UOCS – III. UVIT catalogue of open clusters with machine learning-based membership using Gaia EDR3 astrometry

ABSTRACT

1 INTRODUCTION

Star clusters are test-beds for the study of stellar evolution of single as well as binary stars in diverse physical environments. Multiwavelength studies of stars in clusters help to reveal the possible formation mechanism of non-standard stellar populations (Thomson et al. 2012; Jadhav, Sindhu & Subramaniam 2019). Open clusters (OCs) in Milky Way span a wide range in ages, distances, and chemical compositions (Dias et al. 2002; Kharchenko et al. 2013; Netopil et al. 2016; Cantat-Gaudin et al. 2020). The relatively low stellar density in the OCs is also an essential factor that helps in understanding properties of binary systems in a tidally non-disruptive environment.

The OCs of our Galaxy are located at various distances from us. Thus, stars detected in any observation will be a mixture of cluster members as well as both foreground and background field stars. The identification of cluster members using a reliable method is therefore extremely important. Earlier, this was accomplished using the spatial location of stars in the cluster region, as well as, their location on different phases of a single star evolution, i.e. the main sequence, sub-giant branch, and red giant branch in the colour–magnitude diagrams (CMDs) of star clusters (Shapley 1916). However, many intriguing and astrophysically significant stars such as blue straggler stars (BSS), sub-sub-giants were not considered members due to their peculiar locations in the OC CMDs (we refer to locations other than main sequence, sub-giant branch, and red giant branch, which are part of the single star evolution, as peculiar). In order to study and understand progenitors of these stars, it is vital to establish their cluster membership. More importantly, we should also be able to estimate the membership probability (MP) of these peculiar stars, which will bring confidence when they are considered as members of an OC.

Using the proper motion (PM) of stars in the vicinity of the clusters, van Maanen (1942) made significant improvements in the membership determination. Vasilevskis, Klemola & Preston (1958) and Sanders (1971) pioneered the techniques of MP determination using vector point diagrams (VPDs). As the accuracy of PM measurements improved, membership determination using VPDs were also enhanced (Sagar 1987; Zhao & He 1990; Balaguer-Nunnez, Tian & Zhao 1998; Bellini et al. 2009; and references therein). Assuming that the field and cluster stars produce overlapping Gaussian distributions in the VPD, new techniques were developed to separate the two populations (Bovy, Hogg & Roweis 2011; Vasiliev 2019). The arrival of Gaia was instrumental in study of star clusters (Gaia Collaboration et al. 2016). Trigonometric parallax and accurate PM from Gaia DR2 has led to accurate identification of cluster members: Hertzsprung–Russell diagram of star clusters help model the stellar evolution (Gaia Collaboration et al. 2018); Cantat-Gaudin et al. (2018) identified cluster members in 1229 OCs and discovered 60 new clusters using (μ_α, μ_δ, ϖ) clustering. Similarly, Liu & Pang (2019), Sim et al. (2019), He et al. (2020), and Castro-Ginard et al. (2020) discovered new OCs by applying visual or machine-learning techniques to Gaia DR2 and identified cluster members.

We started a long-term programme for the study of UV bright stellar population in the OCs using Ultra Violet Imaging Telescope (UVIT) payload mounted on the ASTROSAT; the first Indian multiwavelength space observatory launched successfully on 2015 September 28. Our initial studies were centred around the well-studied OCs, NGC 2682 (M67), and NGC 188 (Subramaniam et al. 2016; Jadhav et al. 2019). In NGC 2682, we found many chromospherically active stars, single and massive white dwarfs (WDs), and post-mass transfer systems (BSSs, BSS+WD, etc.), particularly those with extremely low mass WDs. Their detection and characterisation are necessary to study their UV energy budget, emission mechanism, and formation pathways.

In order to identify such types of stars in other OCs, we selected clusters that are safe to be observed using UVIT (those at high galactic latitude and without bright stars in the UVIT field of view) and also have high probability of detecting UV stars. In this work, we extend our UVIT study of OCs to Berkeley 67, King 2, NGC 2420, NGC 2477, NGC 2682, and NGC 6940. They span a range of age (0.7–6 Gyr) and distance (0.8–5.8 kpc). Table 1 lists the parameters such as location in the sky, distance, age, mean PM, and radius of the OCs under study. The relevant literature surveys are included in Appendix  A.

We presented the results from NGC 2682 observations in Sindhu et al. (2019) and Jadhav et al. (2019). In this paper, we include more recent and deeper photometry for NGC 2682. It is also one of the most studied OCs with well-established CMD; hence, we compare the behaviour of other OCs with NGC 2682 to interpret the optical and UV CMDs in further sections. We also use it to validate our membership determination method against previous efforts. This paper aims to analyse the UV–optical CMDs and overall UV characteristics of these clusters. A detailed study of the noteworthy sources will be presented separately.

We used multimodal astrometric and photometric data from latest Gaia EDR3 (Gaia Collaboration et al. 2020) to create a homogeneous catalogue of cluster members in the OCs. The membership determination of OC stars, in particular the UV bright population of BSSs, binaries, and WDs, requires careful incorporation of data quality indicators from Gaia EDR3. The reduced errors in Gaia EDR3 (∼0.71x for parallax and ∼0.44x for PM; Lindegren et al. 2020; Riello et al. 2020) have therefore been used in the membership selection process. PMs of field and cluster stars can be approximated by Gaussian distributions (Sanders 1971), which can be separated analytically, and individual MP can be estimated from the distance of a star from field and cluster centre in the VPD. However, this method does not distinguish between field stars that have the same PM as cluster members. Therefore, parallax and CMD position could be used to remove field stars. Also, parallax, colour, and magnitudes have non-Gaussian distributions. In order to optimally use all the Gaia parameters, we chose supervised machine learning (ML) to segregate the cluster members. Use of ML techniques is increasing in astronomy to automate classification tasks, including cluster membership (Gao 2018a,b,c,d; Zhang et al. 2020; Castro-Ginard et al. 2020). However, as most ML techniques do not include errors in the data, we used probabilistic random forest (prf, Reis, Baron & Shahaf 2019), which incorporates errors in the data. To train the prf, we first selected the cluster members by deconvolving the PM Gaussian distributions using a Gaussian Mixture Model (gmm; Vasiliev 2019). The overall method also provides the much-needed MPs, which are necessary for stars which follow the non-standard evolution.

