Newly detected open clusters in the Galactic disk using Gaia EDR3

Multiple OCs at different distances along the line of sight are superimposed, making it very difficult to accurately decompose them and find the hidden OCs. To solve this puzzle, we suggested in Paper I to make improvements on samples for the purpose of finding hidden OCs by focusing on small spatial regions and considering the effect of distance. Hence, in this work, we independently searched for OCs in different distance bins: ¡1 kpc, 1–2 kpc, 2–3 kpc, 3–4 kpc, 4–5 kpc, and ¿5 kpc, where each bin includes tens of million stars. Simultaneously, this technique can also reduce the computational procedure.

Another key aspect of the sample-based clustering search method is to decide the spatial sizes of different regions. In our previous work, rectangles of $1^{\circ}$ $\times$ $1^{\circ}$ were used by Paper I. Here, we have made an improvement on this point, where the sizes varied according to the spatial density of the regions. We still divided the regions into squares, but the sizes of the squares in different distance bins are in the range of [$1^{\circ}$, $10^{\circ}$], where the higher the density of stars, the smaller the size. This improved measure, which adapts to stellar population densities automatically, is a good solution to the problem of uneven spatial distributions among stars when searching for star clusters. Finally, we yielded about 40 000 spatial boxes in the six distance bins.

After preparing the samples (as described in Sect. 3.1) we began to search for spatial overdensity structures using the unsupervised clustering algorithm, DBSCAN. This is a density-based algorithm, so it offers advantages that allow it to find clusters of arbitrary shapes. As the member stars in an OC have common positions and proper motions, we applied DBSCAN in the five-dimensional (5D) space ($l$, $b$, $\varpi$, $\mu_{\alpha^{*}}$ and $\mu_{\delta}$). The DBSCAN algorithm defines a cluster based on two parameters: $\epsilon$ and $minPts$, which are used to describe the closeness of the sample distribution in the neighbourhood. The parameter $\epsilon$ is automatically computed in each sample using a Gaussian kernel density estimation method and the $k$-nearest neighbours algorithm (more details see Paper I). In this work, we were still focused on smaller regions as Paper I to detect unnoticed OCs, namely, the sizes of the squares in different distance bins were set in the range of [$1^{\circ}$, $10^{\circ}$]. Meanwhile, the parameter $minPts$ is the minimum number of objects within $\epsilon$ that can be considered as a cluster, and since it was been shown in Paper I that many hidden OCs could be hunted with $minPts$ = [6, 10] in small regions, we adopted the same values in this work.

In addition, for stellar clusters located at the borders of the boxes in Sect. 3.1, we took the following measures to dispose of them. If there were two or more clusters with compatible mean parameters within 3$\sigma_{i}$ (where $\sigma$ is the standard deviation) in the 5D parameter space, $i$ = $l$, $b$, $\varpi$, $\mu_{\alpha^{*}}$ and $\mu_{\delta}$, they were considered as substructures of the same star cluster. After further confirmation by visual inspection, we combined these substructures or re-detected the entire cluster. In the following steps, we introduce how we determined if the overdensity structures found with DBSCAN were potentially real OCs or just statistical clusters.

As mentioned by Cantat-Gaudin & Anders (2020), while the apparent proper-motion dispersion of an OC does not constitute an accurate diagnosis of its dynamical state, it can serve as a sufficient empirical basis for distinguishing reasonable OCs from implausible ones. Hence, we filtered the searched star clusters in Sect. 3.2 by their internal proper-motion dispersions. Recently, we found that this method was also adopted in Hunt & Reffert (2021). In this study, we adopted more rigorous dispersion parameters.

An OC, as a gravitationally bound system, has a small velocity dispersion. The typical dispersion of a globular cluster (GC) is from 5 to 10 km s^-1 (e.g., Lapenna et al., 2015; Baumgardt & Hilker, 2018). In turn, OCs have smaller dispersions. For example, the study by Mermilliod et al. (2009) showed that the typical dispersion of an OC is $\sim$ 1 km s^-1. However, recent studies, using line-of-sight velocities obtained from high-resolution spectroscopy, indicated that an OC has an internal dispersion below $\sim$ 2 km s^-1 (e.g., Donati et al., 2014; Cantat-Gaudin et al., 2014; Vereshchagin & Chupina, 2016; Overbeek et al., 2017; Hatzidimitriou et al., 2019). Interestingly, a recent study that focused on the relationship between the total proper-motion dispersions and parallaxes of OCs identified in Gaia DR2 (Cantat-Gaudin & Anders, 2020) showed that the dispersions of most OCs more distant than $\sim$ 1 kpc (i.e., parallax smaller than 1 mas) are larger than 2 km s^-1 but below 0.5 mas yr^-1, which may result from measurement uncertainties or uncertainties associated with the difficulty of distinguishing between OC member stars and contaminating field stars. Thus, we selected the OC candidates using the proper-motion criterion:

For the OC candidates obtained in Sect. 3.3, here we go on to introduce how we proposed them as potentially real OCs. On the one hand, we made references to the characteristics of known OCs described in some previous studies (e.g., Cantat-Gaudin & Anders, 2020; Cantat-Gaudin et al., 2020; Tarricq et al., 2021; Dias et al., 2021); for instance, an OC candidate can be considered as a potentially real OC if it could be shown to clearly pass its members, distance, age, or velocity relative to the field stars, as well as the density of the background stellar distribution, for instance. Furthermore, the member stars of an OC formed in the same molecular cloud, so its color–magnitude diagram (CMD) should follow an empirical isochrone. Hence, we visually inspected the CMDs of the OC candidates found in this work in order to propose the more reliable ones.

In addition, if an OC candidate appeared to be potentially real, we estimated its RV and error as well as its age for further research. As for the weighted standard deviation of its RV, we adopted the same equation described by Soubiran et al. (2018):

where $RV_{\rm OC}$ is the mean value of the member stars, $w_{i}$ = 1/$\varepsilon_{i}^{2}$ refers to the individual radial velocity measurements and $\varepsilon_{i}$ is the RV error for star $i$ provided in Gaia EDR3.

Many efforts have been devoted to determining the ages of OCs in Gaia (e.g., Bossini et al., 2019; Cantat-Gaudin et al., 2020). We also determined the ages of the proposed new OCs using the same method adopted in some previous studies (e.g., Liu & Pang, 2019; Hao et al., 2020; He et al., 2021), which is aimed at constructing the best isochrone for the member stars in an OC candidate. The isochrones are derived from the PARSEC library (Bressan et al., 2012) updated for the Gaia DR2 passbands with the photometric calibration of Evans et al. (2018). These isochrones we used contain logarithmic ages (i.e., log(age/yr)) from 5.92 to 10.13 and metal fractions ($z$) from 0.015 to 0.029, as well as a series of isochrones are generated with steps of $\Delta$ log(age/yr) = 0.02 and $\Delta$ $z$ = 0.001, respectively.

The fitting function is the key to constructing a reliable isochrone for an OC and isochrone fitting pipelines have been produced in several studies (e.g., Perren et al., 2015; Bonatto, 2019). As in some previous works, e.g., Liu & Pang (2019) and He et al. (2021), we used the following fitting function to fit the CMDs for OCs:

where $n$ is the number of member stars in an OC candidate, and $\textbf{\emph{x}}_{k}=[{\it G}_{k}+\Delta_{\rm G}+{\it A}_{\rm G},\ ({\it G}_{\rm BP}-{\it G}_{\rm RP})_{\it k}+{\it E}({\it G}_{\rm BP}-{\it G}_{\rm RP})]$, $\textbf{\emph{x}}_{k,nn}$ is the position of the $k$th member star and the nearest neighboring point to this star in the isochrone, respectively. For the $\textbf{\emph{x}}_{k}$, $\Delta_{\rm G}$ is the distance modulus, A_G denotes the line-of-sight extinction, and ${\it E}({\it G}_{\rm BP}-{\it G}_{\rm RP})$ indicates the reddening in $G$ magnitude of an OC candidate.

The extinction A_G and reddening ${\it E}({\it G}_{\rm BP}-{\it G}_{\rm RP})$ of an OC candidate were corrected as follows. When fitting isochrones, we set the parameter A_G from 0.0 to 4.0 with a step of 0.02 and ${\it E}({\it G}_{\rm BP}-{\it G}_{\rm RP})$ = 0.50 A_G, considering the approximate relation between A_G and ${\it E}({\it G}_{\rm BP}-{\it G}_{\rm RP})$ in Gaia (Andrae et al., 2018) as well as an extinction curve of $R_{v}$ = 3.1 for the Milky Way galaxy (Cardelli et al., 1989; O’Donnell, 1994). In addition, parameter $\overline{d}\ ^{2}$ is the mean square distance between OC members and their closest neighboring points in the isochrone. For each OC candidate, we minimized $\overline{d}\ ^{2}$ by calculating the average squares of the distances between member stars and corresponding points in each theoretical isochrone. As mentioned by Liu & Pang (2019), this method is sensitive to the discrepancy between isochrones and the observational data.

