11institutetext: School of Management and Economics, Kunming University of
Science and Technology, Kunming, China
22institutetext: Center for Astrophysics, Guangzhou University, Guangzhou,
China
33institutetext: Peng Cheng Laboratory, Shenzhen, 518000, China
44institutetext: Dali University, Institute of Astronomy, Dali, China,
<EMAIL_ADDRESS>
Received 20xx month day; accepted 20xx month day

# LISC Catalog of Open Clusters.III. 83 Newly found Galactic disk open
clusters using Gaia EDR3

Huanbin Chi (gbsn迟焕斌) 1122 Feng Wang (gbsn王锋) 2233 Zhongmu Li (gbsn李忠木) 44

###### Abstract

As groups of coeval stars born from the same molecular cloud, an Open cluster
(OC) is an ideal laboratory for studying the structure and dynamical evolution
of the Milky Way. The release of High-Precision Gaia Early Data Release 3
(Gaia EDR3) and modern machine-learning methods offer unprecedented
opportunities to identify OCs. In this study, we extended conventional HDBSCAN
(e-HDBSCAN) for searching for new OCs in Gaia EDR3. A pipeline was developed
based on the parallel computing technique to blindly search for open clusters
from Gaia EDR3 within Galactic latitudes $\left|b\right|$ $<$25 ∘. As a
result, we obtained 3787 star clusters, of which 83 new OCs were reported
after cross-match and visual inspection. At the same time, the main star
cluster parameters are estimated by colour-magnitude diagram fitting. The
study significantly increases the sample size and physical parameters of open
clusters in the catalogue of OCs. It shows the incompleteness of the census of
OCs across our Galaxy.

###### keywords:

techniques: photometric — star clusters: general — stars: individual: IP Vir,
YZ Boo

##  1 Introduction

An open cluster (OC) is a star cluster in which all member stars are
gravitationally bound to each other. In the Milky Way, most of such clusters
are found in the disc region. Their formation is thought to be related to the
structure of the Galaxy. The stars of an OC usually form in the same molecular
cloud and therefore have approximately the same age and metallicity. Thus the
member stars of an OC distribute on an isochrone in the colour-magnitude
diagram (CMD). This can supply some clues to the studies of the evolution of
stars. Therefore, it is essential to find OCs in the Galaxy and study their
stellar properties in detail.

Many efforts have been made to compile some catalogues of OCs, particularly
after the publication of the data releases of Gaia (DR2, EDR3, DR3) (Lindegren
et al. 2018; Gaia Collaboration et al. 2021, 2022). The data of the Gaia
satellite supply the celestial positions, parallaxes, and proper motions ($l$,
$b$, $\varpi$, $\mu_{\alpha}$ and $\mu_{\delta}$), in three photometric bands
(G, GBP and GRP) for more than 1.8 billion sources. It gives us a golden
opportunity to search for OCs. Thousands of new OC candidates are found by
different methods, and this enlarges the sample of Galactic OCs significantly.
In addition, they have been also useful to discard several unlikely OCs of
them. For example, Cantat-Gaudin et al. (2018b) discovered 60 new OCs using
the data of Gaia DR2. After that, Cantat-Gaudin & Anders (2020); Sim et al.
(2019); Liu & Pang (2019) found 41, 207 and 76 new OCs in 2019, respectively.
Castro-Ginard et al. 2021; He et al. 2021; Ferreira et al. 2020; Hunt &
Reffert 2021 identified 582, 74, 34, and 41 new OC candidates respectively.
Recently, Hao et al. 2022 used a sample-based clustering search method with a
high spatial resolution to hunt 704 potential open clusters. He et al. 2022b
and He et al. 2022a reported 541 new open cluster candidates and 46 new nearby
star clusters at high-Galactic-latitude regions. One such typical work is the
series works done by Cantat-Gaudin et al. 2018a, Castro-Ginard et al. 2018,
Cantat-Gaudin et al. 2019, Castro-Ginard et al. 2019, Cantat-Gaudin et al.
2020, Cantat-Gaudin & Anders 2020, Castro-Ginard et al. 2020, Castro-Ginard et
al. 2022, which method based on clustering algorithm K-means or DBSCAN and
more than 3, 000 OCs are reported (hereafter CG series). However, most of the
OCs in the Galaxy is still not discovered, and the results are affected a lot
by the method that is used for searching for OCs. Younger populations often
have complex internal structures such that there is no single way to decompose
them into clusters according to Krumholz et al. (2019). It is valuable to try
different methods to search the Galactic OCs.

This work aims to identify more OCs by taking an effective method, i.e.,
e-HDBSCAN. The paper is organized as follows. We introduce data preparation in
Sect. 2. In Sect. 3, we explain the method for searching OCs. The results and
discussion are next given in Sect. 4. Finally, we conclude this work in Sect.
5.

Figure 1: Comparison of distribution.

