We select the stars in a circular region with centre at ( l , b ) = ( 79.8 ∘ , + 0.8 ∘ ) of radius 1.5˚ taking into account the following criteria: 1) The values of the proper motions components are − 5 < μ α cos δ < 5 mas yr⁻¹, − 10 < μ δ < 0 mas yr⁻¹ (except the case of Roslund 6 whose proper motion values are − 1 < μ α cos δ < 10 mas yr⁻¹ , − 1 < μ δ < 10 mas yr⁻¹ ) because a visual inspection of the Vector Point Diagram (VPD) of the region showed low proper motions for the possible OCs candidates. 2) The stars having the Dup value in the catalogue equal to 1 are not selected because they have multiple source identifiers. 3) The parallax values adopted are ϖ > 0.4 mas. This is based on the range of observed parallaxes in region by Orellana et al. (2021) [9]. 4) Stellar parallaxes having fractional error f = σ ϖ ϖ > 0.20 are excluded. This restriction reduces the problems in the transformation of parallax to distance. 5) The stars with RUWE parameter ≤ 1.4 [22] are selected because this value is a quality indicator of the astrometric solution. The final sample consists of 23,106 stars with G ≤ 19.5 mag, this cutoff in the magnitude is due to the adopted value of the fractional error.

3.2.1. HDBSCAN Algorithm

We apply the HDBSCAN (Hierarchical Density Based Spatial Clustering of Applications with Noise) clustering algorithm [23] to the Gaia DR3 astrometric parameters ( α , δ , μ α cos δ , μ δ , ϖ ) to detect the clusters and their members in the Cygnus OB2 region. HDBSCAN is an unsupervised learning tool that allows us to identify stellar groups with different density and shape. This algorithm can work with multidimensional data, which must be previously normalized. Normalization allows us to compare different astrometric parameters and make inferences about their distribution. When the entire set of parameters is on the same scale, it is possible to identify and visualize the relationships between them and make meaningful comparisons. In this work, we use Min-Max scaling which transforms the values of each set of parameters between 0 and 1 by

where x is the original value of the astrometric parameter; min ( x ) and max ( x ) are the minimum and maximum values of the parameter in its dataset, respectively and x s c a l e d is the normalized value of the parameter.

The algorithm requires a metric that calculates the distance between points in the normalized dataset to identify the different densities. The Euclidean metric is the most commonly used [24].

HDBSCAN needs two hyperparameters previously defined to be executed [23]: minimum number of samples (mPts) and minimum cluster size (mcSize). One of them, mPts, defines the minimum number of neighbouring stars that any star must have to be considered in a grouping. The other hyperparameter, mcSize, is the minimum number of stars required to define a cluster. Different combinations of these hyperparameters give different sizes of clusters. Thus: 1) small minimum number of samples and minimum cluster size results in many small clusters; 2) small minimun number of samples and large minimun cluster size results in larger clusters and 3) a large minimun number of samples and large minimun cluster size results in very large clusters.

Besides, the HDBSCAN algorithm has the disadvantage of identifying false clusters. The identification of real clusters is carried out by adopting the following empirical criteria proposed by Hunt & Reffert (2021) [25]:

a) the dispersion of the total proper motion of their members must satisfy

b) the radius of the open cluster containing half of its members ( r 50 ) must be less than 20 pc;

c) those candidates that have a density compatible with the field stars are discarded. This is implemented by calculating the distance from each star to its ninth nearest neighbour.

In order to determine the optimal values of mPts and mcSize to detect the OCs, and setting mPts and mcSize to the same value as recommended by Campello et al. (2013) [23], several runs of HDBSCAN are performed using different combinations of these hyperparameters, both values are in the 5 - 80 range.

Then, for each pair mPts-mcSize we evaluate if the different clusters fulfil a), b) and c) criteria in order to obtain well-characterized OCs.

3.2.2. Stellar Membership Determination and Cluster Parameters

A probable cluster member is found when its HDBSCAN membership probability is P ≥ 0.5 , following the Bayes minimum error rate decision rule [26]. The number of stars that fulfil this condition is the number of members N c , and their coordinates guide to compute the cluster radius r c .