The paper is arranged as follows: Section 2 has the details of UVIT observations, Gaia data and isochrone models. The membership determination technique is explained in Section 3. The membership results and UV–optical photometry are presented in Section 4 and discussed in Section 5. Supplementary tables and figures are included in the Appendix. The full versions of Gaia EDR3 membership catalogue (Table B1) and UV photometric catalogues of the six OCs (Table B2) are available online.

2 DATA AND MODELS

2.1 UVIT data

The observations were carried out during December 2016 to December 2018 using different UV filters of ASTROSAT UVIT payload (ASTROSAT proposal IDs: A02_170, A04_075, G07_007, and A05_068). The log of UVIT observations is presented in Table 2, along with total exposure time in each filter. We planned observations in at least one FUV and one NUV broadband filter in order to get wavelength coverage across the UV regime for detailed study. Due to payload related issue, NUV observations were done only for early observations such as Berkeley 67, King 2, and NGC 2477. Unfortunately, no cluster members could be detected in UV observations of Berkeley 67 despite observing it in two FUV filters due to lack of FUV bright stars. The remaining three OCs (NGC 2420, NGC 2682 and NGC 6940) were observed in FUV filters alone.

Exposure time for different filters ranges from 1875 to 6596 s with a typical value of ∼ 2000 s. We used ccdlab to create science ready images by correcting for drift, field distortions, and flat fielding (Postma & Leahy 2017). Astrometry was done by cross-matching stars from UVIT (point spread function, PSF ∼1.5 arcsec) and Gaia DR2 data (PSF ∼0.4 arcsec) using iraf. The PSF full width at half-maximum (FWHM) of UVIT observations ranges from 1.1 to 1.8 arcsec with a mean value of ∼1.4 arcsec. The circular field of view of the UVIT has a radius of 14 arcmin, whereas the typical radius of the usable UVIT images is slightly less (Tandon et al. 2017).

We performed PSF photometry on all UVIT images using daophot package of iraf. We used 5σ detection and limited the catalogue up to the detections with magnitude errors < 0.4 mag. The magnitude versus PSF error plots for all the images are shown in Fig.   B1. The magnitudes were corrected for saturation following Tandon et al. (2017). We removed artefacts arising from saturated/bright stars and false detection at the edge to create the final list of UVIT-detected sources for each observed filter. We included the saturated stars in the catalogue; however, their magnitudes represent the upper limit (they are brighter than these values), and their astrometry may be incorrect by a few arcseconds. In this way, over 100 stars were detected in each image and the details of this are listed in Table 2.

2.2 Gaia data

The Gaia EDR3 data for all clusters were compiled by constraining spatial and parallax measurements. We used the r50 (radius containing half the members) mentioned in Cantat-Gaudin et al. (2020) to get the majority of the members with minimal contamination in the VPD. This region was used to calculate MPs in the gmm model. We tripled the radius for running the prf algorithm to detect more members in the outer region. The definition and formulae of independent/derived Gaia parameters used in this work are shown in Table 3. The errors of ra, dec, pmra, pmdec, and parallax are taken from Gaia EDR3. Upper limits of the photometric errors in g are calculated using the ‘mag_error’ formula in Table 3 (similar for errors in gbp, grp, bp_rp bp_g and g_rp). Errors in ruwe and aen are assumed to be zero.

The parallax_cluster, ra_cluster,dec_cluster, and radius_cluster (as mentioned in Table 1) are used to select sources near cluster using following ADQL query:

2.3 Isochrones and evolutionary tracks

We used parsec isochrones¹ (Bressan et al. 2012) generated for cluster metallicity and age, adopted from Dias et al. (2002) and WEBDA.² We used Kroupa (2001) initial mass function for the isochrones. As the UV images would detect WDs, we included WD (hydrogen rich atmosphere, type DA) cooling curves in the CMDs. We used tracks by Fontaine, Brassard & Bergeron (2001) and Tremblay, Bergeron & Gianninas (2011) for Gaia filters³ and UVIT filters (Bergeron private communication). As the turn-off masses of the OCs under study range from 1.1 to 2.3 M_⊙, we included WD cooling curves of mass 0.5–0.7 M_⊙ (Cummings et al. 2018). The extinction for all filters was calculated using Cardelli, Clayton & Mathis (1989) and O’Donnell (1994). We used reddened isochrones and WD cooling curves in this paper.

3 MEMBERSHIP DETERMINATION

3.1 Gaussian mixture model

For such sources, a gmm is created using pmra and pmdec, as only these parameters have distinct Gaussian distribution for the cluster members. Two isotropic Gaussian distributions are assumed for the field and member stars, which were initialized with previously know values of cluster PM and internal velocity dispersion. We used GaiaTools⁴ to maximize the likelihood of the gmm and get mean and standard deviation of the two Gaussian distributions. Simultaneously, the MPs of all stars in the field are calculated.

gmm cannot use the other parameters provided by Gaia EDR3 catalogue (parallax, ra, dec, g, bp_rp, etc.) due to their non-Gaussian distributions. gmm does not organically account for systematic parameters leading to loss of interesting stellar systems with variability, binarity, and atypical spectra. However, gmm can convincingly give the average CMD and VPD distribution of stars in a cluster. This can be further enhanced with the inclusion of photometric and systematic information. Hence, we used a supervised ML method to improve membership determination and utilize the non-Gaussian parameters.

3.2 Probabilistic random forest

A random forest consists of multiple decision trees. Each decision tree consists of nodes, where the values of the features are compared with thresholds. These thresholds are optimized in the training phase by using a sample of known sources, each with a given set of features (e.g. photometry, astrometry, etc.) and labels (member, non-member). The decision trees repeatedly split the sample up until only one class of source remains at the end of each split. Finally, the average classification of all the decision trees is used, each of which is trained on different subsets of the sample.

The major drawback of traditional random forest is that there are no uncertainties (errors) assumed during these calculations. The probabilistic random forest (prf) algorithm,⁵ developed by Reis et al. (2019), takes care of errors in the data, which is essential for any astronomical data set. It assumes all features and labels as probability distribution functions and out-performs traditional random forest algorithms in case of noisy data sets.

To create a training set for the prf algorithm, we first calculated the MPs using the gmm method. We used stars within r50 radius (Cantat-Gaudin et al. 2020) from the cluster centre to reduce field star contamination. The training set was created for each cluster by labelling |$P\_GMM\gt 0.5$| as members and others as non-members. The training set and testing set were created by randomly splitting the data set in 3:1 ratio, respectively. The prf requires the features, their errors and the known class (gmm membership labels) as inputs for training. The output contains fractional MP for each star and the feature-importance. After training the prf on stars within radius r50, we applied the algorithm on the stars within 3×r50 of cluster centre to increase the sample size.

