LISC Catalog of Star Clusters. I. Galactic Disk Clusters in Gaia EDR3

This work searches for the candidates of Galactic disk star clusters in Gaia Early Data Release 3 (Gaia EDR3) and determines their basic parameters from color–magnitude diagrams (CMDs). A friends-of-friends method for membership determination and stellar population models including binary stars (ASPS) and rotating stars are adopted. As a result, 868 new star cluster candidates are found, besides 2729 known ones. When checking the CMD of each candidate, 61 new candidates show main sequences including a turnoff, which suggests that they are real star clusters. The basic parameters, including distance modulus, color excess, metallicity, age (or age range), primordial binary fraction, and rotating star fraction, are determined carefully by fitting the morphologies of CMDs of 61 newly identified star clusters and 594 known star clusters, which have relatively clear main sequences. The CMDs are fitted in considerable detail to ensure the reliability of property parameters of clusters. All final results are included in a new star cluster catalog, which is named LI team’s Star Cluster (LISC), and the catalog is available in the Zenodo repository.


Introduction
Star clusters (SCs) are of key importance for studying the structure and history of the Milky Way (Cantat-Gaudin et al. 2018). An SC is a group of stars that are gravitationally bound and born in the same starburst. Usually, the initial metallicity and age of stars in a cluster are thought to be the same. The member stars of a cluster share a common position (l, b, ϖ) and proper motion (μ α , μ δ ). There are two kinds of SCs, i.e., globular clusters (GCs) and open clusters (OCs). GCs, in general, contain thousands to millions of stars forming relatively dense and conspicuous structures, while OCs are usually much less populated (a few hundred or thousand stars), forming loose structures that may be very difficult to detect, especially when projected against dense stellar fields of the Milky Way. Accurate position and proper motion of stars are important for searching Galactic OCs, as this information dominates the cluster identification in most methods (Gaia Collaboration et al. 2016). The limitation of ground-based observations makes it difficult to get enough accurate information. This makes it hard to discover a large sample of SCs, in particular distant and small OCs. Fortunately, the Gaia mission supplies us with a good chance to break through the limitation partially. Gaia is a space astrometry mission of the European Space Agency (ESA; Gaia Collaboration et al. 2016). It provides absolute astrometry (positions, proper motions, and parallaxes), broadband photometry in the G band, lowresolution blue and red (spectro)photometry (B P and R P ), and integrated G BP and G RP photometry for all objects. Many works have used Gaia data to hunt for SCs in recent years. More than 3000 SCs (most are OCs) are finally discovered (e.g., Cantat-Gaudin et al. 2018 andLiu &Pang 2019). This increases the number of known SCs significantly and moves forward the knowledge of SCs a lot. The stellar population properties of these clusters are also investigated. One can refer to the papers of, e.g., Claydon et al. (2017) Ferreira et al. (2021), and Dias et al. (2021) for some details about these studies. Most previous works on SC catalogs are based on the data of Gaia Data Release 1 or 2 (Gaia DR1 or Gaia DR2), and the size of the Gaia survey data is increasing. It is valuable to do some comprehensive studies by utilizing newer data.
The third intermediate Gaia data release, Gaia Early Data Release 3 (Gaia EDR3; Gaia Collaboration et al. 2021), came out in 2020. This release is based on the data collected during the first 34 months of the Gaia mission. It consists of an updated source list, astrometry, and broadband photometry in the G, G BP , and G RP bands compared to previous releases. In addition, an updated list of radial velocities from Gaia DR2, which is cleaned from spurious values, is included. Gaia EDR3 represents a significant improvement in both the precision and accuracy of the astrometry and broadband photometry. This release therefore should be treated as an independent release from previous ones. It represents a significant advance over Gaia DR2, with parallax precisions increased by 30%, propermotion precisions increased by a factor of 2, and the systematic errors in the astrometry suppressed by 30%-40% for the parallaxes and by a factor of about 2.5 for the proper motions. The new release allows us to recheck the known SCs and search for new SCs with a higher reliability. This paper uses the Gaia EDR3 data to do such work. A main aim is to search for Galactic disk SCs in Gaia EDR3. It will identify the previous findings and discover some new SCs.  Note. The best-fit and observed CMDs are compared in Figures 3-6. Parameters ϖ, μ α cosδ, and μ δ are the average values of member stars of a cluster. The standard deviations of the three parameters are also given in the table. If t range is given instead of t for a cluster, its SPT is CSP. Otherwise, it is SSP.
In addition, it aims to determine the stellar population properties of all SCs with good-quality color-magnitude diagrams (CMDs). An updated catalog of Galactic disk SCs, LI team's Star Cluster (LISC) catalog, which includes the position, proper motion, and reliable stellar population properties (for SCs with good CMDs), will be built. The structure of this paper is as follows: Section 2 introduces the star sample, and Section 3 describes the discovery of SC candidates. Then, Section 4 determines the stellar population properties of SCs via fitting the observed CMDs in detail. Finally, Section 5 provides a conclusion and discussion of this work.