Among the N c members, we define as the highly probable members N h p those with P ≥ 0.80 . These N h p lead to calculate the coordinates of the cluster centre ( α c , δ c ), the components of the mean proper motion ( μ α cos δ c , μ δ c ), and calculate the mean value of the parallaxes of the members weighed for their squared uncertainty ϖ c . An estimation of the distance d ϖ c is calculated by the inverse of ϖ c , taking into account the general offset of −0.017 mas [20].

With the goal to know some physical parameters of the clusters found from the proper motion and parallax analysis, we add the study of colour-magnitude diagram (CMD) with Gaia photometric data.

Since Cygnus OB2 is one of the major stellar formation region, it is important to distinguish whether the red colour of each star is due to dust present in the line of sight or it is inherent to the star itself. To achieve this, we cross-match the optical Gaia data of the stars identified as cluster members with the near-infrared (NIR) photometric data from the 2MASS catalogue (JHK bands). For this, we take a maximum angular distance of 1''. Then, using the NIR photometric data, we calculate the reddening-free photometric parameter Q N I R = ( J − H ) − 1.7 × ( H − K ) [27] to avoid any confusion arising from the intrinsic degeneracy between reddening and spectral type. We substantiate our star classification by analysing the Q N I R value on the guidelines provided by Borissova et al. (2012) [28] and Messineo et al. (2012) [29]. Then, − 0.3 < Q N I R < 0.5 indicates early main sequence stars, Q N I R < − 0.3 Pre-Main Sequence Stars (PMS) or Young Stellar Objects (YSO) and 0.5 < Q N I R late reddening stars.

The extinction value ( A v ) for clusters is estimated using the new three-dimensional (3D) map of dust reddening, which integrates Gaia DR2 parallaxes, stellar photometry data from Pan-STARRS1 and 2MASS, and a hierarchical Bayesian model of dust distribution [30]. The A v value derived from this approach is applied in conjunction with the reddening law: A G = 0.83627 A v , A B P = 1.08337 A v , and A R P = 0.63439 A v , to fit the appropriate isochrone. When the A v value appears to be inaccurate, we adopt an initial assumption of an A v that closely aligns with the values provided by Wright et al. (2015) [31]. Additionally, we consult the APASS¹ catalogue to obtain the V and B photometric data for each star, which are combined with JHK 2MASS bands to estimate the visual extinction for each cluster.

The PARSEC v1.2S isochrones [32] are adjusted to the observed data in the photometric diagram G vs ( G B P − G R P ). To achieve this, we consider the cluster’s distance derived from its parallax determination and adopt an initial value of visual absorption as explained previously, which sometimes requires refinement through successive isochrone adjustments. Estimating the age of the open cluster using broadband photometric data and a limited number of stellar members leads to less reliable results. For this reason, we fit multiple isochrones and in all of them we use solar metallicity as a fixed parameter. The true metallicity value of a cluster is determined through the spectral analysis of its individual members. For this reason, we consulted the spectroscopic catalogue by Fu et al. (2022) [33], in which the open cluster Collinder 421 is reported to have a metallicity index of [Fe/H] = −0.02 ± 0.04 dex, and the Qin et al. (2023) paper [34], where Roslund 6 is given a metallicity index of [Fe/H] = −0.01 ± 0.10 dex. Therefore, as a first approximation, solar-metallicity isochrones could be adopted for all the open clusters studied in the region. In the figures presenting the CMDs for each open cluster, we show the minimum and maximum values of the selected age range with solar metallicity isochrones.

The astrometric analysis of the Cyg OB2 region is done following the procedure given in subsections 3.2.1 and 3.2.2. For different values of the hyperparameters (mPts-mcSize), the HDBSCAN algorithm is applied to the sample and several groupings are found. We evaluate if these groupings fulfill the empirical criteria a), b) and c) in order to detect OCs. Therefore, the values of the pair (mPts-mcSize) that well characterize the detected 24 OCs for each final run are given in Table2.

Table2. The pair (mPts-mcSize) that well characterize the detected 24 OCs.

