Investigating 56 High Galactic Latitude Open Cluster Candidates in Gaia DR3

Using Gaia DR3 data, we revisit 56 high Galactic latitude (∣b∣ ≥ 30°) open cluster (OC) candidates with poor shapes of color–magnitude diagrams (CMDs), including unclear and paired main sequences (MSs). We aim to confirm their physical reality and explore whether the special MS morphology is intrinsic to genuine OCs. Initially, we redetermine cluster memberships by integrating five outlier detection algorithms into pyUPMASK. However, this work fails to reproduce the 56 clusters. Instead, we find an alternative set of 56 clusters, six of which are non-duplicates. To ascertain whether the six clusters are real OCs, we build synthetic CMDs to derive reliable cluster properties, including fundamental parameters, binary fraction, and mass of the cluster. Subsequently, we investigate the structural parameters and the age–mass and mass–radius relations of the six candidate OCs. Finally, we utilize a multidimensional approach, incorporating cluster properties, spatial structure, kinematic attributes, and CMD verification, to assess their physical reality as genuine OCs further. Our results suggest that the six candidates should be physical OCs, exhibiting well-defined CMD characteristics. Moreover, we discover two of the six OCs as potential binary clusters.


Introduction
More than 14,000 Galactic open cluster (OC) candidates have been reported in the latest and comprehensive Unified Cluster Catalogue (UCC; Perren et al. 2023), of which fewer than 400 clusters in the high-latitude regions have been presented through previous published research (e.g., Schmeja et al. 2014;Cantat-Gaudin et al. 2018;Liu & Pang 2019;Cantat-Gaudin et al. 2019;He et al. 2022;Li et al. 2022a;Li & Mao 2023;Hunt & Reffert 2023).The study of high Galactic latitude OCs can provide excellent opportunities to trace the structure and kinematics of the Milky Way, and to explore the stellar formation, evolution, and destruction.Camargo et al. (2016) investigate two embedded clusters at a very high Galactic latitude, which are unexpectedly flying from the Galactic halo toward the Galactic disk.Camargo et al. (2016) suggest that the high-latitude clusters usually survive close to the Galactic plane and are later scattered to higher regions due to disk heating.Moreover, this paper indicates the interaction of shock waves generated by spiral density waves within the dense, magnetized Galactic disk can also be a contributing factor, leading to the displacement of star-forming gas toward higher latitudes.Additionally, there is some prominent research on high Galactic latitude OCs, e.g., merger events (Kereš et al. 2005;Sancisi et al. 2008), resonance-driven gentle perturbation (Martinez-Medina et al. 2016), and the potential insight formation from high-latitude molecular clouds (Camargo et al. 2016).
Many studies have been conducted on OCs located in the high Galactic latitude region in the past.The initial installment of the first unbiased source catalog of the Monitor of All-sky X-ray Image documented a total of 48 high-latitude star clusters (Hiroi et al. 2011).Subsequently, the Milky Way Star Clusters (MWSC) catalog introduced an additional 139 newly identified high-latitude OCs (Schmeja et al. 2014).With the publication of high-precision data by Gaia and the development of clustering algorithms based on machine learning, more detailed studies are ongoing for high Galactic latitude OCs.Kos et al. (2018) took advantage of the five-dimensional space of Gaia DR2 and GALAH data to perform a reidentification of five sparse high-latitude alike clusters.They revealed that only NGC 1901 is a real OC, along with a detailed membership analysis for this cluster.He et al. (2022) searched 46 OCs with |b| 20°using the DBSCAN algorithm and Gaia EDR3 data.DBSCAN is a density-based clustering algorithm capable of identifying clusters of any shape in data sets with noise (Ester et al. 1996), and it has been successfully applied in the search for OCs in many other works (e.g., Cantat-Gaudin et al. 2018;Castro-Ginard et al. 2019;Castro-Ginard et al. 2022;Hao et al. 2022;He et al. 2022).Li & Mao (2023) reported the discovery of 56 new high-latitude OC candidates, as included in the LISC II catalog of star clusters.The discovery was made using the Friend-of-Friend and pyUPMASK algorithms in the Gaia EDR3 data.In general, around 300 OCs or candidates in the high Galactic latitude region (|b| 25°) have been diligently studied.(e.g., Hiroi et al. 2011;Schmeja et al. 2014;He et al. 2022;Li & Mao 2023).