Star Sample
As a main part of the third Gaia release, Gaia EDR3 appeared on 2020 December 3. The catalog contains the improved astrometry and photometry of Gaia DR2, and fiveparameter (positions, proper motions, and parallaxes) astrometric solution of the Gaia EDR3 is done for around 1.5 billion sources (Damljanović 2021;Forveille & Kotak 2021;Gaia Collaboration et al. 2021). This supplies a new opportunity to many astrophysical studies, including those on SCs. Because the source list of Gaia EDR3 is independent of DR2 and DR1, and from DR2 to EDR3 the changes impact up to 5% of the sources, it is certain that there will be some new findings when hunting for SCs in Gaia EDR3. We therefore select our star sample from this new release.
In order to build a database in accord with the previous catalogs of Galactic disk OCs (e.g., Dias et al. 2002;Kharchenko et al. 2013;Castro-Ginard et al. 2018 and Liu & Pang 2019), we take some rules similar to previous works to define our star sample. In detail, all stars are limited to the disk region, Galactic latitude |b| < 25°, brighter than 18 mag in G band, with proper motions (μ α cosδ and μ δ ) less than 30 mas yr −1 and parallaxes ϖ between 0.2 and 7.0 mas. These rules help us to exclude the observational artifacts due to faintness and constrain our sample to a maximum distance of about 5 kpc.

Star Cluster Hunting
Although there are many kinds of cluster-hunting methods, their main ideas are usually not very different. In general, an SC is found by the similarity of stellar position and proper motion. We therefore use the friends-of-friends (FoF) method of Liu & Pang (2019). This method can search for cluster   Step Unit candidates by the longitude l, galactic latitude b, parallax ϖ, and proper motion μ α cosδ and μ δ of stars effectively. Because it will take too long time to search for the whole parameter space at one time, the position space of l, b and ϖ are divided into 4096 domains, and the SC search is carried out in each domain at first. There is a sufficiently overlapping region (0.2 mas in ϖ dimension and 10 pc in the l and b dimensions) between two adjacent domains that SCs can also be identified even when they are located at the border of domains. We carry out parallel computing to speed up the cluster-hunting process. The FoF cluster-hunting method identifies SCs in the 5D parameter space X = (l, b, ϖ, μ α cosδ, μ δ ). All parameters are normalized to the range (0, 1) by taking a weight of w = (cosb, 1, 0.5, 1, 1)/(0.2cosb + 0.7). A cluster is identified when the distance of a star to its nearest neighbor is smaller than the linking length factor (b FoF ) times the average distance of the domain. Because some stars are included in different domains, the SCs sharing more than half stars are merged into one after hunting clusters in each domain. This reports many cluster candidates with fewer than 50 stars. The candidates that contain no less than 50 member stars are considered as potential clusters by this work as SC usually contains more than dozens of stars. As a result, 3597 potential clusters are found from Gaia EDR3. The cluster candidate number is obviously larger than the result of Gaia DR2 (Liu & Pang 2019), which reported 2443 SCs.