Figure 1 shows the spatial distribution of all clusters identified in the line of sight of Cygnus OB2. Table3 shows the values of the cluster parameters found and defined in Subsection 3.2.2. A catalogue containing the position ( α , δ ) , the Gaia DR3 identifier, the parallax ϖ and its error σ ϖ , the proper motion components μ α cos δ , μ δ and the G magnitude of the members of each cluster will be available online.

Figure 1.Spatial distribution of the 24 OCs found in the region. Dolidze 8 is drawn in blue circles, Cr421 in black dots, OC-124 in black circles, NGC6910 in green dots, OC-123 in pink circles, FSR 0224 in brown circles, HSC 618 in green circles, UBC 585 in yellow dots, FSR 0227 in turquoise triangles, Roslund 6 in blue triangles, IRAS-20306+4005 in red dots, OC-128 in red circles, HSC 625 in yellow circles, Bica 1 in brown dots, Bica 2 in blue dots, FSR 0238 in pink dots, FSR 0236 in turquoise dots, HSC 630 in green triangles, RSL-03 in turquoise circles, Dolidze 11 in red triangles, RSL-04 in black triangle, RSL-05 in yellow triangle, RSL-06 in pink triangle and HSC 626 in brown triangles.

At the beginning of our investigation, a cross-match of the 24 open clusters detected with those known in the region (see Table1) indicated that we had found 18 known clusters and six new ones identified as RSL-01, RSL-02, RSL-03, RSL-04, RSL-05 and RSL-06. We detected that the clusters Bica 1, Bica 2, FSR 0238 and FSR 0236, among the known clusters, are located in the core of the Cyg OB2 association.

During the process of this work, a new OC census is published by Hunt & Reffert (2023) [19] using Gaia DR3. In their publication, RSL-01 is identified as IRAS-20306+4005 and RSL-02 as HSC 630 (see Table1 and Table2). Figure 2 shows the stellar positions, VPD, and parallax histogram for the four new OC members found, IRAS-20306+4005 and HSC 630, while Figure 3 displays the same for Bica 1, Bica 2, FSR 0236 and FSR 0238.

We want to remark that: a) the parallax histogram of IRAS-20306+4005 shows a large range of values. This is because most of the members of this cluster have magnitudes 17 < G < 19 mag with parallax uncertainties of 0.4 mas; b) an inspection of the RSL-06 VPD shows a considerable dispersion of its members that has not been possible to justify. However, the stellar position, the parallax histogram and the Gaia photometric diagram show it as a cluster. To make a final decision, we will wait for a new series of data from the Gaia mission and we consider RSL-06 as a tentative cluster.

Table3. Centre coordinates ( α c , δ c ) , mean proper motion ( μ α cos δ c , μ δ c ), number of members N c , number of highly probable members N h p between parentheses, radius r c , mean parallax ϖ c and estimated distance d ϖ c of the detected OCs in the region.

[*] We compute the mean parameters from all the members found in the region of this study, where the north part of the cluster is occupied.

In the case of Roslund 6, we compute the mean parameters from the N c members found in the region of this study, where the north part of the cluster is occupied.

Figure 2. Stellar positions (left column) and VPD (middle column) for the N c members of the new four OCs detected, IRAS-20306+4005 and HSC 630 (grey circles represent field stars). The N h p members are plotted with red filled circles and the rest of the members with yellow filled circles. The OCs parallax histograms (right column) are shown for the N c members (red) and for the N h p members (filled with pattern).

Figure 3. Stellar positions (left column) and VPD (middle column) for the N c members of Bica 1, Bica 2, FSR 0236 and FSR 0238 located at the core of Cyg OB2 (grey circles represent field stars). The N h p members are plotted with red filled circles and the rest of the members with yellow filled circles. The OCs parallax histograms (right column) are shown for the N c members (red) and for the N h p members (filled with pattern).

4.1.1. Comparison with Other Works

First, we compare our results given in Table3 with the ones given in the literature (see Table1). It can be seen that our values of the centre coordinates, the mean proper motion components and the mean parallax are in good agreement with the literature. The exceptions are the Hunt & Reffert (2023) [19] parameters for FSR 0238 which do not match ours and those obtained by other sources.

