.28 ± 0.07 mW m⁻² (Bucciarelli & Stanghellini 2023), the adopted cluster distance and the measured electron density, and following Corradi et al. (2015), we estimated an approximation of the nebular ionised mass larger than 0.47 M_⊙. The calculated ionised mass is large compared to typical PNe that can partially be explained by the nebular complex structure, since for determining the ionised mass using the available data we had to assume spherical geometry and homogeneous structure. The PN NGC 2818 is complex in both geometry and different structures. Thus, the determination of the ionised mass here is an approximation based on the available data. A more precise determination of the ionised mass would require detailed three-dimensional data encompassing the nebula’s full spatial extent. Previous morpho-kinematic studies of this PN using 3D modelling tools, such as ShapeX (Steffen et al. 2011), show the significant role of non-uniform structures and varying expansion velocities in shaping its observed characteristics (Vázquez 2012; Derlopa et al. 2024). While these models provide a deeper understanding of the nebula’s morphology and dynamics, extending them to derive ionised mass with high precision would require integrating additional observational datasets, such as integral field spectroscopy, which is beyond the scope of this study.

The PN has a relatively high and variable Hα surface brightness, especially at certain locations, as evident in Figure 3. This is especially noteworthy given its large, physical size. Some reasons that can explain this are its relatively young age and relatively high CSPN luminosity, complex structure with multiple components and underlying mechanisms, and possible binary CSPN evolution (see Sect. 1). The relatively high CSPN luminosity and temperature (given the presence of He II emission in the PN) imply that the CSPN has recently entered the white dwarf (WD) cooling track, still having considerably potential of ionising the nebular gas, resulting in a relatively high surface brightness of the PN. Common envelope binary evolution would imply that the ejected material was mostly distributed along the axis of symmetry of the binary orbit (Jones 2024) and thus, the gas concentrated mostly in specific geometrical areas. This could explain both the nebular high surface brightness present at certain components and its bipolar shape.

Knowing the CSPN V magnitude, as converted from Gaia DR3 photometry (see Sect. 1), and using the adopted distance and PN reddening, we found the CSPN absolute magnitude to be M_v = 5.9 ± 0.3. By plotting the CSPN absolute magnitude and the derived nebular kinematic age along with the corresponding (i.e. for Z = 0.01) Miller Bertolami (2016) evolutionary tracks, we estimated a CSPN final mass of 0.58 ± 0.01 M_⊙. The quoted error reflects the uncertainties in the derivation of the CSPN absolute magnitude and nebular age.

Consequently, we over-plotted on the Miller Bertolami (2016) tracks a series of CSPN effective temperatures, from 50 to 300 kK in steps of 10 kK, and their corresponding luminosity for the derived CSPN absolute magnitude, in an attempt to estimate the CSPN effective temperature (see Fragkou et al. 2022). We found the CSPN effective temperature T_eff = 130 ± 12 kK (the error indicates the nebular age and CSPN magnitude uncertainties), well within the range of what expected for a CSPN of a Type I bipolar PN (e.g. Corradi & Schwarz 1995). In a further and independent attempt to estimate the CSPN effective temperature, we followed the Zanstra method (Zanstra 1931). From the absolute nebular Hβ flux, the CSPN V magnitude corrected for interstellar extinction and the He IIλ4686 Å/Hβ ratio from Dufour (1984), we found a Zanstra T_eff(H I) = 128 ± 39kK and T_eff(He II) = 155 ± 47kK (an error of 30% is adopted for the Zanstra temperatures) in excellent agreement with the value estimated from the evolutionary tracks. Rani et al. (2023) find a CSPN effective temperature of 190 kK from SED fitting. According to our calculations, for the CSPN to be that hot, it would require the nebular age to be less than 1100 yr, and thus either its expansion velocity should be larger than 700 km s⁻¹ or its distance less than 330 pc, which are not supported from our evidence. We believe that this discrepancy is a result of the limited points and the outdated CSPN visual magnitudes from Gathier & Pottasch (1988) that Rani et al. (2023) uses for the SED fitting and thus, their estimates cannot be reliable. For our derived CSPN effective temperature of 130 kK, we estimated a CSPN luminosity of log L/L_⊙ = 2.46 ± 0.14.

From the corresponding isochrone for the cluster’s adopted physical parameters, and taking into account the time required for a star to leave the MS and reach the post-Asymptotic Giant Branch (post-AGB) phase, we estimated a CSPN initial mass of 2.33 ± 0.10 M_⊙. The quoted error here reflects the uncertainties of the cluster’s physical parameters employed for the isochrone fit. The physical parameters of the PN NGC 2818 and its host cluster NGC 2818A, are summarised in Table 2.