Newly Identified Star Clusters
Most of the cluster candidates are possibly not new findings because of the overlap of sources of Gaia DR1, DR2, and EDR3; we therefore match our results with some previous catalogs, i.e., Kharchenko et al. (2013), Cantat-Gaudin et al.  Casado (2021). If the distance between two cluster centers is less than the radius of a newly identified cluster, the two clusters are thought of as the same one. In other words, such clusters are known clusters. By this way, we find that 868 candidates are not included in previous catalogs and are potential new clusters. Note that these potential clusters are found roughly by the l, b, ϖ, μ α cosδ, and μ δ of stars. There should be more physical connections among these stars, but they are not considered in the cluster-hunting process. This implies that some cluster candidates may be not real clusters. Other methods are therefore needed to verify the results. In order to find real clusters from the cluster candidate sample, CMDs of all candidates are checked in detail. If a candidate has a relatively clear main sequence, it is supposed to be a real cluster, because the similarity of distance, color excess, stellar age, and metallicity of cluster member stars leads to some CMDs similar to the isochrones of theoretical stellar populations. Therefore, when the observed CMD of a candidate shows a somewhat clear main sequence and it can be fitted by an isochrone, it is considered to be a real cluster. However, it is regrettable that the CMDs of most new candidates are not clear or different from the isochrones of stellar populations. Thus, they are not assigned to certain SCs. Finally, the results suggest that 61 are real clusters within the 868 newly identified candidates. The first four columns of Table 1 present the name, R.A., decl., parallax ϖ, and cluster radius r sc of 61 newly identified SCs. Figure 1 shows the distribution of the newly identified candidates, including 61 real new clusters, 807 uncertified candidates without clear CMDs, and 2729 known clusters that are matched with previous works. Note that the name of a cluster is given by the combination of catalog name (LISC) and its serial number in the catalog.

Determination of Stellar Population Properties
The stellar population properties of SCs are usually determined by fitting the isochrones of theoretical populations to the observed CMDs. Such a method works well if the stellar populations of clusters are single-star simple stellar populations (ssSSP), in which all member stars of a cluster are single stars with the same metallicity and age. Many previous works on the stellar populations of SCs in Gaia took the isochrone fitting technique. Binary stars and (or) rotating stars were ignored in most works. In such a case, the results can be rather uncertain if binary stars, rotating stars, or multiple populations are contained in SCs. It is fortunate that we can infer the stellar population type (SPT) of a cluster roughly according to the shape of the observed CMD. For example, it will be a binarystar stellar population (bsSP) if there is a binary-star sequence on the lower right of the main sequence, and it may be a composite stellar population (CSP) or simple stellar population (SSP) with rotating stars if it shows an extended main-sequence turnoff (eMSTO). This judgment can guide CMD fitting to get more accurate population properties, because the incorrect choice of SPT in CMD fitting may lead to large uncertainties in the final results (e.g., Li et al. 2015Li et al. , 2016. In this work, the CMDs of 3597 cluster candidates are checked by eye to define their possible SPTs before CMD fitting. It is found that the quality of observed CMDs of most cluster candidates is poor (without a clear main sequence), and only those of 61 newly identified clusters and 594 previously discovered clusters can be fitted relatively reliably. The SPTs of clusters are divided into three types, i.e., ssSSP, binary-star simple stellar population (bsSSP), and those with eMSTO. Actually, this classification helps improve not only the reliability but also the speed of CMD fitting.