##  2 Data Preparation

###  2.1 Data Set

Gaia EDR3, the European Space Agency released early third data releases in
2020. The position, velocity, and magnitude data of more than 1.8 billion
stars, and trigonometric parallax, proper motion, and photometric data of more
than 1.3 billion stars are provided in this data release (Cantat-Gaudin 2022).
Furthermore, the systematic errors in astrometry are reduced by (30 $-$ 40)%
for the parallaxes and by a factor of 2.5 for the proper motions, whereas for
photometry, the systematic error is reduced to below 1% (Riello et al. 2021).

To create the data set, we extracted stars with $\varpi$ $>$ 0.2 mas in Gaia
EDR3 firstly because most OCs are located near the galactic equator $|b|<$ 20
∘ (Dias et al. 2012; Kovaleva et al. 2021). In addition, to reduce the
pollution of field stars, as same as Cantat-Gaudin & Anders (2020), we chose
stars with G $<$ 18 mag because not only the error of Gaia astrometric data
increases with the decrease of star brightness but also due to the
completeness limit of the Gaia DR2, the sample used by Cantat-Gaudin & Anders
(2020). This described in detail by Gaia Collaboration et al. (2018).

We further filtered the data set with three criteria: 1) $G$ $<$ 18 mag
(Lindegren et al. 2018); 2) 0.2 mas $<$ $\varpi$ $<$ 7.0 mas; 3)
$\mu_{\alpha}\cos\delta$ $<$ 30 mas yr-1, $\mu_{\delta}$ $<$ 30 mas yr-1 and
$|b|$ $<$25∘. It should be noted that stars with $G$ $<$ 18 mag and which
possess a parallax uncertainty of more than 0.2 mas or better were added to
our sample, which is as same as previous works Cantat-Gaudin & Anders (2020);
Liu & Pang (2019); Ferreira et al. (2020); Li et al. (2022).

Finally, we obtained a data set of 186,464,070 stars with 5-Dimension feature
space,
$X=\\{l,b,\varpi,\mu_{\alpha}\cos\delta,\mu_{\delta},G,G_{RP},G_{BP}\\}$,
where $l$ and $b$ denote spatial galactic coordinates, $\varpi$ is
trigonometric parallaxs, $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ mean
proper motions, and $G,G_{RP},G_{BP}$ are photometric data . It is worth to
point that corrections of magnitudes in $G$ is not taken into account since it
have no impact in the detection of OC but it can be in the determination of
the clusters features from their colour-magnitude diagrams.

###  2.2 Data Preprocessing

Same to many previous studies, we selected five parameters, i.e.,
$\\{l,b,\varpi,\mu_{\alpha}\cos\delta,\mu_{\delta}\\}$, for the identification
of open cluster. We constructed a quintet

$X=\\{l,b,\varpi,\mu_{\alpha}\cos\delta,\mu_{\delta}\\}$

for each star, respectively.

To better facilitate the clustering calculation and improve the clustering
effect, referring to Liu & Pang (2019), we calculated weight ($w$) for each
star and further updated the quintet using

$x^{\prime}=\frac{x-min\left(x\right)}{max\left(x\right)-min\left(x\right)}$
(1)

$\bm{w}=\dfrac{(\cos\mathit{b},1,0.5,1,1)}{0.2\cos\mathit{b}+0.7}$ (2)

$X_{d}=\bm{w}*X$ (3)

Here, cos $b$ is due to the contraction of $l$ at a given $b$ in spherical
geometry.

##  3 Method of Identification of Open Clusters

###  3.1 e-HDBSCAN

The Hierarchical Density-Based Spatial Clustering of Applications with Noise
(HDBSCAN) is a clustering algorithm proposed by Campello et al. (2013, 2015).
It is an improvement of the DBSCAN (Ester 1996) algorithm that is density-
based and has been widely to identify OCs.

Compared with DBSCAN, HDBSCAN can detect overdensities of varying densities in
a dataset. HDBSCAN does not depend on a hyperparameter ($\xi$), which is used
in DBSCAN as a particular neighbor radius. Instead, it condenses the minimum
spanning tree by pruning off the nodes that do not meet the minimum number of
sources in a cluster. It only demands the user to set a minimum cluster size
which is easy to do in OCs hunting with astronomical domain knowledge. Some
recent works suggest that HDBSCAN can solve many issues encountered by DBSCAN
and was more sensitive than the algorithm of GMMs, DBSCAN, which are widely
used in search OCs (Hunt & Reffert 2021).

HDBSCAN is the most sensitive and effective algorithm for identifying open
clusters in Gaia data (Hunt & Reffert 2021). Therefore, we adopt HDBSCAN
algorithm to blind search OCs in the study by extending the conventional
HDBSCAN algorithm. This allows one to use a big data environment to search for
new OCs in Gaia EDR3.