Then, as Hunt & Reffert (2023) [19] identify the OCs in the region that have been previously studied using Gaia DR2 data, we compare our lists of members with theirs. This comparison distinguishes between common members—stars identified in both datasets—and non-common members, which are exclusive to either our study or theirs. (see Figure 4). We find differences in the number of members, although the catalogue used (Gaia DR3) and the method (HDBSCAN algorithm) are the same. Table4 shows the low percentage of members in common.

We notice that their results contain very faint members, for which parallax uncertainty may distort the spatial distributions in transforming parallax to distance [35][36]. To check if this happens, for each OC we examine the histogram of the geometric distance ( r g e o ) of both lists of members using the data from Bailer-Jones et al. (2021) [37].

Table4. Hunt & Reffert (2023) [19] members in common with ours.

Figure4. Bar diagram comparing the number of members for each open cluster between our work and that of Hunt & Reffert (2023) [19]. The names of the clusters are displayed along the X-axis, while the Y-axis represents the total number of members. The bars are grouped to distinguish between members identified exclusively in our study (yellow), members identified exclusively in Hunt & Reffert’s catalogue (blue), and common members found in both lists of members (green).

As an example, Figure 5 shows the comparison of results from this study and those from [19] for Dolidze 8. Figure 5b plots the results for Dolidze 8 where the histogram of our members shows a Gaussian distribution and the one of Hunt & Reffert (2023) [19] members is skewed to the right, indicating false positives and a distance range between 800 and 3300 pc.

To explain the presence of these false positives, the uncertainties in the parallaxes of the members are plotted against r g e o in Figure 5c. It can be seen that the Hunt & Reffert (2023) [19] members with greater parallax uncertainty produce the skewness that distorts their spatial distribution in Figure 5b.

On the contrary, Figure 5b and Figure 5c do not show this distortion for our members. This is due to the adoption of stellar parallaxes with fractional error f = σ ϖ ϖ ≤ 0.20 (criterion iv) in our sample. For this reason our members have smaller parallax uncertainties, as seen in Figure 5c.

Figure5.Results for the open cluster Dolidze 8. a) parallax histograms for [19] (green) and this work (filled with pattern). b) geometric distance histograms r g e o obtained from [37], for [19] (green) and this work (filled with pattern). c) uncertainty in parallax σ ϖ against r g e o for members from [19] (green filled circles) and this work (open black circles).

Table5. Mean proper motion and parallax of the stellar over-densities determined by Orellana et al. (2021) [9].

We also notice that the members of Bica 2 identified by Hunt & Reffert (2023) [19] are located in the place where OC census carried out prior to Gaia era identifies Bica 1 and Bica 2 separately [38]. Our analysis finds both clusters. Besides, it is not possible to detect HSC 624 in our work, even several runs of HDBSCAN have been done using different values of mPts and mcSize; instead we detect two new OCs named RSL-03 and RSL-05. The former corresponds to the northeast part of HSC 624, and the latter to the southwest part of it.

4.1.2. Spatial Structure along the Line of Sight of the 24 Open Clusters

We analyse the spatial structure along the line of sight of the selected circular area. In Figure 6, we plot the mean proper motion components of the open clusters detected in this study with dots (except Roslund 6, Cr 421 and Dolidze 8 whose values are out of the range of the axes of the figure). The different colours represent the scale of the estimated distances.

Figure6. Vector point diagram (VPD) of the region except Dolidze 8, Cr421 and Roslund 6. OCs mean proper motion are plotted with filled circles, and the members of Cyg OB2 association, Left and Right stellar groups are plotted with dots.

Also, we plot the members of the Cyg OB2 association, Left and Right over-densities found by Orellana et al. (2021) [9] with the colour according to their distance. The red circle contains the proper motion values of the members of Cyg OB2, and the green ones contain the proper motion values of the members of the Left and Right over-densities. The mean proper motion of Cyg OB2 association, Left and Right over-densities are plotted with crosses (see Table5).