Some high-latitude clusters display ambiguous colormagnitude diagram (CMD) appearances, e.g., unclear main sequence (MS), paired MSs, broadened MSs, unbound star members, and dense lower MS stars.Paired MSs, such as the one positioned on the far left of Figure 1, exhibit two MSs within a single star cluster that appear as twins.These features still present uncertainties in the interpretation of physical clusters.The more well-characterized CMDs are, the higher the reliability of star clusters.However, those with poor appearances are particularly worthy of study due to the insights they provide into the physical reality and nature of star clusters.In Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.contrast, just as the scattered field stars within the analyzed region, the distribution of cluster members may not adhere to the profile described in King (1962), so the CMD appearance as depicted by the stellar sequences cannot serve as an intuitive judgment for a genuine OC (Burki & Maeder 1973;Piatti et al. 2023).Consequently, studying these objects as physical real OCs and investigating their cluster properties are critical for comprehending the evolution of the stellar system and the structure of the Milky Way (Lada & Lada 2003;Portegies Zwart et al. 2010;Krumholz et al. 2019).During our previous work (Chen et al. 2024), we revisited 77 OC candidates with multiple MSs using Gaia DR3, and we found that these clusters should be real OCs, and the impact of clustering algorithms together with source data quality on numbers of star cluster memberships is very obvious.Meanwhile, the result shows that binary stars and stellar rotation play an important role in multiple MS phenomena.In addition, Griggio et al. (2022) suggest that synthetic stellar populations, i.e., chemical abundance spreads, can explain the broadened MS in M37.On the contrary, the broadening of the MS in the M38 is attributed to binary stars and differential reddening.Long et al. (2023) investigated the cluster properties of 16 OCs in more detail, including, e.g., basic parameters, blue straggler candidates, binary fraction, and rotation-age-color relations.In this study, we reinvestigate 56 high-latitude OC candidates with poor CMD shapes, selected from the LISC II stellar cluster catalog.Perren et al. (2023) find that the parallax distances of these 56 clusters are very inconsistent with those estimated by distance modulus, and they are recovered 0% within the latest HUNT23 catalog (Hunt & Reffert 2023).The catalog is an allsky cluster catalog enhanced by Gaia DR3 data and the most comprehensive one before the UCC, which includes over 7000 clusters, 4105 of which are highly reliable.It also provides extensive membership lists for numerous OCs, often incorporating features such as tidal tails.The inability to recover the 56 clusters may be due to significant discrepancies in two distance parameters (parallax and distance modulus), extinction limits, or the fact that they are not real star clusters.We utilize an improved version of the pyUPMASK algorithm based on Gaia DR3 data to redetermine cluster member stars.Our main purpose is to reinvestigate the physical reality of uncertain 56 high-latitude clusters, as well as to make clear the special MS morphology and the nature of star clusters, and to provide their cluster properties reliably.
In Section 2, we introduce a sample of 56 high Galactic latitude OC candidates and provide a detailed description of the data sources used in this study.In Section 3, we describe an improved method for identifying cluster members using the pyUPMASK procedure.Subsequently, we derive isochrone fitting parameters using the Padova stellar evolution code.The fundamental parameters, binary fraction, and the total mass of the cluster are derived by building synthetic stellar populations.We consider various physical properties of the stellar system, such as spatial distributions, structural parameters, age-mass and mass-radius relations, and CMD features, to further validate the physical reality of clusters in our sample.In Section 4, we present detailed information on cluster member stars and cluster properties.A summary and conclusions are provided in Section 5.