We assessed the performance of the following parameters, as features which can impact the membership determination: ra, dec, pmra, pmdec, parallax, g, g_rp, ruwe, aen, pmR0, and many others. The meaning of the features used are mentioned in Table 3. Radial velocities (RVs) are limited to stars with g <15; hence, they were not used as a feature. We tried more than 22 feature-combinations to optimize the membership determination. We judged the different combinations by

• their ability to recreate MP similar to gmm using ‘accuracy score’ in testing phase. The accuracy score is defined as

  $$\begin{eqnarray*} \rm {accuracy}\ score = \frac{correctly\ predicted\ class}{total\ testing\ class}\times 100, \end{eqnarray*}$$

  (4)

  although the accuracy score itself is not enough to select the final feature-combination, one can weed out poorly performing combinations.

• the distribution of members in VPDs (cluster should occupy compact circular region in the VPD e.g. Fig. B2).

• the distribution of members in CMDs (Minimal contamination to the CMD, although it is a subjective judgement).

• the distribution of members in PM–parallax plot (Cluster should occupy small range in both PM and distance).

Based on their individual merits, the notable feature-combinations are listed in Table 4.

3.3 Selection of features and membership criteria

We trained prf using 1–1000 trees and saw a plateau in accuracy score after 150–200 trees. As Oshiro, Perez & Baranauskas (2012) suggested that the optimum number of trees lies between 64 and 128; hence, we chose 200 trees for further analysis. Almost all feature-combinations had an accuracy score of 92–98 per cent, as all were designed to select the cluster members. Hence, choosing the best combination is not trivial.

As expected pmra, pmdec, and parallax are important features for membership. The cluster’s distribution in VPD is Gaussian, and the random forest does not completely replicate this quadratic relation between pmra and pmdec. Hence, we defined a new parameter called pmR0, which is the separation of the source from the cluster centre in the VPD. The PM cluster centre was obtained from the gmm results. pmR0 helped constrain the cluster distribution to a circular shape. To test the importance of individual features, we introduced a column with random numbers as a feature. Among the Gaia features, ra and dec. showed very comparable feature-importance as the random column. However, upon further inspection, we found that inclusion of ra/dec. does not harm the prf, while improving the membership determination (King 2 is an example, which is the farthest cluster in our set and has smallest sky footprint). Due to known overestimation of gbp flux in fainter and redder stars (Riello et al. 2020), we used g and g_rp as features.

Figure 1.

Comparison of different MPs from prf feature-combinations for NGC 2682. The numbers in brackets represent the number of stars in that particular category. (a) Comparison of F6 and F10, where black dots are good-quality sources (qf = 1) and red circles are poor-quality sources (qf = 0). The green dashed box represents sources with |$P\_F10 \lt 0.7 \le P\_F6$|⁠. (b) CMD of NGC 2682 according to membership criteria in equation (5), the grey dots are members (⁠|$P\_F10 \gt 0.7$|⁠), while the green triangles are the candidates (⁠|$P\_F10 \lt 0.7 \le P\_F6$|⁠). (c) Comparison of F6 and F8 to demonstrate the MP dependence on CMD location. The colour is according to (P_F6 − P_F8), as shown in the right-hand panel. (d) CMD of stars coloured according to (P_F6 − P_F8). The stars with peculiar CMD position are bluer.

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While analysing the different feature combinations, we found that adding photometric information (F8) to astrometric information (F6) leads to lessening the MP of stars in peculiar CMD locations. This is demonstrated in Figs 1(c) and (d). Most stars have the same MP from F8 and F6; however, the BSSs in NGC 2682 have larger P_F6−P_F8 due to absence of many stars in the same location in the training set. For further discussion, we will refer to (P_F6−P_F8) as peculiarity. Unfortunately, as other clusters do not have many BSSs, the peculiarity can be used to distinguish between stars on the MS and sub-giant/giant branch.

3.4 Comparison with literature

Fig. 2 shows the comparison of prf with gmm (Cantat-Gaudin et al. 2018; Gao 2018a; Gao 2018d). The actual numbers of different types of stars are listed in Table 5. Although intuitive, the meaning of ‘added’, ‘rejected’ etc. is given in Table 5 footnote. Although Lindegren et al. (2020) warn against direct cross-match between DR2 and EDR3 due to changes in epochs, the astrometric shift for cluster members is < 10 mas (well within the crossmatch radius). All comparisons were done over the same field of view.

Figure 2.

Grouped histogram for common candidates, common members, added members, and rejected stars. The totals of four classes are normalized to 100 for easy visualization and the numbers are tabulated in Table 5. The likely members by prf and other techniques are represented by Common Memb (dark green) and Common Cand (lime). Red bars are stars added as members by prf (classified as field by other techniques or missing from literature catalogues). Blue bars are stars rejected (classified as field) by prf , but these are members in other techniques. Most of the rejected stars are faint and with larger pmR0. The dotted lines separate the comparisons with different methods and papers viz. gmm, Cantat-Gaudin et al. (2018), Gao (2018a), Gao (2018d) and Geller, Latham & Mathieu (2015). All comparisons are done for the same field of view.

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gmm and prf used different set of parameters. As seen Fig. 2, the classification by prf was similar to gmm. The accuracy score (reproducibility) of prf was between 90 and 99 per cent for the six clusters. However, there are some differences, which are expected and embraced. The major difference was seen in the rejection of gmm members (2–25 per cent), most of which were in G > 19 mag region. Among stars brighter than 19 mag, the percentage of rejected stars drops to 0–4 per cent, almost all having poor astrometric solutions (ruwe >1.2).

Cantat-Gaudin et al. (2018) used clustering in the (μ_α, μ_δ, ϖ) space to identify the members using Gaia DR2 data. They selected the stars with parallax within 0.3 mas and PM within 2 mas yr⁻¹ of the cluster mean. The probabilities were calculated using upmask, an unsupervised clustering algorithm. prf has identified significantly more (260–2500) new members compared to Cantat-Gaudin et al. All the added stars have acceptable CMDs, VPDs, and PM–parallax distributions. As the magnitude limit of Cantat-Gaudin et al. catalogue was 18, many new members are added in the fainter end of the MS. The rejected members (0–52) typically have either high ruwe-low pmR0 or low ruwe-high pmR0. As the added stars far outnumber the rejected stars, this is a good optimization.