For all of our detected spatial star clusters, we first cross-matched them with known OC catalogs in Gaia (i.e., Cantat-Gaudin et al., 2018; Castro-Ginard et al., 2018; Cantat-Gaudin et al., 2019; Castro-Ginard et al., 2019; Sim et al., 2019; Liu & Pang, 2019; Ferreira et al., 2019; Hao et al., 2020; Castro-Ginard et al., 2020; Ferreira et al., 2020; He et al., 2021; Ferreira et al., 2021; Hunt & Reffert, 2021; Castro-Ginard et al., 2021b). If a stellar cluster found in this work and a known OC from these catalogs were found to have compatible mean parameters within 3$\sigma_{i}$ in the 5D astrometric parametric space, $i$ = $l$, $b$, $\varpi$, $\mu_{\alpha^{*}}$ and $\mu_{\delta}$, we considered this star cluster as cross-matched and a visual inspection was also adopted at the same time to confirm this assessment.

Although our aim is to detect hidden OCs in our Galaxy, we still re-detected a large amount of previously known OCs in the Gaia data; for instance: 889 OCs that listed in the catalog ($\sim$1 200 known OCs) of Cantat-Gaudin et al. (2018) were refound; we were able to find 37 OCs in the catalog (41 known OCs) of Cantat-Gaudin et al. (2019); 647 OCs reported in Castro-Ginard et al. (2018, 2019, 2020, 2021b) were cross-matched; and so on. In total, the 1 759 stellar clusters we obtained were cross-matched with the above catalogs, located in the Galactic latitudes of $|b|\leq$ 20^∘, which is comparable with the result (1 559) in the recent work of Castro-Ginard et al. (2021b), showing a high re-detection efficiency.

Before Gaia, Dias et al. (2002) presented a list of OCs based on revised data compiled from previous catalogs and from isolated papers published before, which contained more than 2 000 objects. Using the near-infrared photometric data of approximately 470 million objects in 2MASS (Skrutskie et al., 2006), and proper motions from the PPMXL catalog (Röser et al., 2010), Kharchenko et al. (2013) completed a survey of all previously known OCs, called the Milky Way Star Clusters (MWSC). This catalog lists 3 006 objects, including known OCs and OC candidates (2 469), GCs, associations, and asterisms.

After completing the step in Sect. 4.1, we cross-matched the remaining clusters with the above two catalogs using the following criteria: if a star cluster falls within a circle of $0.5^{\circ}$ radii (Castro-Ginard et al., 2019, 2020) of one object listed in these two catalogs, we selected it. Then, if their mean proper motions were within 3$\sigma_{i}$ of the cluster found in this work and their distances were compatible, we considered this star cluster as being matched. The catalogs in Dias et al. (2002) and Kharchenko et al. (2013) do not provide the mean parallax and associated uncertainty for each OC but an estimation of the distance instead, so the criterion is that the known OCs are within the distance errors of our detected clusters. The distance of our detected cluster is the inverse of the mean parallax of member stars (Castro-Ginard et al., 2020), and the assumed errors come from three times the standard deviation of parallax. Although most of the OCs in these two catalogs had already been taken into account by the cross-matching of our star clusters with the sample of Cantat-Gaudin et al. (2018), we still found 120 known OCs in the MWSC catalog and 71 known OCs in the catalog of Dias et al. (2002), along with 20 OCs that are repetitive.

In order to cross-match with known GCs more accurately, we investigated the GC catalog reported by Baumgardt et al. (2019), who presented the mean proper motions and space velocities of 154 Galactic GCs using a combination of Gaia DR2 proper motions and ground-based line-of-sight velocities. Finally, we found that 82 star clusters we obtained were cross-matched with the GCs listed by Baumgardt et al. (2019), and the proper motions and RVs provided by Gaia EDR3 are consistent with those in the catalog.

There are 106 GCs presented by Baumgardt et al. (2019) located at the Galactic latitude of $|b|\leq$ 20^∘, and, thus, the proportion of GCs detected here is $\sim$ 80%. Each GC found here contains thousands of stars, and the detection of Galactic GCs is a good test of our proposed method. Meanwhile, for the remaining $\sim 20\%$ of GCs that were not detected by us, their non-detection might be the result of their far distances make their member stars being too faint.