It can be seen that the estimated distance of several clusters is between 1600 and 1800pc, similar to the distance of Cyg OB2 and their mean proper motions lie inside the red circle. These clusters and their numbers in Figure 6 are FSR 0224 (no. 12), FSR 0236 (no. 10), FSR 0238 (no. 9), RSL-04 (no. 6), RSL-05 (no. 7), RSL-06 (no. 8), HSC 625 (no. 17), OC-123 (no. 20), OC-128 (no. 21), NGC 6910 (no. 14), Bica 1 (no. 22) and Bica 2 (no. 23). This suggests that these OCs would be connected to Cyg OB2 association.

We also notice that the estimated distance of HSC 630 (no. 4) is similar to the distance of the Left over-density, and that the mean proper motion of the OC lies inside the green circle. Then, HSC 630 would be connected to the Left over-density.

In the case of the Right over-density, there is no OC in the region having similar mean proper motion and estimated distance.

An important result of the photometric analysis is the age of an OC. Its determination is a serious problem related to the contamination by field stars, unresolved binarity of the cluster stars and variable interstellar reddening.

In order to reduce the first and second effects on the astrometric membership determination, we impose restrictions on the sample (Subsection 3.1) that allow the photometric analysis to be more reliable.

The Gaia DR3 catalogue allows us to reach fainter magnitudes which provide many more cluster members. However, we must be careful with the contamination by field stars that can be produced by the astrometric parameter uncertainties. The effect of parallax uncertainty has been reduced by considering σ ϖ ϖ ≤ 0.20 in our sample (criterion iv) and demonstrated in 0.0.3. The rest of the possible field stars are eliminated by defining the highly probable members N h p as those with P ≥ 0.80 (section 3.2.2).

Regarding stellar binarity, Belokurov et al. (2020) [39] demonstrate that a high RUWE value is an effective indicator of it, as well as Lindegren (2022) [40] remarks that RUWE is its main indicator. Following Castro-Ginard et al. (2024) [41], we can say that our sample is free of its contamination by considering a RUWE ≤ 1.4, which is the criterion v) adopted in Subsection 3.1. Therefore, the astrometric members obtained in 1 are ready for a reliable photometric analysis.

Interstellar reddening is another important factor to address when determining the age of open clusters. In a region with variable interstellar reddening, to know the extinction value becomes a challenging task. The correct fit of the isochrone to the observations is directly dependent on the value of A v . In this work, this value is estimated using the new three-dimensional (3D) dust reddening map and is then applied in conjunction with the Gaia photometric reddening law, as explained in Subsection 3.3.

We present the evaluation of the Gaia DR3 photometric diagram of the four RSL new open clusters identified, IRAS-20306+4005 and HSC 630 plotted in Figure 7, and those in the core of Cyg OB2 association, plotted in Figure 8. Red filled circles correspond to the N h p members, and the yellow circles indicate the rest of the members. The isochrone is fitted based on the red filled circles. In all the CMD figures, the isochrone presented in black corresponds to the most probable age estimated for each OC, while the isochrones in yellow and green, as observed, also appear to fit the stellar member observations. Then, an estimation of the error in the age is the difference between the ages of yellow and black isochrones and between the ages of green and black ones. The isochrones in light blue and blue represent the age range investigated.

Figure7.Gaia photometric diagram for the probable members of the four RSL new open clusters, IRAS-20306+4005 and HSC 630. Light gray dots correspond to the field population. Red filled circles are the N h p members of each cluster obtained in this paper while the yellow ones are the rest of the members. Open blue circles are the members found by Hunt & Reffert (2023) [19]. Magenta triangle in the IRAS-20306+4005 CMD represents the star with IR excess identified as BY DRA Variable by Chen et al. (2020) [43]. The black isochrone corresponds to the most probable age estimated for each OC. The magenta isochrone represents the evolutionary model of stars reported by Hunt & Reffert (2023) [19].