Stellar Population Model and CMD Fitting
This work employs the ASPS stellar population synthesis model (Li et al. 2012(Li et al. , 2015(Li et al. , 2016 for CMD fitting. It is a model that contains different kinds of stellar populations, including ssSSP; bsSSP; single-star composite stellar population (ssCSP); binary-star composite stellar population (bsCSP); simple stellar population of single, binary, and rotating stars (sbrSSP); and composite stellar population of single, binary, and rotating stars (sbrCSP). The widely used initial mass function (IMF) of Chabrier (2003), eight metallicities (Z = 0.0001, 0.0003, 0.001, 0.004, 0.008, 0.01, 0.02, and 0.03), 151 ages (0-15 Gyr with an interval of 0.1 Gyr), 100 primordial binary fractions ( f bin : 0-1.0 with an interval of 0.01), and six primordial rotating star fractions ( f rot : 0, 0.1, 0.3, 0.5, 0.7, and 1.0) are taken for the theoretical stellar populations. Some fitted distributions of rotation rate of rotating stars (Royer et al. 2007;Li et al. 2016) are adopted. Both single and binary stars are evolved by the rapid stellar evolution code of Hurley et al. (2002). The evolutionary parameters of stars are transformed into magnitudes via the BaSeL 3.1 spectral library (Lejeune et al. 1997(Lejeune et al. , 1998Westera et al. 2002). The stellar evolution code and spectral library have been used widely in different kinds of stellar population synthesis studies.
When determining the cluster properties, we make use of the V versus (V − I) CMD and Powerful CMD code (Li et al. 2017). The stellar population model and CMD-fitting code are the same as our previous works, e.g., Li et al. (2021). The V and I magnitudes are taken here because their uncertainties are relatively small and the magnitudes can be transformed from the G BP and G RP magnitudes using some transformation functions (Jordi et al. 2010). The Powerful CMD code compares the star fractions of theoretical and observed CMDs in different CMD regions, to seek the best-fit stellar population models. For each cluster, seven parameters, i.e., distance modulus m − M, color excess E(V − I), metallicity Z, young stellar age t, age range t range , initial binary fraction f bin , and primordial rotating star fraction f rot , are determined. In fact, some results, e.g., t and m − M, depend on the SPT classification of clusters. The parameter ranges of CMD fitting are presented in Table 2. It is noted that f bin affects the mainsequence width, while t range and f rot affect the eMSTO of intermediate-age clusters (Li et al. 2012(Li et al. , 2016 obviously.

Stellar Population Properties of Newly Identified Clusters
The stellar population properties of newly identified clusters are determined by the combination of Powerful CMD fitting and human verification. Because there is a slight differential reddening in each cluster (see Figure 2 for the distribution of differential reddening of stars), we correct for the differential reddening before fitting to CMDs. Our correction method is similar to the work of Milone et al. (2012). Some rough population parameters are first determined by Powerful CMD fitting. The ranges of input parameters can be seen from Table 2, but the steps of parameters are much larger than those listed in the table. Then, we check the goodness of CMD fitting by a goodness indicator named weighted average difference (WAD; see Li et al. 2017) and by eye. If a CMD is not fitted well, we narrow the range of input parameters and fit the CMD repeatedly, taking the steps of Table 2, until a satisfying fitting is obtained. The satisfying fitting corresponds to the least WAD   between the observed and best-fit CMDs. The method is same as our previous work (Li et al. 2021). This ensures the quality of the fitting. The CMDs of 61 newly identified clusters are finally reproduced with enough accuracy. The best-fit stellar population properties are accordingly determined. One can see Figures 3-6 for the comparison of the best-fit (red triangles) and observed (black points) CMDs of these clusters, while Figures 7-9 present the distributions of three cluster parameters. Their stellar population properties are shown in Table 1. Note that the G BP -band and G RP -band magnitudes have small uncertainties (about 0.012 and 0.006 mag, respectively), and the photometric scattering makes the primordial binary fractions of clusters a little larger than their real values. This effect cannot be corrected because we do not know the magnitude uncertainties of each star. Therefore, the binary fractions ( f bin ) shown here are the upper values when clusters were born. In order to make the figures clearer, CMDs with similar magnitude ranges are plotted in a line.
From Figures 3-6, we see that the observed CMDs have been reproduced as well as possible. Besides the isochrone of Figure 10. Comparison of observed and best-fit CMDs of some example known SCs. All SCs have eMSTO structures, and their SPTs seem to be CSPs. single stars, the binary-star sequence on the main sequences of clusters is also reproduced. It is clear that most of these clusters contain some binaries. If single-star stellar population (ssSP) models are used to fit the CMDs of these clusters, there should be large uncertainties in the result because of the effects of binary interactions and indistinguishability of binary components (Li et al. 2016). Moreover, the eMSTO structures of clusters are reproduced by stellar populations including age spread and (or) rotating stars. The good agreement of best-fit and observed CMDs suggests that the results are reliable and can be used for future works. Table 1 lists the best-fit stellar population properties of the abovementioned newly identified SCs. The distance modulus m − M, color excess E(V − I), metallicity Z, age t or age range t range , initial binary fraction f bin , and primordial rotating star fraction f rot are presented in the table. The position information of these clusters has also been shown in this table, so that one can easily match our catalog with others. As can be seen, these  Figures 7-9 show the distributions of age (or age of youngest member stars), metallicity, and primordial binary fraction of 61 newly identified SCs. We find that these SCs are younger than 2.5 Gyr (Figure 7), and most of them are metal-poor (Z 0.01; Figure 8). The primordial binary fraction of these clusters seems less than 0.55 (Figure 9).