Gao (2018a) used Gaia DR2 to determine membership of NGC 2477 (and three other clusters) using a gmm. Although there are 1695 common members, prf has added 2193 stars and rejected 133 stars. Majority of added stars are near the cluster parallax and pmR0 < 1.5 mas yr⁻¹. The rejected stars are again typically results of ruwe/aen and pmR0 trade-off.

Gao (2018d) utilized a random forest of 11 Gaia parameters (ra, dec, parallax, pmra, pmdec, g, gbp, grp, bp_rp, bp_g and g_rp) to calculate the MPs of NGC 2682. Gao did not remove stars with high systematic errors, and the random forest algorithm did not incorporate uncertainties in the astrometric data. The use of EDR3 data, inclusion of errors and using the F6 and F8 feature-combinations, has led to 233 more members. Geller et al. (2015) calculated the MPs in NGC 2682 using a combination of RV measurements (up to 40 yr baseline) and previous PM data (Yadav et al. 2008). Their catalogue is magnitude limited due to its spectroscopic nature. Among the cross-matched Geller et al. members, we classify 3 per cent stars as field, due to larger ruwe or different PM/parallax.

Comparison with previous literature confirms that F10 membership is adequate for membership, and we will use F10 as primary membership criteria. Due to the limitations (systematic and statistical errors) in Gaia EDR3, we included the candidate classification to account for the likely cluster members (using F6).⁶ We used both members (selected from F10) and candidates (selected from F10 and F6) for further analysis.

Importantly, our method was able to add a significantly large number of stars in all the clusters, ranging from 200 to 2500 stars per cluster (Table 5). Therefore, this is a significant improvement over the previous studies using Gaia DR2, mostly in the faint MS. This will certainly help in the detailed analysis of the clusters and locate interesting candidates that are bright in the UV.

4 RESULTS

4.1 The catalogues

The results of this study are presented in the form of seven catalogues, a membership catalogue and six catalogue of UVIT photometry. The membership catalogue (for sources with |$P\_F6\ \rm {\small {or}}\ P\_F10 \gt 0.1$|⁠) contains Gaia EDR3 astrometry and photometry (ra, dec, g, g_rp), MPs (P_GMM, P_F6, P_F8 and P_F10), quality filter (qf), and membership classification (M: member, C: candidate, and F: Field). The example of the catalogue is given in Table B1 (full version is available online). Table B2 shows the example of UV catalogue of NGC 6940, which is observed in F169M filter. The full catalogues of six clusters are available online. The catalogues contain RA (J2016), Dec. (J2016), UV magnitudes, magnitude errors, MPs (P_F10 and P_F6), and membership classification (M: member, C: candidate, and F: Field). We have included saturated stars in the catalogue, whose magnitudes give the upper bound to the actual numerical value.

We cross-matched the Gaia and UVIT catalogues with a radius of 1 arcsec to get merged catalogues using topcat.⁷ We checked for crowding and issues during cross-matching process (e.g. duplicity), but both Gaia and UVIT catalogue showed an insignificant number of stars within 1 arcsec of each other (2 for all UVIT detections and <0.4 per cent in Gaia detections). These merged catalogues were used for further analysis.

4.2 Cluster properties

All the parameters are tabulated in Table 6. Gaia EDR3 sources near each cluster are are divided into three subsets: members, candidates, and field. The VPDs and CMDs of all clusters for these individual subsets are shown in Fig. B2.

4.3 Individual clusters

NGC 2682 has a prominent binary sequence, red giant (RG) branch and BSS population (Fig. B2). We detected many candidates as BSSs, MS stars, and a few RG stars. The MS candidates typically have |$\rm {\small {qf}}=0$|⁠. The optical CMDs of stars detected in the FUV filters are shown in Figs 3(a)–(c). The CMDs contain all Gaiamembers, UVIT-detected sources, isochrone and WD cooling curve of 0.5 M_⊙. Overall, we detected 84, 31, and 58 members in F148W, F154W, and F169M, respectively. Fig. 3(d) shows the UV–optical CMD of sources cross-matched between Gaia EDR3 and F148W. The turn-off of the isochrone lies at 24 mag, which is the limiting magnitude of F148W observations. All the stars on optical MS are located above the turn-off in UV–optical CMD. Hence, as previously seen in Jadhav et al. (2019), almost all MS stars detected in optical CMD have FUV excess. The photometry presented here is two magnitudes fainter than Jadhav et al. (2019) in F148W, and we have detected a good number of MS stars in the 22–24 mag range, with FUV excess. Fig. 3(e) shows the F148W (F148W − F169M) CMD (the MS/turn-off is the vertical line at ∼ 0.5 colour). The sources show a large spread in FUV colour, ranging from 0.0 to 1.3 mag.

Figure 3.

The CMDs of NGC 2682 with UVIT and Gaia photometry. Gray dots are Gaia EDR3 members according to equation (5). Red squares, green triangles, and black crosses are members, candidates, and field stars detected in particular filters. The blue line is an isochrone with Log(Age) = 9.6, DistanceModulus = 9.64, E(B − V) = 0.05 mag, [M/H] = 0 dex; the dashed blue line is WD cooling curve for a 0.5 M_⊙ WD; the light blue arrows represent the reddening vectors with direction and magnitude in each CMD. (a), (b), and (c) The optical CMDs with stars detected in F148W, F154W, and F169M filters, respectively. (d) The UV–optical CMDs with F148W and g filters. (e) The UV CMD with F148W−F169M colour. (f) UV–optical CMD of sources cross-matched with Williams et al. (2018) catalogue of possible WDs. The CMD also shows three quasars (blue stars) detected by F148W filter.

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FUV images can be used to detect WDs. However, as they are faint in the optical wavelengths, Gaia is not suitable to detect them. In order to effectively identify the WDs, we cross-matched the F148W-detected sources with the WD catalogue of Williams et al. (2018). Fig. 3(f) shows the CMD of all cross-matched sources and the WD cooling curve. The membership information and g-band photometry (for this subplot alone) are taken from Williams et al. (2018). F148W has detected 10 member WDs, 6 field WDs, and 3 quasars. All these sources follow the WD cooling curve.