After cross-matching with the known Galactic OC and GC catalogs, there were many star clusters remaining whose cluster nature was yet to be determined. Among these clusters, 910 ones met the proper-motion criterion described in Sect. 3.3. These 910 star clusters were considered as potential OC candidates. We visually inspected the features of these star clusters, as described in Sect 3.4. After this inspection, 704 OC candidates were proposed to be potentially real OCs.

Based on the same format as the table presented in previous works (e.g., Castro-Ginard et al., 2020, 2021b), we show the mean parameters and standard deviations (i.e., 1$\sigma$ errors) of each OC candidate in Table 1, including its right ascension (RA), declination (Dec), $l$, $b$, parallax ($\varpi$), proper motions ($\mu_{\alpha^{*}}$ and $\mu_{\delta}$), age ($\log$($t$)), $RV$ ($V_{r}$), number of member stars ($N$), and its apparent angular size, which was computed by $\theta=\sqrt{\sigma_{l}^{2}+\sigma_{b}^{2}}$ following Castro-Ginard et al. (2020). The full version of Table 1 can be found online at the CDS ¹¹1https://cdsarc.u-strasbg.fr/ftp/vizier.submit//new_oc_v3/, including the table of member stars of OCs. For our newly found OCs, Fig. 1 shows some examples of the distributions of the member stars in astrometric space and their CMDs. It is obvious that the OCs we proposed typically show a high concentration of member stars in all five astrometric parameters, especially the proper motions, and their member stars in the CMDs are almost concentrated on potentially theoretical isochrones.

As shown in Fig. 2, we made a parallactic comparison between the newly found OCs and the previously known OCs in Cantat-Gaudin et al. (2020), which shows a high level of consistency. For the newly found OCs, the mean parallaxes of vast majority (99.3$\%$) range from 0.06 to 3.00 mas, which yield distances from $\sim$ 330 pc to $\sim$ 16 kpc when estimating the distance as the inverse of the mean parallax. However, we note that this method is not ideal as it ignores the parallax uncertainties (e.g., Lindegren et al., 2021b). In addition, $\sim$ 15% of the OCs are closer than 1 kpc, $\sim$ 34% are located between 1 and 2 kpc, $\sim$ 37% between 2 and 4 kpc, and $\sim$ 14% of the OCs are further than 4 kpc. Among the newly found OCs, 214 of them have stars with RVs in Gaia EDR3, of which 71 OCs contain more than two stars with RVs.

For the newly found OCs, $\sim$ 85% are located at Galactic latitudes of $|b|\leq$ 5^∘, $\sim$ 9% are located in 5^∘ ¡ $|b|$ $\leq$ 10^∘ and only $\sim$ 6% are located at Galactic latitudes $|b|>\$10^∘, showing they are concentrated in the Galactic disk. The distributions of the new OCs in the Galactic plane are shown in Fig. 3, which indicates that the distribution of the new OCs follows a particularly similar distribution to the previously reported ones. Fig. 4 presents the distribution of the new OCs and known OCs in the galactocentric radius ($R$) and altitude ($z$) above the Galactic middle plane, showing they are very consistent, and this result is also concordant with Castro-Ginard et al. (2021b). Hence, all of the above distributions of our newly found hidden OCs significantly densify the distribution constructed by previously known OCs.

The ages of the proposed OCs are color-coded in Fig. 4, which reveals the consistency of the age estimations with the previously known OC population compiled by Cantat-Gaudin et al. (2020). Besides, it can be seen that these new OCs gradually migrated further from the Galactic disk as they age, which has been mentioned by Hao et al. (2021).

The distribution of the 299 newly found OCs with ages younger than 20 million years projected on to the Galactic plane is shown in Fig. 5, where the spiral arms defined by masers associated with high-mass star formation regions with Very Long Baseline Interferometry parallax measurements (Reid et al., 2019) are also displayed for comparison. More than 70% of the young OCs are located in the spiral arms outlined by high-mass star formation region masers or bright O-B type stars (Xu et al., 2018, 2021), especially the more populous ones and the distribution of young OCs is similar to those of O-B type stars in Gaia. Hence, our result also confirmed that the young OCs are good tracers of the Galactic spiral structure, as described in some recent works (e.g., Hao et al., 2021; Castro-Ginard et al., 2021a; Poggio et al., 2021).