Due to the large number of sources in Gaia EDR3, cluster analysis is hard to
be performed on a stand-alone generic computer. Based on HDBSCAN, we proposed
an enhanced Hierarchical Density-Based Spatial Clustering of Applications with
Noise (e-HDBSCAN) approach. The e-HDBSCAN is written in Python3 and
implemented using Message Passing Interface (MPI), which can run well under a
Linux-based high-performance computing cluster, thereby improving the
clustering efficiency. e-HDBSCAN splits the data grid, further merges and
fuses the clustering results based on the parallel clustering of the grid
data, and eliminates clusters that do not meet the statistical criteria by
proper motion judgement on the membership of the obtained clusters. This
overcomes the shortcomings of the traditional stellar agglomeration method,
which needs multiple trials and is time-consuming. It is worth pointing out
that the extended framework of our proposed algorithm is applicable not only
to HDBSCAN but also to other clustering algorithms. The flowchart is shown in
Figure 2. In summary, the biggest value of e-HDBSCAN is that traditional
HDBSCAN is enhanced with a parallel split-and-conquer strategy to ensure that
large data beyond the memory of a single machine can be processed.

Figure 2: Flowchart of e-HDBSCAN method. The process of this schedule consist
of 3 stages. Step 1 is Grid clustering in Parallel within Gaia EDR3 to get
rough clusters. Then, to merge clusters is performed in step 2. After fusion
of those clusters, we implement proper motion dispersion diagnosis for
identify of OCs in step 3. Power-CMD fitting and visual inspection is carried
out subsequently.

###  3.2 Step 1: Grid clustering in Parallel

To obtain rough star clusters conveniently, we partitioned the source data
into multiple grids first. We then carried out the clustering algorithm in
each data grid, as it is too large to read all sources into the computer
memory for processing at once.

After extraction of sources within Gaia EDR3 as our source selection criteria
as mentioned above, we obtained some grids by splitting sources into gridding
data slices uniformly, which got in 3D spatial coordinates $\\{l,b,\varpi\\}$
using KD_tree method. It is worth mentioning that each domain size is larger
than two times the 20pc in dimensions of the Galactic latitude and longitude,
which is the typical scale of a star cluster (Brown et al. 2010). Besides, to
eliminate gridding with high uncertainty, the minimum domain size is set to
larger than 0.2 mas in $\\{\varpi\\}$ dimension space. Then, we used HDBSCAN
clustering algorithm in the weighted 5D parameter space $X$ calculated as 1, 2
and 3 for each data grid.

###  3.3 Step 2: Merging Partitions

Many open star cluster candidates appear in more than one domain. We adopt a
merge strategy to account for clusters in the borders of the grid. If more
than 50% of the minimum of members in each pair of star clusters are the same,
we merge the clusters. What needs to be mentioned is that the value of the
parameter minPts in the algorithm is based on the physical prior of star
cluster composition, and we set to 50, which is consistent with (Liu & Pang
2019) and our previous series work (Li et al. 2022). To speed up the
clustering process, we carry out parallel computing using Mpi4py (Dalcin et
al. 2008) that speeds up the computation time and allows us to process a
volume of data that does not fit in the memory of a single machine.

We adopted a recursive merge strategy to account for clusters at the edge of
the data regions. We merge star clusters in two adjacent regions if more than
fifty percent of their minimum members are the same. The overlapping regions
in the model were limited to no less than 20 pc. Thus, there is no
intersection point where the two clusters share less than 50%, unless the
cluster is larger than 60 pc and symmetrically straddles the established
overlap region. In fact, this is rarely the case.

###  3.4 Step 3: Proper Motion Dispersion Diagnosis

It is obvious that the detection of more true positive OCs always also
resulted in false positive OCs (Hunt & Reffert 2021). On the other hand,
HDBSCAN may identify either statistical clusters, asterisms, or other physical
groups located in the same field (Tarricq et al. 2022). In this work, it is
suggested that the objects identified by the e-HDBSCAN method with mean proper
motions and parallaxes. If they were real open clusters that should be
consistent to the value computed by Castro-Ginard et al. (2020). That means
the mean proper motion dispersion of true positive OC candidates should be
compatible with a real OC. Draw on the method of Cantat-Gaudin & Anders
(2020); Hao et al. (2022), which used internal proper-motion dispersions to
filter unreliable open cluster candidates. We further diagnosed those hunted
candidates in Sect. 3 with this method. To select only high-quality OC
nominated objects, we use the rigorous proper-motion criterion 4 and 5, which
is adopted by Cantat-Gaudin & Anders (2020).

$\sqrt{\sigma_{\mu_{a^{*}}}^{2}+\sigma_{\mu_{\delta}}^{2}}\leq
0.5\mathrm{mas}\ \mathrm{yr}^{-1}\&\text{ if }\varpi<1\text{ mas }$ (4)
$\sqrt{\sigma_{\mu_{a^{*}}}^{2}+\sigma_{\mu_{\delta}}^{2}}\leq
5\sqrt{2}\frac{\varpi}{4.7404}\mathrm{mas}\ \mathrm{yr}^{-1}\&\text{ if
}\varpi\geq 1\text{ mas }$ (5)

We filter out most of candidates that are not real by this criterion. It is
worth mentioning that this criterion is necessary for the identification of
OCs. It does not imply that clusters with dispersion higher than the criterion
in these formulas are real clusters. However, by doing so, we can filter out
most of the candidates that do not meet this criterion, obtain high-quality
cluster candidates, and reduce the final identification effort.