Berkeley 67’s VPD (Fig.   B2) shows that the mean cluster motion and mean field motion are within a few mas yr⁻¹ of each other. The cluster has only ∼400 members; hence, there is not much overdensity in the VPD. Thus, it is particularly challenging to determine the membership for Berkeley 67. The CMD shows a large spread in the MS. We suspect the large spread is the result of the differential reddening in the cluster region, whose effect is enhanced by the high extinction towards the cluster. UVIT images of Berkeley 67 in F148W (exp. time = 2683 s) and F169M (exp. time = 1317s) filters detected no member stars. Therefore, the cluster does not have any FUV bright members. N242W and N245M images detected 64 and 19 members, respectively. We did not detect any BSS. Figs 4(a) and (b) show the Gaia CMDs of these NUV-detected members. We observe turn-off stars in both NUV filters, with the wider N242W filter going till 17 mag. N242W filter detects two RGs that are rarely detected in the UV regime. Fig. 4(c) shows the N242W, (N242W − g) CMD for Berkeley 67, which again confirms the large scatter.

Figure 4.

(a), (b), and (c) The optical and optical–UV CMDs of Berkeley 67. The markers are same as Fig. 3. The isochrones for Berkeley 67 has log(age) = 9.2, DistanceModulus = 11.53, E(B − V) = 0.8 mag, [M/H] = 0 dex. (d) Optical CMD of King 2 with F148W detected members denoted by red squares and N219M detected members denoted by blue filled triangles. The isochrones for King 2 has log(age) = 9.7, DistanceModulus = 13.8, E(B − V) = 0.45 mag, [M/H] = −0.4 dex. (e) and (f) The optical and UV–optical CMDs of NGC 2420. The markers are same as Fig. 3. The isochrones for NGC 2420 has Log(Age) = 9.3, DistanceModulus = 12.0, E(B − V) = 0.15 mag, [M/H] = −0.4 dex; WD cooling curve is for 0.6 M_⊙ WD.

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King2 is the farthest cluster included in this work. This is evident from the small apparent core radius (0.5 arcsec) and high feature importance for ra and dec. The parallax measurements are unreliable at the distance of ∼5 kpc. The cluster and field centres in the VPD are very close, and hence, there may be contamination from field stars, among the members. Nevertheless, there are many BSSs and red clump stars present in the cluster (Fig. B2). We detected 5 and 3 members each in F148W and N219M filter, respectively (Fig. 4d). This 5-Gyr-old cluster located at a large distance has the MS turn-off at 18 mag (in g-band), and hence, we detected only the brightest of BSSs in UV. Overall, there are five member BSSs and 1 candidate BSS in UV images. Two of the BSSs have both FUV and NUV detections. We detect one blue and faint (g-band) object, which is likely a foreground WDs.

NGC 2420 lies in a relatively less dense region with the field to member stars ratio of ∼1 (Fig. B2). It has a clearly defined binary sequence and a RG branch, with a few BSSs. The UVIT image has stars up to two magnitudes below the MS turn-off, including a BSS. The UV CMD shows that the candidates are located close to the turn-off, though they are much fainter in the optical CMD, suggesting a brightening in the UV. However, the excess UV flux is not as prominent as NGC 2682. Similarly, a few members also show UV excess flux, but the change in the magnitude is not as large as in NGC 2682.

NGC 2477 is a very dense cluster in a high stellar density region (38 000 stars and 3900 members in 18 ^′ radius). The Gaia CMD shows a well-defined binary sequence, RC stars, and ∼5 BSSs. The turn-off has a large spread in g band. There is spread in the members below 18 mag, indicating that the probability cut-off should be slightly higher than 0.7. We detected 92 and 576 members in F148W and F263M, respectively (Figs 5a and b). Fig. 5(c) shows the F148W, (F148W − g) CMD with 2 BSSs and MSTO stars. Fig. 5(d) shows the N263M, (N263 − g) CMD with a large range in NUV magnitude consisting of red clump stars and MS stars. Fig. 5(e) shows the F148W (F148W − N263M) CMD; here, we see the turn-off stars and many field stars with bluer UV colour.

Figure 5.

(a) and (b) The optical CMDs of NGC 2477. (c), (d), and (e) The UV–optical and UV CMDs of NGC 2477. The markers are same as Fig. 3. The isochrones is for log(age) = 8.9, DistanceModulus = 10.9, E(B − V) = 0.4 mag, [M/H] = 0 dex; WD cooling curve is for a 0.7 M_⊙ WD.

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NGC 6940 is situated in a very dense stellar environment (stellar density is 13 times that of NGC 2682 neighbourhood). The cluster is well separated from the central field in the VPD and has a significant parallax (∼ 1 mas); hence, it is easy to extract (Fig. B2). The CMD shows a clear binary sequence and red clump stars. NGC 6940 also has a relatively broad MS with a spread near its turn-off, although less prominent compared to NGC 2477. We detected members up to 2 mag below turn-off (Fig. 6a) including a giant. We did not detect any BSS in this 1-Gyr-old cluster.

Figure 6.

(a) and (b) The optical and UV–optical CMDs of NGC 6940. The markers are the same as Fig. 3. The isochrones is for log(age) = 9.0, DistanceModulus = 10.0, E(B − V) = 0.2 mag, [M/H] = 0.0 dex; WD cooling curve is for a 0.6 M_⊙ WD.

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5 DISCUSSION

5.1 Membership determination

There are multiple ways of determining memberships. The choice of method is mainly dictated by the aim of the study. Any simple method such as VPDs for membership estimation is adequate for studies requiring the estimation of cluster parameters such as mean PM, age, and distance. Here, our objective is to identify UV bright member stars in OCs that could be in non-standard evolutionary stages. This requires the implementation of rigorous methods to assign membership to such stars, as discussed below.

Feature-importance: The prf method gives the importance of each feature as one of the results during the training phase. The normalized feature-importance is shown in Fig. 7. The most important features are pmR0, ruwe, aen, pmra, pmdec, and g. The distance of the stars from the cluster centre in the VPD, pmR0, is an important feature as expected. The high importance of ruwe/aen is because they are cut-offs established during the training of the algorithm. The g importance is aided by the dependence of all errors on the magnitude. The ra/dec importance is more for King 2 and NGC 2420 when compared to other clusters. They have core radii of 0.^′5–1.^′2, while other clusters are typically larger. The smaller spatial distribution of members is causing an increase in the importance of ra/dec. As expected, the importance of parallax increases for nearby clusters (NGC 2420, NGC 2477, NGC 2682, and NGC 6940).

Figure 7.

Normalized feature-importance for F10 for all six OCs.

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Efficacy in various environments: The prf technique works for OCs with a diverse cluster-members to field-stars ratio (0.01 to 1.3), thereby helping in efficient detection of members. The presence of systematic errors and including CMD locations through magnitude and colour tends to remove poor quality as well as peculiar stars. Therefore, we introduced the candidate classification to list such stars. For these six clusters, we found the candidates to members ratio to be 0.04–0.08.