Cluster Samples
We selected a sample of 56 high-latitude OC candidates from the LISC II catalog (Li & Mao 2023) as our initial working sample for this study, labeled as the initial sample.The feature selection of these objects is their CMDs with unclear MS branches, especially the broadened MSs and unique paired MSs, as shown in Figure 1.In addition, these 56 clusters cannot be recovered by the HUNT23 catalog (Hunt & Reffert 2023;Perren et al. 2023), and their parallax distances exhibit strong inconsistency with the photometric distances derived from the distance modulus.The distribution of these 56 objects in the Galactic coordinate system is illustrated in the bottom panel of Figure 2, showing them to be closely grouped in two regions, with parallax distances of 2 ∼4.7 kpc from the Sun.
We downloaded sources from the Gaia DR3 archive1 as star samples, which include astrometric, photometric, and radial velocity spectra data, i.e., R.A. (α), decl.(δ), proper motion components (m d a cos , μ δ ), parallax (ϖ), Gaia filters (G, G BP , G RP ), and RVs (V R ).Compared to Gaia EDR3, Gaia DR3 photometrically corrects the missing G flux of 5,401,215 sources and the G band of some sources (e.g., Damljanović 2021;Ye et al. 2022;Gaia Collaboration et al. 2023a, 2023b).Given that some OCs have extended regions (Carrera et al. 2019;Zhong et al. 2022), we define a search region with the cluster center coordinate of a cluster from the initial cluster sample as its center.This region has an angular radius of 3°for the purpose of searching for measurements.Following the data analysis of Gaia DR3, the uncertainty of a source with G = 17 mag is about 0.07 mag, while for a source with G = 20 mag, the uncertainty increases to about 0.4 mag.Many works adopt a magnitude cut of G > 18 mag (e.g., Cantat-Gaudin et al. 2018;Castro-Ginard et al. 2019;Castro-Ginard et al. 2022).Correspondingly, the quality filters, including ϖ, and the renormalized unit weight error (RUWE) are implemented (e.g., Liu & Pang 2019;He et al. 2022;Chi et al. 2023).In addition, the signal-to-noise ratio is an important indicator of the accuracy of the astrometric measurements for sources; e.g., Long et al. (2023) set G error 0.005 to remove uncertainty sources, and the G-band magnitude could go down to ∼21 mag.Hunt & Reffert (2023) adopted a quality flag of at least 0.5 to ensure both as complete clusters and cluster membership lists as possible (Rybizki et al. 2022).
Contrary to the dense star distribution within the Galactic disk, the high Galactic latitude regions display lower-density stars.However, in this work, we still encounter a crowded region with around 12 million sources.To mitigate uncertainties in the data, we implemented a combined quality cut, selecting sources with G < 18 mag, parallax_over_ error > 10, astrometric_excess_noise < = 1, and RUWE < 1.4.

Clustering
Following the sample selection and data preparation outlined above, we employ the pyUPMASK algorithm (Pera et al. 2021) to reidentify the member stars of these 56 clusters.This opensource, unsupervised clustering algorithm has been effectively utilized in numerous endeavors to construct catalogs of Galactic OCs.(Cantat-Gaudin et al. 2018, 2019, 2020;Chi et al. 2023).This procedure mainly consists of five steps: 1. Remove outliers from the data sources and perform principal component analysis of the data to reduce dimensionality; 2. Select appropriate clustering algorithms using the Python library scikit-learn; 3. Eliminate clusters with a random uniform distribution by utilizing functions such as stdRegion, Isolation Forest, and Local Outlier Factor; 4. Apply the Gaussian-uniform mixture model for data cleaning; 5. Estimate the kernel density estimator (KDE) probabilities for the cluster members.
In this study, the same process as outlined by the pyUPMASK algorithm can be applied, with the exception of step 3. First, we choose HDBSCAN (m clSize = 10) as the clustering method to find out the clumps in five-dimensional stellar parameters, i l b , , , cos , in step 2.Then, we propose a refined membership assignment approach to reassess the memberships of our objects in step 3.This is primarily achieved by incorporating two outlier detection algorithms, namely, Elliptic Envelope and Histogram-based Outlier Score, into the third step of the pyUPMASK code base to evaluate the clustering outcomes.Figure 3 provides a detailed illustration of the step 3 update.These five outlier detection algorithms are simply described as follows: stdRegion is a built-in function in the pyUPMASK process, mainly used to determine outliers in the data that differ from the average value by more than the specified standard deviation range based on input data.The Isolation Forest function is an anomaly detection method based on decision trees, which is stable and suitable for processing massive data.The Local Outlier Factor function is a robust method for detecting outliers in data sets by analyzing the statistical significance of their local neighborhoods.It can effectively detect outliers in various data types and distributions.The Elliptic Envelope algorithm identifies outliers by locating the elliptical envelope that contains the majority of the data points within a given confidence level.The Histogram-based Outlier Score algorithm focuses on the statistical analysis of histograms to identify abnormal data points, and it depends on the choice of the binning strategy and the threshold.Typically, each clustering result employs these five outlier detection algorithms to eliminate field stars, resulting in five distinct outcomes for each cluster.Finally, we select the optimal outcome based on the CMD patterns, and the criteria for selection are detailed in the subsequent subsection.An example from the same source, processed using the previously mentioned five algorithms, is shown in Figure 4.It can be seen that the five algorithms yield different member stars for the same data set.Notably, the last panel shows that the number of member stars is less than 10, indicating that certain algorithms are failing to generate clustering results.This suggests that each algorithm exhibits varying degrees of specificity and sensitivity toward different feature data sets, thereby resulting in marked discrepancies among their recognition outcomes.