##  4 Results

We extract 186,464,070 sources of Gaia EDR3 using the source selection
criteria presented in the previous section and obtain 4091 grids after
uniformly gridding data slices in 3D spatial coordinates $\\{l,b,\varpi\\}$
using KD_tree method. A total of 7756 local clusters are detected in step 2.
After merging the rough local clusters, 3,787 open clusters are finally found.

Different from other works based HDBSCAN algorithm (Ye et al. 2021; Tarricq et
al. 2022; Casamiquela et al. 2022), in the present work, the e-HDBSCAN method
systematically searched nearby ($|b|<25^{\circ}$) all-sky regions using this
algorithm. In addition, we strictly limit the number of members of open
cluster candidates to be larger than 50. For consistency with our previous
series of work Li et al. (2022), we set the minPts of the HDBSCAN algorithm to
50 in this process while Castro-Ginard et al. (2018) set this parameter equal
to 8 when using density clustering. The another aspect is that we perform this
algorithm in a weighted 5D parameter projection space, namely,
$\\{l,b,\varpi,\mu_{\alpha}\cos\delta,\mu_{\delta}\\}$ in the 4,091 splitting
searching grids as mentioned above. Due to the schemes mentioned above, it is
possible to find new objects even in regions that have already been searched
in previous work.

###  4.1 Cross Match

Many OC candidates were found and reported in previous works. We collected and
compiled those catalogues and cross-matched them with our candidates. To
eliminate as many OCs as possible that have already been found and obtain OC
candidates that have not been unnoticed before, we consider an OC to be
positionally matched to a catalogued one if their centres lie within a circle
of radius r = 0.5 degrees and rest of the astrometric mean parameters are
compatible within 5 $\sigma$ (where $\sigma$ is the uncertainties quoted in
both catalogues for each quantity) which is consistent with Hunt & Reffert
(2021) and Castro-Ginard et al. (2021).

We first performed cross-matching with the pre-Gaia cluster catalogue. The
pre-Gaia cluster catalogues (MWSC) contained 3006 star clusters gathered by
Dias et al. (2012) and Kharchenko et al. (2013), of which 2976 objects
localized at Galactic latitude $<$ 25 degrees, aggregated from various data
sources. Since they do not allow for a sufficiently excellent comparison in
the proper motion space, we only performed a 0.5-degree positional cross-match
based on sky coordinates. Second, to serve the following crossover, we
collected the best-known catalogues of the identified clusters described above
and compiled those as MWSC, CG2017, Hao3794, UBC series, CWNU, Dias1743 and
Hao704, respectively. The CG series contained 2017 OCs provided by Cantat-
Gaudin & Anders (2020). Hao et al. (2021) report a considerably larger
catalogue including 3794 OCs (Hao3794) and UBC series reported by CG series,
which consist of Cantat-Gaudin et al. (2018a), Castro-Ginard et al. (2018),
Cantat-Gaudin et al. (2019), Castro-Ginard et al. (2019),Cantat-Gaudin &
Anders (2020), Cantat-Gaudin et al. (2020), Castro-Ginard et al. (2020),
Castro-Ginard et al. (2022). In recent times, He et al. (2022b) have reported
541 new open cluster candidates found in Galactic Disk Using Gaia DR2/ EDR3
Data (CWNU). Dias et al. (2021) present a catalogue of updated parameters of
1743 open clusters based on Gaia DR2 in 2021 (Dias1743). And Hao et al. (2022)
recently provided 704 newly detected open clusters in the Galactic disk using
Gaia EDR3 (Hao704). Similarly, we use the same cross-matching method for some
previous catalogs, i.e., Liu & Pang (2019), Ferreira et al. (2020), Hao et al.
(2020), Li et al. (2021), Hunt & Reffert (2021). Finally, using the same
method, we cross-matched 46 newly reported clusters of high Galactic
latitudes, which were found in the region of $|b|>20^{\circ}$ by He et al.
(2022a).

As a result, 530 candidates are not included in those published catalogues,
implying that they are new potential OCs that require further identification.

###  4.2 Qualification

Since members of OCs have similar motions and ages, they should exhibit
clustering characteristics in spatial distribution position and kinematic
space and show a clean in color-magnitude diagram (CMD).