Versatility of the technique: The algorithm is adaptable and one can choose a particular feature-combination depending on the requirements. For example, for a statistical study of clusters, a feature combination with ra, dec, and parallax would be enough. To find peculiar stars in the CMD, one could measure the difference between F6 (ra/dec, pmra/pmdec,parallax, and pmr0) and F8 (F6 + g and g_rp). Peculiar stars typically have lower P_F8. The prf technique can also be applied to any data-set besides Gaia EDR3. Moreover, the inclusion of RUWE/AEN as features indicates any systematic terms, if present in any other data set, can also be incorporated in the algorithm.

Classification of BSSs: In the field of NGC 2682, there were 10 potential BSSs (bluer and brighter than the turn-off). prf classified two as members, six as candidates and two as field. Many of these stars are photometric variables or binaries (Geller et al. 2015), which can lead to high |$\rm {\small {ruwe}}$| and hence classification as candidates. The two field stars have cluster parallax and RV (not considered as a membership criteria in prf). However, they have larger pmR0 leading to their rejection as members. For such stars with large PM deviation from the cluster mean, deeper RV measurements and accurate parallax will be useful in constraining membership. High peculiarity in combination with high ruwe of the BSSs is the reason for these stars to be categorized as candidates. Hence, the technique (equation 5) is capable of selecting BSSs (albeit as candidates).

Existence of Candidate class: All the cluster candidates lie near the cluster centre in the VPDs. Their number increases as they get fainter; this mirrors the fact that the systematic errors in Gaia EDR3 are larger for fainter stars. The CMD of NGC 6940 candidates (Fig. B2) shows that the majority of them lie on the binary sequence. A similar but lesser effect is seen in NGC 2477 and NGC 2682. Binary systems are known to produce high ruwe values due to variability or unsymmetrical PSF (Deacon & Kraus 2020), hence they can have low P_F10 and get classified as candidates.

Detection of peculiar stars using multiple feature-combinations: In Fig. 1(e), we compared the MPs with and without g and g_rp as features (F8 and F6, respectively). F6 has no knowledge of CMD positions, so it uses only spatial location and velocity to classify stars. However, F8 selects stars with common CMD positions and rejects stars with uncommon CMD positions. This effect is demonstrated by the positive values of |$P\_F6-P\_F8$| for BSSs in NGC 2682 (Fig. 1d). We refer to large |$P\_F6-P\_F8$| as peculiarity. Such peculiarity can be seen for the BSSs in NGC 2682, NGC 2477, and King 2. However, for King 2 majority of stars bluer than bp_rp < 1.1 mag have similar peculiarity regardless of their magnitude. Other clusters in this study do not have many BSSs, and they only showed large |$P\_F6 - P\_F8$| near limiting magnitude.

5.2 Individual clusters

NGC 2682: The detection of stars on the MS in the UV CMDs, suggests that many MS stars have excess UV flux. Jadhav et al. (2019) presented the reasons for UV excess such as the presence of hot WD components, chromospheric activity and hot-spots on contact binaries. Such UV excess detected among the MS stars is unique to NGC 2682; as for all other clusters, only a few stars on the MS show UV excess. In Figs 3(a) and (d), a few WD members and many field stars are found near the WD cooling curve. The CMD location suggests these can be WDs. Their MPs are low due to astrometric and photometric errors. As NGC 2682 is a well-studied OC, we used deep photometric catalogue of Williams et al. (2018). They identified hot and faint stars in u, (u−g) plane and carried out spectroscopic observations to confirm the WDs from their atmospheric signatures. We cross-matched all F148W detections with Williams et al. (2018) catalogue and found ten member WDs and six field WDs, along with the three quasars. Therefore, UVIT observations are well suited to detect WDs in NGC 2682.

Berkeley 67: The cluster has very high reddening [E(B − V) = 0.8 mag]. Thus, small relative changes in reddening have a substantial impact on magnitude/colour and cause a broadening of MS in the CMD. We tried binning the Gaiamembers spatially and analysed the distributions in the CMD plane. Initial estimates suggested that the E(B − V) values have a range of 0.7–1.0 mag. The reddening map is shown in Fig. 8. We detected one RG member in NUV that lies in the low reddening region. Further investigation is needed to determine the exact cause of UV brightening of the RG. Fig. 4 (c) shows members distributed in MS and sub-giant branch. From the UV CMD, it indicates the spread at the optical turn-off can be due to subgiant stars or due to differential reddening. As the extinction vector is parallel to the subgiant branch, any differential reddening will increase the spread in the same direction.

Figure 8.

Spatial location of RGs in Berkeley 67 overplotted on the reddening map. The plot contains all Gaiamembers/candidates (as black dots), N242W members/candidates (as red circles), and the RG detected in N242W filter (as red square).

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King 2: As the oldest and farthest cluster in this work, only bright BSSs are detected by UVIT. Jadhav (2021; under review) presented the detailed analysis of the detected BSS population, including detection of Extreme Horizontal Branch/subdwarf B-type stars as companions to BSSs.

NGC2420: We detected the BSS present in the cluster in the UV. We found ∼6 stars (out of 59), located on the MS, to show signs of excess UV flux. Some stars are found at the turn-off, and three are candidates. One of the candidate has ruwe = 3.9, while the other has no Gaia colours. High ruwe is known to be caused by variability and/or binarity (Deacon & Kraus 2020). The missing colour/high ruwe and excess UV flux points towards a hotter companion or variability. Multiwavelength analysis and X-ray observations of these stars can shed light on their evolutionary status.

NGC 2477: We have detected a large number of stars in FUV (108) and NUV (629); hence, it is ideal to study the UV properties from the MS up to the red clump. This massive cluster is also ideal to study the UV properties of stars in the broad MS turn-off present in this cluster. Overall, the UV CMDs are aligned with the UV isochrones, not indicating a collective UV brightening alike NGC 2682 among the MS stars. However, there are a couple of stars showing considerable UV excess, which require multiwavelength study.

NGC 6940: The UV CMD has some field stars near the WD cooling curve. These can be members or runaway WDs, which are quite faint in g. Some turn-off stars are found to be brighter than the turn-off in the UV CMD, suggesting excess FUV flux. We detected a giant with g= 7.3 mag and bp_rp= 3.7 mag in FUV at the limiting magnitude. It is a variable star of spectral type M5II-III D (Wallerstein 1962). The isochrone suggests that this is likely to be a post-asymptotic giant branch (AGB) star. Due to the low temperature (T|$_{eff}^{Gaia}$| = 3355 K), the stellar continuum cannot emit detectable FUV flux. Further study is needed to characterize the emission mechanism.