In these figures, Hunt & Reffert (2023) [19] members are plotted with open blue circles. They are not considered to fit ours isochrones because they may be contaminated by false positives, as shown in Subsection 4.1.1. The magenta curve is the isochrone achieved with the photometric parameters proposed for each open cluster by Hunt & Reffert (2023) [19].

Figure 8. Gaia photometric diagram for the probable members of the four known open clusters in the core of CygOB2. Symbols as in Figure 4. Cyan and green triangles represent stars with IR excess identified as YSO by Kuhn et al. (2021) [44] and X-ray source as [45], respectively. Black triangle is the emission-line star identified as Schulte 64 by Bhattacharyya et al. (2021) [46]. The black isochrone corresponds to the most probable age estimated for each OC. The magenta isochrone represents the evolutionary model of stars reported by Hunt & Reffert (2023) [19].

4.2.1. New OCs

• RSL-01 ≡ IRAS-20306+4005

This cluster, located at less than 1 kpc in the southern edge of the study region, in the line of sight of the Cygnus-X DR 15 Region [42], is plotted in Figure 1 with red dots. The isochrone for the Gaia DR3 catalogue data of the 22 N h p members (upper left in Figure 7), is fitted using a visual absorption value of, A v = 1.3 − 0.03 + 0.02 mag, as determined for this Galactic region in the 3D map. The uncertainties in the A v value correspond to those provided by the map. To estimate the age of this cluster, we fit isochrones within an age range of 2 to 15 Myr, ultimately determining an age of 8 ± 1 Myr. Most of the 32 possible members are likely to be late spectral types, with only a few exhibiting early spectral types (B and A).

One of its members, the Gaia DR3 2064713443456205696 star, ( α , δ ) = ( 308.0477 , 40.3021 ) has a reddening-free photometric parameter Q N I R = − 1.17 ± 0.13 , and according to what we stated in Section 3.3, this Q N I R value would indicate that this could be a PMS or an YSO star. Additional information available regarding this star indicated in Figure 7 with a magenta triangle is that Chen et al. (2020) [43] classify it as a probable BY Draconis Variable star and they are of K-M type, similar to the spectral type that we can estimate with our best-fitting isochrone. Besides, we notice that all members of Hunt & Reffert (2023) [19] that are below the isochrone determined by us have large uncertainties in the parallax. Their distance histogram shows that 6 of them may be false positives, according to the analysis performed in 4.1.1. The magenta isochrone represents the evolutionary model of stars formed 4.8 Myr ago with solar metallicity, located at a distance of 936 pc and subject to a visual extinction of 3.7 mag, as determined from the 50th percentile results published by Hunt & Reffert (2023) [19].

• RSL-02 ≡ HSC 630

HSC 630 is an OC located near the center of the examined region, at an estimated distance of 1346 pc from the Sun, plotted with green triangles in Figure 1. The best-fitting isochrone for its 11 N h p members is obtained with the visual absorption value, A v = 2.1 − 0.05 + 0.08 mag, derived from the 3D map. By studying this region employing images from the Digital Sky Server (DSS), it is evident that the initial dust has already been swept away, which would be consistent with a visual absorption value of only two magnitudes. The age of this OC is investigated within the range of 4 to 22 Myr, and the most probable formation age is 12 ± 1 Myr. The Gaia DR3 2068009749251662336 star with G = 12.38 mag and ( G B P − G R P ) = 0.74 mag would be the earliest, probably a late B spectral type star whose age corresponds very well with the cluster age. The rest of the members are likely of spectral types A, F, and G. The magenta isochrone represents the 50th percentile results by Hunt & Reffert (2023) [19] with A v = 1.9 mag, an age of 6 Myr and a distance of 1294 pc.

• RSL-03

This cluster, located near the centre of the study region, at an estimated distance of 1575 pc from the Sun, is plotted in Figure 1 with turquoise circles. From the 9 N h p members of RSL- 03, the best-fitting isochrone for the Gaia DR3 catalogue is obtained with a visual absorption of A v = 5.2 − 0.14 + 0.04 mag, found with these errors in the 3D map. The age of this OC is investigated within the range of 4 to 22 Myr, with an estimated formation age of 14 ± 1 Myr. The spectral type of these stars would be between B and F0. Although the open cluster HSC 624 determined by Hunt & Reffert (2023) [19] has not been detected (see subsection 4.1), for comparison, we have included their isochrone in Figure 7 because its northeast part coincides with our RSL-03. The physical parameters of HSC 624 determined by Hunt & Reffert (2023) [19] at the 50th percentile for the members of this cluster are similar to ours, with a distance of 1.6 kpc, an age of 15 Myr, and A v = 5.1 mag.