A real OC should follow a certain pattern in an isochrone. Following the
method of Liu & Pang (2019); Hao et al. (2022), we fit the CMDs using the
PARSEC theoretical isochrone models (Bressan et al. 2012). And then, we
divided new candidates into three classes according to isochrone fitting
results and selected which has good isochrone fitting and a relatively clean
main sequence. After this, we get 184 likely open clusters that need further
confirmation. Furthermore, we performed a visual inspection among those
candidates in their positional distributions (PDs), vector point diagrams
(VPDs), colour-magnitude diagrams (CMDs) and $\varpi$ versus
$\sigma_{\mu_{a^{*}}}$ distributions. An example is shown in Figure 3.
Finally,83 candidates were considered real OCs. In Figure 1, we present the
sky distribution of OCs compared with Cantat-Gaudin et al. (2020) (CG20).

(a)

(b)

(c)

(d)

Figure 3: Visual Inspection of LISC III 1044, LISC III 2601, LISC III 1301 and
LISC III 1762, respectively. Leftmost plots: position of the OC in ($\alpha$,
$\delta$). Inner left plots: ($\varpi$ , $\mu_{a^{*}}$ ) distribution, whilst
inner right plots: ($\mu_{a^{*}}$, $\mu_{\delta}$ ) distribution. Rightmost
plots: CMD of OC.

###  4.3 Determination of Stellar Population Properties by CMD-fitting

Many previous works on determining the stellar populations of OCs in Gaia took
the isochrone fitting technique. To further reduce the uncertainty of
estimation of the main parameters of OCs, it is necessary to consider that
binary stars, rotating stars, and multiple populations exist in OCs.

This work employs the advance stellar population synthesis model (ASPS) (Li et
al. 2012) for CMD fitting using $Powerful\\_CMD$ tool (Li et al. 2015, 2016).
Since CMD fitting is not the focus of this paper, one can read our recent
paper, Li et al. (2022), for more details. Seven parameters, i.e., distance
modulus $(m$–$M)$, color excess $E(V$–$I)$, young stellar age ${t}$, age
spread $t_{sp}$, binary fraction $f_{bin}$ and rotating star fraction
$f_{rot}$ , are determined for each cluster. Some best fitting CMDs are given
in Figure 4, 5, 6 and the best-fitting parameters in Table 1. We show the
colour-magniutde diagrams in V-I vs Mv plane because the Powerful CMD code
takes only B, V and I magnitudes, the photometry obtained from Gaia bandpasses
are transformed to V, I photometry. Refer to the Riello et al. (2021),
$G_{BP}$ and $G_{RP}$ transform to $V-I$ and $M_{V}$ by equation 6.

$\left\\{\begin{array}[]{l}M_{V}-G_{BP}-0.02696+0.1086(V-I)-0.009148(V-I)^{2}+0.004715(V-I)^{3}=0\\\
G_{RP}-0.01612+1.274(V-I)-0.08143(V-I)^{2}-G_{BP}=0\end{array}\right.$ (6)

The isochrones that were calculated by Li et al. (2017). Using the rapid
stellar evolution code of Hurley et al. (2002) are used for CMD fitting. The
best isochrone is chosen according to the statistical difference between the
theoretical and observed CMDs. In detail, the CMD is divided into some grids
and the difference is computed via

$\mathrm{WAD}=\Sigma[|F_{\mathrm{ob}}-F_{\mathrm{th}}\|]$ (7)

where $F_{ob}$ and $F_{th}$ are star fractions of the observed stars and
simulated stars in a grid. In the CMD fitting metallicity Z and stellar age
are set to free parameter.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

Figure 4: Comparison of best-fit and observed CMDs of 15 new identified open
clusters with clear main sequence. Blue points are for observed stars and red
ones are for best-fit stellar populations. The complete figure set (83 images)
is available on line.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

Figure 5: Same as Fig. 4 but for other 15 OCs.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

Figure 6: Same as Fig. 4 but for other 15 OCs. Table 1: Parameters of the
final 83 New OCs. Some best-fit and observed CMDs are compared in Figure 4.