Isochrone Fitting
After obtaining cluster member stars of the statistic clusters found by the pyUPMASK, we build the observed CMDs of clusters using three photometric bands, G, G BP , and G RP .We refer to our previous works (e.g., Chen et al. 2022;Li et al. 2022b;Chen et al. 2024) to correct the photometry of these clusters for differential reddening.Subsequently, we assemble the simple stellar population model to recognize reliable OC candidates via isochrone fitting developed from the Padova database (Marigo et al. 2017).We calculate the fitting function d2 and the narrowness of the MS (r n < 0.1) to evaluate the best-fitting CMDs, and the expressions are shown in Equations (1)-(4).
where X k and X k,nn are the positions of the kth member stars and the closest stars to them, respectively.
. v 1 and v 2 are two eigenvalues, which is the covariance matrix M of the distribution of color and magnitude for stars.
For each object, we obtain five cluster member star results from the five outlier detection algorithms.In order to assess the   optimal results, we select values of minimum d2 and/or r n from the isochrone fitting, and visual inspection of the CMD, as the final selection criteria for cluster member stars.Ultimately, we identify 56 clusters in this work.To differentiate them from our initial sample, we label them as the present sample.As a result, we conduct a crossmatching between the two samples using a parallax-based decision.If they are larger than the distance of 150 pc, they are unable to be matched.The results indicate that the present recovery rate of the sample is also 0% of the initial amount due to a significant disparity in distance.
Meanwhile, we estimate the basic parameters of clusters from the present sample using the best-fitting isochrones, including age t age , metallicity Z, distance modulus m − M, and color excess E(G BP − G RP ).The astrometric and isochrone fitting parameters of some of the clusters are listed in Table 1.It can be seen that some clusters exhibit nearly identical parameters, which may be explained by probable duplicates or binary clusters.Therefore, we refer to the method described by Perren et al. 2023, in conjunction with the Kolmogorov-Smirnov (K-S) test to discover duplicated clusters.The top , and parallax (ϖ).Bottom panels: a comparison of the distributions of the five parameters for potential duplicates conducted using KDE.The areas enclosed by the red and green lines represent the distributions of two separate groups of samples, respectively.The brown area denotes the overlapping distribution.The vertical axis measures the degree of covariation, which is calculated based on the covariance matrices of the two groups of sample parameters.panel of Figure 5 shows the results of the K-S test and distributions of coordinate, parallax, and proper motions for the potential duplicates.In addition, we conduct a crossmatching analysis of cluster memberships to identify duplicated clusters further, leveraging the Gaia DR3 source identifiers.The results show that within 56 clusters, only six are considered nonduplicates.Figures 6 and 7 display differential reddening correction and isochrone fitting CMDs, respectively, for the six clusters.
Using the TOPCAT tool (Taylor 2005), we establish a radius of 0°. 5, in line with previous successful studies (e.g., Castro-Ginard et al. 2019;Cantat-Gaudin & Anders 2020;Hao et al. 2022), to perform a crossmatching between the six objects and the known clusters in the UCC catalog as well as   the SIMBAD database.This method allows for the matching of two star clusters with NGC 1901 and HSC2314, while the remaining unmatched clusters may be considered potential new OC candidates.