5.3 General discussion for all clusters

WD detections: Cross-match of Williams et al. (2018) catalogue and Gaia EDR3 resulted in only four WDs in NGC 2682. While the cross-match with F148W resulted in detection of 16 WDs. The F148W image has detected stars up to 21.7 mag in g band and 21.8 mag in u band. This indicates that UV images are more suitable to detect hot WDs as compared to Gaia. CMDs of a few other clusters imply presence of photometric WDs: King 2 (Fig. 4 d), NGC 2477 (Fig. 5 d), and NGC 6940 (Fig. 6 b). However, comparison with deeper catalogues is required for detecting WDs in these clusters. The membership determination of WDs is challenging due to deficiency of long-baseline deep observations in other open clusters. Although all the WDs have significant PM errors (Gaia EDR3 and Yadav et al. 2008), the spread in PM is clearly visible. It is interesting to note that three of the Gaia detected WDs in NGC 2682 lie at/just outside the edge of the cluster in the VPD.

Comparison of Gaia DR2 and EDR3: The membership analysis was done for both Gaia DR2 and EDR3. As EDR3 has halved the errors in PM, there were some changes in the members. EDR3 data has led to the addition of sources in the fainter end, which have PM similar to the cluster. We could probe the membership of all the stars in the cluster without any magnitude cut-off due to better accuracy in PM and inclusion of errors in the MP determination. The total percentage of candidates has dropped from 11 to 5 per cent, and the VPD distribution of NGC 2682 members was elliptical in DR2 which is now circular in EDR3 data, reflecting better handling of systematics in EDR3.

Future improvements: There are scopes to improve the membership determination process in future based on the following points:

• The use of RV can constrain the spatial motion of members; however, deeper RV data are needed to get cluster membership for fainter stars.

• The use of distance from the fiducial isochrone in the CMD could constrain the spread visible in the fainter region of the CMDs.

• We miss some stars with slightly different space velocity, as the primary selection criterion is PM (e.g. 2 PM and RV members from Geller et al. 2015). Such stars are important to understand the kinematics of the cluster. Increasing the weightage and accuracy of parallax and CMD location can help identify such stars.

The method developed here is generic and can be applied to non Gaia data as well. We recommend a feature-combination similar to F8 (ra, dec, pmra, pmdec, pmr0, parallax/distance, photometric information) to constrain the spread in CMD and VPD. Additionally, comparison with equivalent F6 (Only astrometric information) will be helpful to identify peculiar stars in the CMD.

6 CONCLUSIONS AND SUMMARY

• We developed an ML-based method to determine the individual stellar membership within OCs using Gaia EDR3. We have tried more than 22 different feature-combinations to calculate the MPs. The stars are classified as members, candidates, and field using a combination of two prf methods. Our primary method (F10) identifies stars that have properties similar to the mean cluster properties and have small systematic errors as members. To incorporate peculiar stars (uncommon CMD locations) and stars with large systematic errors, we utilized another method (F6) that only uses spatial location and velocity coordinates. We compared and validated the performance of our methods with past membership studies. Additionally, we created a technique to identify stars with peculiar CMD position and demonstrated that it could identify BSSs.

• We demonstrated that the prf algorithm could be used to determine the MPs in a variety of clusters. It is found to be robust, reproducible, versatile and efficient in various environments (variation in stellar density, reddening, age, etc.). We have identified 200–2500 more cluster members, primarily in the fainter MS, compared to previous studies (which used Gaia DR2 data). The algorithm presented here is generic and could be changed to suit other data sets or scientific problems. It is editable by selecting different features or creating new features, as required.

• We present a catalogue (Gaia EDR3 based) of six clusters that provides spatial location, MPs, and classification in Table B1. The presence of candidate stars suggests a need for better astrometry and photometry, which will be available in future Gaia releases and other large-scale surveys. We used the Gaia catalogue to identify cluster members in UVIT images. We present the UVIT catalogue of six OCs in one or more filters along with its membership information in Table B2 (full catalogues are available online). We estimated cluster properties such as mean PM, distance, mean RV, and core radii from the identified member population.

• We detected 3–700 member stars in various UVIT images of six clusters, apart from ∼13 per cent candidates. We detected BSSs in King 2, NGC 2477, NGC 2420, and NGC 2682. FUV photometry presented here will be used to understand the formation pathways of BSSs. We also detected giant members in FUV (NGC 2682, NGC 6940) and NUV (Berkeley 67, NGC 2477). While most of the NUV detections are expected due to their luminosity and temperature, their FUV detections are unusual. We detected 10 WD members in FUV images of NGC 2682. UV CMDs indicates that there are a few possible WDs in NGC 2477, NGC 2682, and NGC 6940.

• As seen in earlier studies, NGC 2682 has unusually high UV bright MS members. We detect no such systematic UV brightening among MS stars in other clusters. Some individual stars do show excess UV flux (RGs; a post-AGB star and a few MS stars). These are good contenders for detailed individual studies. The VPD of NGC 2682 is also notable due to its elliptical shape.

• The massive cluster NGC 2477 has 92/576 members detected in FUV/NUV, which will be useful to study the UV properties of stars in the extended turn-off and various evolutionary stages from MS to red clump.

The UV and Gaia catalogues provide a comprehensive data set to inter-compare UV emission across various types of clusters and study stellar properties. We plan to perform a detailed analysis of the interesting sources identified in this study using panchromatic data (such as UVIT, Gaia EDR3, and X-ray) in future studies.

Facilities: UVIT/ASTROSAT, Gaia. UVIT project is a result of a collaboration between Indian Institute of Astrophysics (IIA), Bengaluru, The Inter-University Centre for Astronomy and Astrophysic (IUCAA), Pune, Tata Institute of Fundamental Research (TIFR), Mumbai, several centres of Indian Space Research Organisation (ISRO), and Canadian Space Agency (CSA). 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).

Software:GaiaTools (Vasiliev 2019), prf (Reis & Baron 2019), topcat (Taylor 2005), iraf (Tody 1993), astropy (Astropy Collaboration et al. 2013), matplotlib (Hunter 2007), numpy (Oliphant 2015), pandas (Wes 2010), scipy (Virtanen et al. 2020).

SUPPORTING INFORMATION

Supplementary data are available at MNRAS online.

Table B1. Example of Gaia EDR3 membership catalogue with MP using gmm and ML.