| ID | l | l_std | b | b_std | plx | plx_std | pmra | pmra_std | pmdec | pmdec_std | N_member | $Z$ | $m-M$ | E $(V-I)$ | t/$t_{sp}$ | $f_{bin}$ | $f_{rot}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  | [deg] | [deg] | deg] | [deg] | [mas] | [mas] | [$mas~{}yr^{-1}$ ] | [$mas~{}yr^{-1}$] | [$mas~{}yr^{-1}$] | [$mas~{}yr^{-1}$] |  |  | [mas] | [mas] | [Gyr] |  |
0 | 931 | 203.643 | 0.412 | 4.020 | 0.108 | 0.239 | 0.016 | -0.308 | 0.266 | -0.828 | 0.293 | 116 | 0.0040 | 12.7200 | 0.2900 | 1.1 | 0.53 | 0.0
1 | 932 | 204.163 | 0.245 | 5.734 | 0.113 | 0.245 | 0.016 | -0.385 | 0.269 | -0.602 | 0.304 | 95 | 0.0300 | 13.4000 | 0.0800 | 1.2 | 0.34 | 0.0
2 | 933 | 205.529 | 1.188 | 4.789 | 0.631 | 0.247 | 0.020 | -0.374 | 0.289 | -0.682 | 0.318 | 1633 | 0.0100 | 13.1300 | 0.2400 | 0.7 | 0.55 | 0.0
3 | 934 | 206.504 | 0.728 | 3.699 | 0.332 | 0.250 | 0.019 | -0.374 | 0.278 | -0.597 | 0.311 | 542 | 0.0300 | 13.5000 | 0.2800 | 0.2 | 0.55 | 0.0
4 | 1031 | 157.044 | 0.448 | 5.264 | 0.544 | 0.258 | 0.026 | 0.504 | 0.272 | -0.907 | 0.372 | 361 | 0.0040 | 12.4000 | 0.6800 | 0.7 | 0.54 | 0.0
5 | 1036 | 151.713 | 0.534 | 5.769 | 0.315 | 0.251 | 0.020 | 0.394 | 0.288 | -0.522 | 0.349 | 401 | 0.0003 | 12.5000 | 0.6700 | 0.9 | 0.53 | 0.0
6 | 1038 | 149.444 | 0.569 | 5.704 | 0.339 | 0.257 | 0.026 | 0.348 | 0.320 | -0.427 | 0.377 | 925 | 0.0040 | 12.6000 | 0.4300 | 1.3 | 0.55 | 0.0
7 | 1046 | 180.344 | 0.364 | 6.652 | 0.359 | 0.280 | 0.027 | 0.181 | 0.340 | -1.671 | 0.371 | 268 | 0.0200 | 12.7000 | 0.4000 | 0.6 | 0.60 | 0.0
8 | 1177 | 180.903 | 0.411 | 11.987 | 0.136 | 0.277 | 0.025 | 0.220 | 0.331 | -1.718 | 0.290 | 106 | 0.0100 | 12.7200 | 0.2000 | 1.8 | 0.51 | 0.0
9 | 1178 | 184.312 | 0.554 | 11.758 | 0.123 | 0.283 | 0.018 | 0.170 | 0.343 | -1.681 | 0.315 | 98 | 0.0100 | 12.8900 | 0.2000 | 1.7 | 0.55 | 0.0
10 | 1179 | 180.577 | 0.490 | 11.363 | 0.142 | 0.262 | 0.018 | 0.267 | 0.347 | -1.774 | 0.307 | 107 | 0.0100 | 13.2700 | 0.3000 | 1.6 | 0.38 | 0.0
11 | 1182 | 195.679 | 0.480 | 11.966 | 0.159 | 0.294 | 0.026 | -0.225 | 0.388 | -1.434 | 0.401 | 149 | 0.0200 | 13.2000 | 0.1500 | 1.0 | 0.46 | 0.0
12 | 1191 | 224.412 | 0.428 | 11.083 | 0.203 | 0.269 | 0.021 | -1.561 | 0.398 | 0.404 | 0.436 | 146 | 0.0100 | 12.8600 | 0.1100 | 2.0 | 0.50 | 0.0
13 | 1196 | 229.813 | 0.560 | 11.790 | 0.207 | 0.279 | 0.029 | -1.981 | 0.430 | 0.877 | 0.492 | 171 | 0.0080 | 12.8600 | 0.1700 | 1.5 | 0.46 | 0.0
14 | 1197 | 226.638 | 0.369 | 11.571 | 0.281 | 0.277 | 0.029 | -1.704 | 0.432 | 0.701 | 0.441 | 100 | 0.0080 | 13.0000 | 0.2300 | 1.4 | 0.48 | 0.0
15 | 1293 | 115.502 | 0.313 | 12.028 | 0.283 | 0.263 | 0.021 | -2.031 | 0.588 | -0.467 | 0.468 | 231 | 0.0300 | 12.7000 | 0.3100 | 2.8 | 0.55 | 0.0
16 | 1299 | 149.949 | 0.309 | 12.246 | 0.197 | 0.271 | 0.024 | 0.662 | 0.290 | -1.145 | 0.388 | 62 | 0.0100 | 13.2000 | 0.8200 | 1.2 | 0.55 | 0.0