The initial-to-final-mass relation (IFMR), associates the physical characteristics of WDs to these of their progenitor stars and is mainly constructed from cluster WDs (e.g. Cummings et al. 2018), since cluster membership allow the determination of their initial masses and properties. A well-established IFMR is essential for depicting the development of vital elements, such as carbon and nitrogen, in entire galaxies. Any additional data point, especially from PNe physically associated with star clusters, offers a significant contribution to the currently, poorly constrained IFMR. In Figure 6, we over-plotted the initial and final masses of the CSPN of NGC 2818, along with the latest IFMR estimates and semi-empirical ‘PARSEC’ fit (Cummings et al. 2018), plus the corresponding data points from the three other PNe currently shown to reside in OCs (Fragkou et al. 2019a,b, 2022).

Fig. 6. IFMR. The cluster-PN initial and final masses over-plotted along the IFMR data points (in grey) and ‘PARSEC’ trend (dotted line) from Cummings et al. (2018) (upper panel) and the Marigo et al. (2020) data points (in grey) and fit (continuous line) depicting the ‘kink’ between 1.5 and 2.2 M⊙ (lower panel).

Our new data point (in blue) also falls in an important gap of the IFMR and generally agrees with the latest IFMR estimates and the data points for the three other PNe in OCs currently known. Our data for the CSPN of PN NGC 2818 falls almost at the same position as the CSPN of PN PHR 1315-6555 in OC Andrews-Lindsay 1 (AL1, yellow point), recently reconfirmed to be a true OC-PN association based on HST proper motions estimates of the CSPN (Bellini et al. 2025). All the previous three OC-PN final masses fall a little lower than the general trend as is the case here too. Moreover, our new data point further confirms and delineates the upwards ‘kink’ found by Marigo et al. (2020) that is proposed to be a result of carbon star formation during the AGB phase. Our new data point is located on a sparsely populated area of the IFMR just beyond this kink implying that the kink does not extend to higher initial masses. More data filling the gap between 2.2. and 2.7 initial masses will help with providing context for the underlying mechanisms that are responsible for this peculiarity of the IFMR.

The PN N/O abundance of 0.99 ± 0.03 determined by Bucciarelli & Stanghellini (2023), does not agree with the predicted yields for a progenitor star of 2.33 M_⊙ (Karakas & Lugaro 2016). This is something that has to be further explored in future studies. It is possibly associated with the mechanisms that produce the kink depicted in the IFMR and perhaps the likely binary nature of at least the CSPN of NGC 2818 and likely several of the other OC-PN too.

6. Conclusions

Creating a link between the properties of a PN with those of its progenitor star is of vital importance. PNe that are physical members of star clusters can provide us with more robust estimates of key such properties, offering additional insights into stellar evolution. However, PNe in Galactic OCs are very rare and any new discovery is significant. We have demonstrated, with robust arguments, that the PN NGC 2818 is likely to be a physical member of the Galactic OC NGC 2818A, an association long debated in previous studies but further secured here. All crucial parameters for establishing an association of a cluster with a PN agree to within the often reduced errors from the new data presented in this study. These include agreement of distance of PN and cluster, location of PN within the cluster tidal radius, plausible cluster physical size, reddening agreement, and most importantly tight agreement of radial velocities given the 1 km s⁻¹ OC velocity dispersions (see Fragkou et al. 2019b, 2022). Taken together these present compelling evidence of true association. Future observations, including deep spectra of the central star, would provide the definitive confirmation needed to strengthen this particular argument. However, such observations are beyond most existing facilities’ capabilities due to the central star’s faintness.

We derived the physical parameters of the cluster, the PN and its CSPN along with these of its progenitor star. Our estimates agree with these from previous studies and with the latest IFMR estimates. Our new data point populates an important gap of the IFMR confirming and further limits the scope of the kink found in the IFMR by Marigo et al. (2020) by showing that it does not exceed into higher initial masses. The PN chemical yields have to be further explored, since they do not agree with current models and this is an important consideration.

So far all identified OC-PNe are evolved bipolars, nitrogen enriched and have relatively high-mass progenitors (see Table 3). This is as expected given the OC age range and so the associated and necessitated high TO masses. Four PN in this OC-PN class have now been found, with one OC-PN having an intermediate progenitor mass that is close to the limit of core-collapse supernova formation, and another OC-PN being the oldest confirmed PN ever found. Interestingly, all their final masses fall below the general IFMR trends from cluster WDs (but just about compatible agree within the errors) and can be effectively joined by a straight line. We have two further cases under study hoping to add in this rare class soon to further explore these issues.