Results
We are unable to reproduce the initial 56 clusters, and instead, we find an alternative set of 56 clusters, of which six are non-duplicates for the present sample.We conduct a comparative analysis of 56 objects from the initial sample and six clusters from the present sample, using the CMD shapes, coordinates, proper motions, and parallaxes, as illustrated in Figure 8.As can be seen, the variations across all dimensions are notably distinct.The CMD appearance and parallax distribution differences are especially significant.Subsequently, we perform a comprehensive analysis of the physical realities associated with the six candidate OCs.

Spatial Distribution of Cluster
The distributions of the Cartesian coordinates (x,y,z) for cluster memberships are crucial for comprehending the dynamic architecture of star clusters.These distributions reveal the overall trends and internal structures of star clusters.We utilize Gaia high-precision astrometric data to determine the positions of stars in the x,y,z plane and distributions of proper motions, as illustrated in Figure 9, to show the dimensions of the clusters.
The radial density profile (RDP) is a frequently employed tool for exploring the spatial distribution of star clusters.We take the center of the star cluster as the origin and then divide the star cluster into i-rings.Next, the stellar surface density within the ith ring is calculated by , where N i is the number of stars in the ith ring between the inner radius r i and the outer radius r i+1 .The King (1962) model is applied to fit values of the stellar surface density, leading to the cluster structural parameters, e.g., the core and tidal radius.The function of RDP fitting is described as where K is the radial density, r is the distance from the center of the cluster, r c is the core radius, and r t is the tidal radius.As shown in Figure 10, the six candidate OCs can be well fitted by the King function.

Binary Fraction and Mass
The mass of a cluster can significantly enhance our understanding of its evolution.Recently, Almeida et al. (2023) presented an effective approach for the reliable estimation of the mass of OCs using Gaia data.This method first generates the synthetic clusters via isochrone fitting parameters based on the Padova database, which takes binary fractions into account.Compared between the synthetic clusters and observed ones in the Monte Carlo method, a mass function is built by fitting the cluster stellar mass distribution.Finally, the total mass of the cluster is calculated by summing the masses of observed stars (single stars and binaries) and unseen stars (low-mass stars, binaries, and remnants of evolved stars).More details can be found in Almeida et al. (2023; see their Section 2).Following this technique, we derive the binary fraction and masses of the six candidate OCs. Figure 11 shows synthetic CMDs generated with the procedure.Finally, the astrometric and cluster properties of the six clusters are reported in Table 2.

Age-Mass and Mass-Radius Relations
The correlations between the mass and other parameters can enable us to understand the stability and dynamical characteristics of the clusters.Joshi et al. (2016) find an age-mass relation from an analysis of nearly 1300 star clusters in the MWSC catalog within 1.8 kpc of the Sun, which is described as where M e is the mass of the Sun, and M and T are the mass and age of the cluster, respectively.The left panel of Figure 12 illustrates a comparative analysis of our findings against the theoretical model.It can be seen that our result is consistent with this function pattern.
In addition, investigating the mass-radius relation is crucial for understanding the temporal evolution of the cluster.Some studies indicate no significant correlation between mass and radius (e.g., Bastian et al. 2005;Scheepmaker et al. 2007;Portegies Zwart et al. 2010), whereas Joshi et al. (2016) point to a discernible correlation between the two factors.Joshi et al. (2016) conclude that the mass-radius relation has two distribution functions, one follows a linear relationship M M 2.08 0.10 log 0.64 0.27 ), and the other can fit a power-law function (R ∝ M 1/3 ) for clusters that lie within the solar orbit, where M is the mass of the cluster and R is the radius of the cluster.The right panel of Figure 12 displays the mass-radius distribution of the six candidate OCs, with the majority being adequately fitted by a power-law function.
To evaluate the physical reality of clusters from the two samples, our analysis considers not only the morphology of CMDs, but also a comprehensive set of cluster properties, such as fundamental parameters, spatial distribution, and mass, among others.We perform an assessment of the physical reality of the six objects as genuine OCs based on five aspects, as suggested by Piatti et al. (2023): spatial distribution, RDP fitting, CMD morphology, and age-mass and mass-radius relations.A voting system is adopted to render a decision, i.e.,   ."NaN" indicates that the fitted values of the King (1962)  model are excessively large.The values in "()" are adopted by Kos et al. (2018) for NGC 1901.
if a cluster scores a Y in three or more of the evaluated aspects, it is considered a physical real star cluster.Because the CMDs of 56 clusters from the initial sample are unable to be well fitted by isochrones of the Padova database, they are difficult to identify as physical real star clusters using the voting system.Table 3 shows that the six objects should be real OCs.