17 | 1301 | 159.115 | 0.316 | 11.887 | 0.334 | 0.267 | 0.027 | 0.745 | 0.346 | -1.394 | 0.368 | 132 | 0.0200 | 13.0000 | 0.3000 | 1.5 | 0.53 | 0.0
18 | 1314 | 218.772 | 0.407 | 13.309 | 0.713 | 0.281 | 0.031 | -1.360 | 0.433 | -0.115 | 0.462 | 567 | 0.0300 | 13.4500 | 0.0900 | 1.4 | 0.52 | 0.0
19 | 1316 | 224.037 | 0.547 | 12.856 | 0.358 | 0.285 | 0.031 | -1.492 | 0.461 | 0.252 | 0.534 | 477 | 0.0080 | 13.0000 | 0.1200 | 2.0 | 0.46 | 0.0
20 | 1319 | 243.166 | 1.007 | 12.843 | 0.342 | 0.279 | 0.029 | -2.763 | 0.552 | 1.887 | 0.633 | 737 | 0.0300 | 12.5500 | 0.0100 | 2.4 | 0.51 | 0.0
21 | 1320 | 238.885 | 1.349 | 12.733 | 0.291 | 0.285 | 0.030 | -2.589 | 0.553 | 1.648 | 0.681 | 931 | 0.0100 | 12.8000 | 0.1000 | 2.3 | 0.50 | 0.0
22 | 1442 | 173.901 | 0.462 | 12.892 | 0.399 | 0.278 | 0.029 | 0.442 | 0.360 | -1.839 | 0.303 | 287 | 0.0300 | 12.7000 | 0.0800 | 1.6 | 0.53 | 0.0
23 | 1682 | 208.639 | 0.157 | -3.006 | 0.123 | 0.632 | 0.031 | -2.079 | 0.472 | -0.410 | 0.418 | 120 | 0.0040 | 10.7500 | 0.9300 | 0.2 | 0.55 | 0.0
24 | 1762 | 203.323 | 0.213 | 5.328 | 0.085 | 0.260 | 0.018 | -0.275 | 0.256 | -0.871 | 0.329 | 64 | 0.0040 | 12.8000 | 0.2600 | 0.9 | 0.19 | 0.0
25 | 1764 | 244.071 | 0.333 | 5.684 | 0.260 | 0.255 | 0.023 | -2.466 | 0.369 | 2.337 | 0.334 | 154 | 0.0300 | 13.5000 | 0.1200 | 1.1 | 0.55 | 0.0
26 | 1789 | 163.055 | 0.196 | 8.818 | 0.235 | 0.276 | 0.024 | 0.676 | 0.320 | -1.433 | 0.379 | 70 | 0.0080 | 13.7000 | 0.6500 | 1.4 | 0.54 | 0.0
27 | 1790 | 180.195 | 0.094 | 8.216 | 0.784 | 0.308 | 0.035 | 0.300 | 0.647 | -1.780 | 0.566 | 500 | 0.0200 | 12.6000 | 0.2800 | 2.7 | 0.50 | 0.0
28 | 1837 | 154.865 | 0.293 | 17.445 | 0.556 | 0.356 | 0.028 | 1.095 | 0.389 | -1.980 | 0.485 | 77 | 0.0300 | 13.6000 | 0.4000 | 0.7 | 1.00 | 0.0
29 | 1911 | 181.198 | 1.060 | -12.631 | 0.221 | 0.472 | 0.019 | 0.882 | 0.517 | -1.827 | 0.468 | 182 | 0.0200 | 11.7000 | 0.4800 | 1.4 | 0.52 | 0.0
30 | 1989 | 128.696 | 0.596 | -12.842 | 0.476 | 0.477 | 0.022 | -1.147 | 0.763 | -1.575 | 0.608 | 153 | 0.0300 | 12.1500 | 0.1900 | 1.3 | 0.51 | 0.0
31 | 2071 | 193.767 | 4.119 | -9.211 | 0.861 | 0.935 | 0.039 | 1.017 | 0.787 | -3.846 | 0.911 | 1294 | 0.0300 | 10.5000 | 0.3200 | 0.7 | 0.53 | 0.0
32 | 2171 | 304.203 | 0.360 | -5.247 | 0.266 | 0.462 | 0.014 | -7.058 | 0.790 | -1.233 | 0.512 | 213 | 0.0040 | 11.6500 | 0.3700 | 1.2 | 0.60 | 0.0
33 | 2226 | 232.338 | 0.281 | -1.304 | 0.322 | 0.467 | 0.015 | -1.400 | 0.463 | 1.154 | 0.666 | 141 | 0.0040 | 10.8000 | 0.1200 | 2.7 | 0.51 | 0.0
34 | 2234 | 243.248 | 0.274 | -1.754 | 0.136 | 0.460 | 0.014 | -2.160 | 0.497 | 2.294 | 0.573 | 128 | 0.0080 | 11.4500 | 0.2600 | 0.2 | 0.51 | 0.0
35 | 2394 | 240.714 | 1.059 | 8.231 | 0.170 | 0.467 | 0.015 | -2.932 | 0.586 | 1.612 | 0.646 | 92 | 0.0080 | 12.2200 | 0.2200 | 1.8 | 0.49 | 0.0