Data availability

The Gemini spectral data are available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr (130.79.128.5) or via https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/696/A146

Acknowledgments

We thank the anonymous referee for pointing out important aspects improving the manuscript. VF thanks Fundação Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for granting the postdoctoral research fellowship Programa de Desenvolvimento da Pós-Graduação (PDPG)-Pós Doutorado Estratégico, Edital n°16/2022. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001 (88887.838401/2023-00). VF was supported by a UNAM postdoctoral fellowship at the beginning of this study. VF and RV were supported by UNAM-PAPIIT grant IN106720. QAP thanks the Hong Kong Research Grants Council for GRF research support under grants 17326116 and 17300417. DRG acknowledges FAPERJ (E-26/200.527/2023) and CNPq (315307/2023-4) grants. LLN thanks Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) for granting the postdoctoral research fellowship E-40/2021(280692). Based on observations obtained at the international Gemini Observatory, a program (Program ID: GS-2023B-FT212) of NSF NOIRLab (acquired through the Gemini Observatory Archive), at NSF NOIRLab and processed using the Gemini IRAF package and DRAGONS (Data Reduction for Astronomy from Gemini Observatory North and South), which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the U.S. National Science Foundation on behalf of the Gemini Observatory partnership: the U.S. National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea). This work made use of the University of Hong Kong/Australian Astronomical Observatory/Strasbourg Observatory H-alpha Planetary Nebula (HASH PN) database, hosted by the Laboratory for Space Research at the University of Hong Kong; This research has made use of the SIMBAD database and the VizieR catalogue access tool, CDS, Strasbourg, France (doi: 10.26093/cds/vizier). The original description of the VizieR service was published in Ochsenbein et al. (2000). This work 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). We thank Dr. Stavros Akras for his valuable input in the analysis of the data.

References

All Tables

All Figures

Fig. 1. Open cluster NGC 2818A. A 450 × 450 arcsec2 colour-composite RGB image of the cluster NGC 2818A. Red is Hα, Green is short-red (SR) and Blue is broad-band blue as extracted from the UK Schmidt Telescope SuperCOSMOS Hα Survey (SHS; Parker et al. 2005) through the Hong Kong/AAO/Strasbourg Hα (HASH) planetary nebula database (Parker et al. 2016). The PN NGC 2818, can be clearly seen on the west side of the cluster’s apparent centre.

In the text

Fig. 2. NGC 2818A CMD. Padova theoretical isochrones overplotted to our cluster Gaia DR3 CMD for stars within 225 arcsec from the cluster apparent centre. The orange points represent the stars with a cluster membership probability of ≥90% (van Groeningen et al. 2023). The green isochrone reflects the error weighted average of literature values and Gaia DR3 distance (age = 1077 Myr, E(B − V) = 0.18, distance = 3.30 kpc, iron abundance [Fe/H] = −0.29), while the blue isochrone is the model that best fits to our high probability membership data (age = 955 Myr, E(B − V) = 0.18, distance = 3.30 kpc, iron abundance [Fe/H] = −0.024). The red dot shows the position of the identified CSPN, located well within the white dwarf region of the cluster as expected.

In the text

	Fig. 3. Planetary nebula NGC 2818. A continuum subtracted Hα-SR SHS PN image indicating the position of the 11 GHOST 1.2 × 1.2 arcsec2 IFU PN (a-f) and their respective sky pointings. The pointing sizes represent the size of the GHOST IFUs.
In the text

	Fig. 4. GHOST spectral data. The 1D spectra showing the Hα and [N II]λ6548,6584 Å doublet for each pointing a-k are provided. In the spectra of pointings b, d, e, f, and i we can see a prominent split of the [N II]λ6548,6584 Å lines and in the pointings b, d, and f a less clear split of the Hα line.
In the text

	Fig. 5. 1D GHOST spectrum of pointing f (centred on the CSPN) showing the [S II]λ 6716,6731 Å doublet used to estimate Ne. Note the mild line splitting as seen in other species for other pointings.
In the text

	Fig. 6. IFMR. The cluster-PN initial and final masses over-plotted along the IFMR data points (in grey) and ‘PARSEC’ trend (dotted line) from Cummings et al. (2018) (upper panel) and the Marigo et al. (2020) data points (in grey) and fit (continuous line) depicting the ‘kink’ between 1.5 and 2.2 M⊙ (lower panel).
In the text