Binary Clusters
There are some fraction of binary clusters (8% ∼ 12%) in the Milky Way (Subramaniam et al. 1995 Angelo et al. 2022).We refer to the method of Song et al. (2022) to detect a pair of clusters among the six OCs, and their coordinates, distributions of proper motions, and parallaxes are displayed in Figure 13.As can be seen, the binary clusters exhibit similar coordinates, parallaxes, and CMDs.Moreover, they particularly share common proper motions, leading to an overlap in the proper motion trajectories of the two clusters.In addition, we conduct an orbital analysis on the paired clusters.Figure 14 reveals that their orbits are closely interwoven.

Conclusions
Based on Gaia DR3 and improved clustering algorithms, we revisit a catalog of 56 high-latitude OC candidates with poor CMD shapes to identify member stars of clusters.We present an updated catalog that is unable to reproduce our initial sample.We offer this updated catalog information, encompassing astrometric parameters related to cluster membership, as well as isochrone fitting parameters for clusters.We analyze the spatial position, distribution of proper motions, and CMD features of 56 clusters obtained by this work, and find that six are non-duplicates.This work further investigates the spatial structure parameters, binary fraction, and the total mass of the cluster for the six clusters.Empirical age-mass and massradius relations are investigated, and the findings are generally consistent with that from a previous study (Joshi et al. 2016).Our main conclusions are as follows: 1.This work fails to reproduce 56 clusters from the initial sample, most of which have member stars with magnitudes fainter than 18 mag.The uncertainty of the data may be the main reason for the misattribution of these likely memberships.In contrast, the cluster member stars in the present sample are selected based on more stringent criteria of source filtering.Moreover, we have incorporated five outlier detection algorithms into pyUPMASK, resulting in five distinct sets of cluster member stars.Furthermore, we identify 56 clusters in the present sample, but upon careful crossmatching, we discover that most of them are duplicates, leaving us with only six unique clusters in the end.These instances demonstrate that the accuracy and input parameters of source stars, in combination with clustering algorithms, markedly affect the assessment of cluster membership.Additionally, a comprehensive investigation into duplication issues warrants rigorous exploration, which is in agreement with Perren et al. (2023).In our upcoming work, we will conduct a study aimed at selecting duplicates based on the comprehensive catalog.2. Comparing the CMDs from the initial sample with those from the present sample, the latter exhibits more wellcharacterized shapes.We utilize a multidimensional approach, incorporating spatial structure, fundamental parameters, kinematic attributes, and CMD features to identify physical real OCs for the two samples.Our results suggest that clusters with poorly characterized CMD shapes are difficult to consider as real star clusters.
The six candidates from the present sample display wellcharacterized CMD shapes, suggesting that they are highly reliable OCs.Even though a single CMD verification is unable to identify a true physical star cluster (Piatti et al. 2023), the CMD appearance is inconsistent with theoretical models of stellar evolution, indicating that it is most likely not a real star cluster.3. We suggest that the special MSs, including those with unclear MSs and paired MSs in our initial sample, are primarily a result of the distance of these objects.The inherent uncertainty of the data exacerbates the difficulty in observing clear sequences.Speculatively, there may be several assumptions behind the observed paired MSs, such as gravitational lensing events, accretion, merging events within stellar systems, etc.We are eager to employ higher-quality data and more sophisticated algorithms in the near future to shed light on these phenomena.4. Finally, we have found a potential binary cluster that exhibits near-complete overlap in CMDs, proper motions, and parallaxes, despite being spatially separated.An orbital analysis has been conducted, and a more detailed study of binary clusters will be presented in our future work.supported financially by various national institutions, especially those involved in the Gaia Multilateral Agreement.We express our sincere appreciation to Perren et al. (2023) for their significant efforts in developing the UCC catalog and database.Additionally, we are deeply grateful to Zhong et al. (2022) for providing expert assistance in the application of radial density calculation techniques and Almeida et al. (2023) for presenting an effective approach for reliably estimating the mass of OCs using Gaia data, which have been instrumental to the success of this research.