• RSL-04

This cluster is located in the southern right edge of the study region, at an estimated distance of 1742 pc from the Sun, and is plotted in Figure 1 with a black triangle. The best-fitting isochrone for the 10 N h p members is obtained with a visual extinction of A v = 2.5 − 0.03 + 0.05 mag, as reported for this Galactic region in the 3D map. The age of the cluster is investigated within the range of 16 to 40 Myr, resulting in 26 ± 2 Myr with A-type and late spectral-type stars. Based on this age, the cluster is among the older open clusters in the Cyg OB2 region.

• RSL-05

RSL-05 is an OC located near the centre of the examined region, at an estimated distance of 1629 pc from the Sun, plotted with yellow triangles in Figure 1. The 16 N h p members of RSL-05 are used to obtain the best-fitting isochrone which suggests a visual absorption of A v = 3.8 mag and an age of 18 ± 2 Myr. Based on this result, this open cluster would be another member of the older groups of open clusters in the Cyg OB2 region. Some stars are likely to belong to spectral types F and G, while the majority are earlier-type stars, specifically B and A. For this open cluster, the visual extinction value obtained in the Galactic region using the 3D map is A v = 4.6 − 0.13 + 0.08 mag, so it differs by approximately 1 magnitude from our result. This discrepancy is likely due to the high concentration of interstellar material in the region, along with the fact that the 3D map was generated using data from the Gaia DR2 catalogue, which has an inherent 30% uncertainty in parallax measurements compared to the Gaia DR3 catalogue. It is evident that the [19] isochrone shown in magenta color exhibits different visual extinction and age, with A v = 5.1 mag and age of 15 Myr. This open cluster should be reanalyzed using the data provided by the upcoming Gaia DR4 catalogue, which is expected to yield more precise and, therefore, more reliable results. Although HSC 624 has not been detected, in Figure 4 we include its [19] isochrone as in the study of RSL-03 because its southwest part coincides with our RSL-05.

• RSL-06

The OC RSL-06 is located near the center of the study region, at an estimated distance of 1682 pc from the Sun, plotted with pink triangles in Figure 1. RSL 06 contains 12 N h p members and the best-fitting isochrone for these stars is obtained with a visual absorption of A v = 5.4 − 0.01 + 0.10 mag, found with these errors in the 3D map. The age is investigated within the range of 4 to 30 Myr, with an estimated formation age of 14 ± 1 Myr. These stars would be from B to A9 spectral type. It is important to note that one of the results obtained from the analysis of these six open clusters is that RSL- 03, RSL- 05, and RSL- 06 are located very close to each other, as shown in Figure 0.0.2. They are the clusters for which the highest values of A v are estimated, ranging between 3.8 and 5.4 magnitudes.

4.2.2. Core of Cyg OB2

• Bica 1 and Bica 2

Bica et al. (2003) [47] detected Bica 1 and Bica 2 by visual inspection while examining the structure of the association Cyg OB2 with DSS images, both objects are located within the core radius of the association and seem to form a physical pair in the association core. Maíz Apellániz et al. (2020) [48] noticed that they are hard to distinguish in proper motion even if they are seen as density concentrations in the plane of the sky. The proper motions in the right ascension of two clusters are very similar while those in declination differ very little.