Table B2. Example of photometric catalogue of all the detected stars in the UVIT images of NGC 6940.

Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.

ACKNOWLEDGEMENTS

We thank the referee for constructive comments and valuable suggestions. We thank E. Vasiliev for help with GaiaTools and P. Bergeron for providing WD cooling curves for UVIT filters. We thank Deepthi S. Prabhu, Sharmila R., and Samyaday Choudhury for helpful discussions and manuscript preparation. RS thanks the National Academy of Sciences, India (NASI), Prayagraj, for the award of a NASI honorary Scientist position; the Alexander von Humboldt Foundation, Germany for the award of Group linkage long-term research programme between IIA, Bengaluru and European Southern Observatory, Munich, Germany, and the Director, IIA for providing institutional, infrastructural support during this work. This work was supported by PhD Placement grant, ID 429088188, under the Newton–Bhabha Fund partnership. The grant is funded by the UK Department for Business, Energy and Industrial Strategy and Indian Department of Science and Technology and delivered by the British Council. This work was further supported by the UKRI’s (UK Research and Innovation) STFC (Science and Technology Facilities Council) PhD studentship.

UVIT open cluster study catalogues are available online as supplementary material and at CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/MNRAS.

DATA AVAILABILITY

The Gaia EDR3 data is available at https://gea.esac.esa.int/archive/. The UVIT images can be accessed through https://astrobrowse.issdc.gov.in/astro_archive/archive/Home.jsp depending upon their proprietary period. The membership catalogue (as Gaia_cat.txt; see Table B1) and UV photometric catalogues of six clusters (as Be67.txt, King2.txt, 2420.txt, 2477.txt, 2682.txt, and 6940.txt; see Table B2) are available online as supplementary material and at CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/MNRAS.

Footnotes

REFERENCES

APPENDIX A: OPEN CLUSTERS UNDER STUDY

Berkeley 67 is a ∼1-Gyr-old OC located at a distance of ∼2.45 kpc. It is a low-density cluster with an angular diameter of ∼14 arcsec. Lata et al. (2004) carried out deep Johnson UBV and Cousins RI CCD photometry of this cluster, while Maciejewski & Niedzielski (2007) obtained BV CCD data as part of a survey of 42 open star clusters. Both studies are based on optical CMD of the cluster.

King 2is a ∼5-Gyr-old OC located at a distance of ∼6 kpc towards the Galactic anticentre direction. It is a faint but rich cluster situated in a dense stellar field. It lags behind the local disc population by 60–100 km s⁻¹ and could be part of the Monoceros tidal stream (Warren & Cole 2009). Kaluzny (1989) obtained BV CCD photometric data for the cluster. A deep Johnson–Cousins UBVR CCD photometric study of the cluster was carried out by Aparicio et al. (1990). They estimated E(B − V) = 0.31 mag in the direction of the cluster and also indicated the presence of |$\gt 25{ per\ cent}$| of binary stars, based on the observed scatter in the CMD of the cluster.

The OC NGC 2420 is ∼1 Gyr old and located at a distance of ∼3 kpc. Cannon & Lloyd (1970) obtained relative PMs and also determined BV photographic magnitudes. The broadband optical CCD photometric study was carried out by Sharma et al. (2006). The ubyCaH intermediate-band CCD photometry of this star cluster was performed by Anthony-Twarog et al. (2006). All these studies indicate that the age of NGC 2420 is older than 1 Gyr.

The intermediate-age (∼0.9 Gyr) southern rich OC NGC 2477 is located at a distance of ∼1.4 kpc (Hartwick & Hesser 1974; Smith & Hesser 1983; Kassis et al. 1997; Eigenbrod et al. 2004; Jeffery et al. 2011). This cluster has a metallicity near Solar ([Fe/H] ∼ −0.17 to 0.07 dex; Friel et al. 2002; Bragaglia et al. 2008) and a high-binary frequency (∼36 per cent) for the RGs (Eigenbrod et al. 2004). Presence of significant differential reddening [E(B − V) = 0.2–0.4 mag] across the cluster was indicated (Hartwick, Hesser & McClure 1972; Smith & Hesser 1983; Eigenbrod et al. 2004). Using Gaia DR2 data down to ∼21 mag, Gao (2018a) identified more than 2000 cluster members. A deep HST photometric study of the NGC 2477 was carried out by Jeffery et al. (2011) to identify WD candidates and estimate their age.

NGC 2682 (M67) is a nearby OC with an age of ∼3–4 Gyr (Montgomery, Marschall & Janes 1993; Bonatto et al. 2015) and located at a distance of ∼800–900 pc (Stello et al. 2016). It is a well-studied cluster from X-rays to IR (Mathieu & Latham 1986; Belloni, Verbunt & Mathieu 1998; Bertelli Motta et al. 2018; Sindhu, Subramaniam & Radha 2018). There are various studies on the membership determination of NGC 2682 (Sanders 1977; Yadav et al. 2008; Geller et al. 2015; Gao 2018d). It contains stars in various stellar evolutionary phases such as main sequence (MS), RGs, BSSs, WDs. NGC 2682 contains 38 per cent photometric binaries (Montgomery et al. 1993) and 23 per cent spectroscopic binaries (Geller et al. 2015). Recently, Sindhu et al. (2019) and Jadhav et al. (2019) detected massive and extremely low mass (ELM) WDs with UVIT observations. The presence of 24 BSSs, four yellow stragglers, two sub-subgiants, massive WDs, and ELM WDs indicates that constant stellar interactions are happening in NGC 2682.

NGC 6940 is a well-known intermediate-age (∼1 Gyr) OC located at a distance of about 0.8 kpc. The membership of the cluster was investigated by Vasilevskis & Rach (1957) and Sanders (1972), while photometric studies were carried out by Walker (1958), Johnson et al. (1961), Larsson-Leander (1964), and Jennens & Helfer (1975). Baratella et al. (2018) presented medium resolution (R ∼ 13000), high signal-to-noise ratio (S/N ∼ 100), spectroscopic observations of seven RG members.

APPENDIX B: SUPPLEMENTARY TABLES AND FIGURES

Figure B1.

The photometric error in the magnitudes. Each subplot shows the magnitude-error plots for a cluster in all available filters. Please refer to the electronic version of the journal for the colour version.

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Figure B2.

VPDs and CMDs of the six clusters. First and third rows are VPDs of members, candidates, and field for respective clusters. Second and fourth rows are CMDs of members, candidates, and field for respective clusters. Isochrones are plotted as blue line for reference.

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