Stellar Population Properties of Known Clusters with Good CMDs
Although the stellar population properties of most known clusters have been studied by previous works, single-star isochrone fitting was often used. The exclusion of binary stars, Figure 12. Similar to Figure 10, but for 20 other known SCs. The SPTs of these clusters seem to be SSPs. rotating stars, and multiple star bursts in stellar population models will certainly lead to uncertainties of some results, because such factors are common in SCs. In addition, Gaia EDR3 increases the precision and accuracy of the astrometry and broadband photometry significantly, so it is necessary to revisit the stellar population properties of known clusters based on the new data. Therefore, we fit the CMDs of some known clusters again and redetermine the stellar population parameters. Because the quality of CMDs of most clusters is poor, only 594 known clusters are studied. All CMDs are fitted carefully to reproduce the detailed morphologies. The CMD fitting is satisfactory when checking the WAD goodness indicator and stellar population parameters such as age spread, binary fraction, and rotating star fraction are obtained. Figures 10-12 show the comparison of best-fit (red triangles) and observed (black points) CMDs of some example SCs. The corresponding best-fit stellar population parameters are presented in Table 3. Note that, similar to these examples, the CMDs of 594 known SCs in the Gaia survey are fitted well and their stellar population properties have been determined carefully.

Conclusion and Discussion
This paper hunts for Galactic disk SCs in Gaia EDR3 and studies the stellar population properties of clusters that have clear main sequences in CMDs. An FoF method is used for seeking SCs, and 3597 cluster candidates are found. The CMDs of cluster candidates that have a clear main sequence are investigated in detail, via the ASPS stellar population model and Powerful CMD code. All the fitting results undergo manual inspection to make sure the stellar population properties are reliable. The main results are concluded as follows: 1. 868 newly identified Galactic disk SC candidates are found compared to eight previous works. 2. The stellar population properties of 61 newly identified SCs that have a somewhat clear main sequence are determined, via CMD fitting. 3. The observed CMDs of 594 known clusters are studied carefully, and their stellar population properties are well determined. 4. Most SCs are shown to consist of both single and binary stars. The initial binary fractions of most clusters are within the range of 0.3-0.55 (Figure 9). 5. The results are included in a new SC catalog, LISC.
Although the FoF method was used successfully by previous works, there are obvious uncertainties in both the number of SCs and stars in each SC. Thus, it is necessary to search for SCs in the Gaia EDR3 data by other methods. When fitting to the CMDs of SCs, only eight metallicities are taken to build stellar population models. The metallicity interval is somewhat large. This affects the goodness of CMD fitting, in particular the parts near the red giant. It will be better to check the stellar population properties with stellar population models with more metallicities.
In order to help the scientists to use our result data, the position and proper-motion information of 3597 Galactic disk clusters in Gaia EDR3 and the fundamental parameters of 655 clusters, together with their observed and best-fit CMDs, are available at the Zenodo repository https://zenodo.org/record/ 5705371#.YZPASbFdsrs.