This work identifies Bica 1 and Bica 2 using the HDBSCAN algorithm, which detects these two objects separately. They are then confirmed as clusters by fulfilling the three criteria outlined in 3.2.1. Proper motion and parallax values suggest that Cygnus OB2 association and each of these clusters are co-moving (see Figure 6). The distance measured for both clusters by Maíz Apellániz et al. (2020) [48] is ~1.7 kpc, in accordance to our results in Table3. Bica 1 has 15 N h p members. The lack of evolved stars makes it impossible to determine the position of the turn-off point, thus complicating the selection of the correct isochrone. The best-fitting isochrone is found by studying an age range of 2 to 10 Myr. The 4 ± 1 Myr isochrone, with a visual extinction of A v = 6.3 − 0.07 + 0.07 magnitudes, provides the best fit. It is a very young cluster of stellar members with early spectral types. The Gaia DR3 2067782111687592704 star located at ( α , δ ) = ( 308.2830 ∘ , 41.2241 ∘ ) with Q N I R = − 0.52 ± 0.08 , indicated with cyan triangle symbol on Figure 8, represents the YSO by Kuhn et al. (2021) [44]. Bica 2 is older than Bica 1 but contains a greater number of probable stellar members with 28 N h p members. It also lacks evolved stars, and the best isochrone fit is found by studying an age range of 2 to 15 Myr with visual absorption, A v = 5 − 0.06 + 0.06 mag. The estimated formation age for Bica 2 is 6 ± 1 Myr. All these stars have early spectral types. The Gaia DR3 2067783559095152768 star located at ( α , δ ) = ( 308.3271 ∘ , 41.2597 ∘ ) and with Q N I R = − 0.18 ± 0.071 , is a Be star identified as Schulte 64 with Spectral type B1 V [46]. This star is indicated by a black triangle symbol in Figure 8. The visual extinction values for Bica 1 and Bica 2, along with their associated errors, are the values assigned to this Galactic region in the 3D map. The magenta isochrone represents the evolutionary model of stars reported by Hunt & Reffert (2023) [19] for Bica 1 and Bica 2, as the authors consider the members of both clusters to be part of a single open cluster. This isochrone corresponds to a stellar cluster located at a distance of 1.6 kpc, formed 3.5 Myr ago, with a visual extinction of 5.6 mag. The age difference shows that both clusters formed at different times.

• FSR 0238

The OC FSR 0238 is located east of the centre of the studied region, at an estimated distance of 1686 pc from the Sun, and is plotted with pink dots in Figure 1. The best-fitting isochrone for these stars suggests a probable visual absorption of A v = 5.2 mag, which differs by one magnitude from the value obtained for the Galactic region using the 3D map ( A v = 6.2 − 0.02 + 0.06 mag). This discrepancy warrants further investigation with the upcoming Gaia DR4. The age is studied in the range of 2 to 24 Myr, and according to our best-fitting isochrone for the 14 N h p members, the age of this open cluster would be 12 ± 2 Myr. This result aligns well with the possible age of the earliest star, Gaia DR3 2067870386152902656, with a spectral type of B V. Although we do not know the exact spectral type of the other members, we can reasonably conclude that they are likely B and A type stars.

• FSR 0236

It is an open cluster close to the core of the Cyg OB2 association at a distance of 1661 pc to the Sun, and is plotted with turquoise dots in Figure 1. The best-fitting isochrone for the 17 N h p members suggests that the visual absorption, A v = 5.0 − 0.04 + 0.08 mag, with the associated errors from the 3D map, represents the interstellar reddening in the region. This A v value is similar to those obtained for Bica 2, and FSR 0238 clusters, which are located in the same region of the Galaxy. The age is study in the range of 2 to 15 Myr and according to our best-fitting isochrone, the age of this open cluster would be 8 ± 1 Myr. The Gaia DR3 2067834514587217536 star located at ( α , δ ) = ( 308.1170 ∘ , 41.3803 ∘ ) and with Q N I R = − 3.05 ± 0.2 , is represented by a green triangle symbol in Figure 8. This star is one of those investigated by Rauw (2011) [45] during the multi-epoch XMM-Newton campaign on the core of the massive Cyg OB2 association, where it is categorized as an X-ray fainter OB star, but not analyzed in detail, with a possible spectral type of O7 V. Our analysis using the PARSEC isochrone suggests that it is likely a late B spectral type and the rest of the members are also likely to be of spectral type B.