Figure 1 .
Figure 1.Some examples of CMDs selected from our initial sample.

Figure 2 .
Figure 2. Distribution of the initial sample of 56 OC candidates in Galactic coordinates, depicted with dots representing clusters.The color bar denotes the distance from the Sun.

Figure 3 .
Figure 3. Process of updating the outlier detection module of the algorithm.

Figure 4 .
Figure 4. Example from the same sources, processed using the aforementioned five algorithms.The CMDs are sequentially obtained from the Elliptic Envelope, Isolation Forest, Histogram-based Outlier Score, Local Outlier Factor, and stdRegion algorithms.

Figure 5 .
Figure 5. Upper panel: results of the K-S test estimated based on the five parameters of clusters 03 and 55, which include R.A. (α), decl.(δ), proper motion components (m d a cos , μ δ ), and parallax (ϖ).Bottom panels: a comparison of the distributions of the five parameters for potential duplicates conducted using KDE.The areas enclosed by the red and green lines represent the distributions of two separate groups of samples, respectively.The brown area denotes the overlapping distribution.The vertical axis measures the degree of covariation, which is calculated based on the covariance matrices of the two groups of sample parameters.

Figure 6 .
Figure 6.Comparison of the observed CMDs (black points) with those corrected for differential reddening (red points) for the six clusters.

Figure 7 .
Figure 7.Comparison of the observed CMDs (blue points) and best-fitting theoretical isochrones (red points) for some examples based on the Padova database.

Figure 8 .
Figure 8.Comparison between the CMDs from NC01 of the initial sample (red points) and one from LISC 3630 of the present sample (blue points), coordinate, proper motions, and distribution of parallax for cluster member stars of one example.

Figure 9 .
Figure 9. Distributions of proper motions and member stars in Cartesian coordinates x.y,z for one example in our present sample.

Figure 10 .
Figure 10.Left panels: RDP of the cluster member stars (red dots).The black dashed line represents the fitting result of the King (1962) model.Right panel: the spatial distribution of the cluster member stars, with their density contours.Bottom panels: the RDP fitting results of the other five clusters.

Figure 11 .
Figure 11.The left panel displays an example of synthetic CMD, showing single (color points) and binary (cross points) member stars.The colors are assigned according to the masses of stars.The right panel depicts the mass distributions of the primary (blue) and companion (orange) stars.

Figure 12 .
Figure 12.Left panel: the age-mass relation.Right panel: the mass-radius relation.Error bars are obtained from the standard deviation of the mass of the star clusters.

Figure 13 .
Figure13.Upper panels: distributions of proper motions and parallaxes for the potential binary clusters of this work.Gray dots and histograms represent the former clusters, while the red dots and histograms correspond to the latter clusters.Bottom panels: similar to theupper panels, but for CMDs and celestial positions.

Figure 14 .
Figure14.Orbits of paired clusters (NC01 and NC02).The circles represent the orbits, with red dots indicating the starting points and blue dots the ending points, respectively.The green arrow denotes the direction of motion.

Table 1
Astrometric and Isochrone-fitting Parameters of Some of the Clusters in the Initial Sample

Table 2
Cluster Properties of the Six OC Candidates in the Present Sample

Table 3
Assessment of the Physical Reality of the Six Clusters ; de La Fuente Marcos & de La Fuente Marcos 2009), and they have similar positions, common proper motions, consistent CMD patterns, etc. (Bhatia & Hatzidimitriou 1988; de La Fuente Marcos & de La Fuente Marcos 2009;