36 | 2396 | 256.331 | 1.286 | 6.358 | 0.336 | 0.465 | 0.016 | -3.915 | 0.640 | 2.713 | 0.643 | 259 | 0.0200 | 12.2000 | 0.3500 | 1.6 | 0.49 | 0.0
37 | 2473 | 185.104 | 1.048 | 12.008 | 0.363 | 0.463 | 0.014 | -0.044 | 0.670 | -2.012 | 0.534 | 206 | 0.0300 | 12.5000 | 0.1200 | 1.4 | 0.52 | 0.0
38 | 2474 | 181.315 | 0.901 | 10.702 | 0.251 | 0.461 | 0.016 | 0.217 | 0.654 | -2.256 | 0.593 | 181 | 0.0080 | 12.4138 | 0.3286 | 1.9 | 0.50 | 0.0
39 | 2595 | 139.851 | 0.821 | 17.152 | 0.933 | 0.463 | 0.015 | 0.591 | 0.632 | -0.428 | 0.756 | 281 | 0.0080 | 12.4138 | 0.2857 | 1.8 | 0.55 | 0.0
40 | 2601 | 194.069 | 0.491 | 19.241 | 0.606 | 0.467 | 0.016 | -0.612 | 0.614 | -2.152 | 0.650 | 88 | 0.0100 | 11.9138 | 0.1786 | 1.3 | 0.41 | 0.0
41 | 2824 | 272.186 | 0.520 | -6.925 | 0.201 | 0.695 | 0.018 | -4.134 | 0.747 | 6.307 | 0.599 | 86 | 0.0300 | 11.6900 | 0.3600 | 0.4 | 0.58 | 0.0
42 | 2920 | 133.222 | 0.758 | -0.719 | 0.191 | 0.679 | 0.023 | -0.758 | 0.708 | -0.547 | 0.679 | 120 | 0.0010 | 10.3200 | 0.8200 | 0.1 | 0.45 | 0.0
43 | 2980 | 208.073 | 1.021 | 8.282 | 0.325 | 0.684 | 0.017 | -0.693 | 0.632 | -2.592 | 0.537 | 96 | 0.0080 | 11.3276 | 0.2086 | 0.6 | 0.53 | 0.0
44 | 2983 | 229.383 | 1.271 | 8.249 | 0.438 | 0.691 | 0.022 | -2.330 | 0.601 | 0.295 | 0.605 | 141 | 0.0010 | 9.8000 | 0.0000 | 2.3 | 0.44 | 0.0
45 | 3249 | 330.295 | 2.754 | -14.026 | 1.046 | 1.995 | 0.119 | -0.713 | 1.059 | -8.323 | 1.208 | 412 | 0.0200 | 9.3000 | 0.2000 | 0.0 | 0.45 | 0.0
46 | 3263 | 34.712 | 0.264 | -11.549 | 0.238 | 1.672 | 0.072 | -0.253 | 0.623 | -4.617 | 0.963 | 144 | 0.0003 | 8.0000 | 0.4500 | 1.9 | 0.37 | 0.0
47 | 3286 | 180.626 | 1.076 | -8.961 | 0.574 | 0.926 | 0.032 | 1.463 | 0.682 | -4.744 | 0.814 | 167 | 0.0100 | 11.2000 | 0.7000 | 0.9 | 0.42 | 0.0
48 | 3312 | 107.309 | 2.886 | -9.992 | 0.353 | 1.828 | 0.083 | 2.677 | 0.961 | -2.107 | 0.968 | 295 | 0.0080 | 8.7800 | 0.2400 | 0.0 | 0.54 | 0.0
49 | 3323 | 260.589 | 0.867 | -7.483 | 0.147 | 1.677 | 0.070 | -6.240 | 0.578 | 7.108 | 0.444 | 57 | 0.0001 | 8.1100 | 0.1000 | 0.0 | 0.55 | 0.0
50 | 3344 | 217.277 | 0.672 | -4.718 | 0.254 | 0.915 | 0.041 | -0.418 | 0.730 | -1.022 | 0.837 | 253 | 0.0040 | 10.0500 | 0.2300 | 0.4 | 0.52 | 0.0
51 | 3345 | 229.477 | 0.468 | -3.382 | 0.261 | 0.933 | 0.030 | -2.024 | 0.990 | 1.085 | 0.877 | 80 | 0.0100 | 10.0900 | 0.2200 | 0.2 | 0.49 | 0.0
52 | 3372 | 121.932 | 1.318 | -5.190 | 0.390 | 0.947 | 0.036 | 0.324 | 1.054 | -1.897 | 0.647 | 116 | 0.0300 | 12.0000 | 0.7500 | 0.1 | 0.51 | 0.0
53 | 3373 | 114.189 | 1.387 | -4.546 | 0.377 | 0.955 | 0.040 | -0.500 | 1.081 | -1.575 | 0.688 | 294 | 0.0200 | 10.1900 | 0.2800 | 0.2 | 0.54 | 0.0
54 | 3411 | 318.974 | 0.460 | 1.480 | 0.294 | 0.940 | 0.065 | -3.754 | 0.892 | -3.030 | 0.689 | 200 | 0.0300 | 11.5000 | 0.8000 | 0.0 | 0.54 | 0.0
55 | 3431 | 158.929 | 1.345 | 1.741 | 0.369 | 0.940 | 0.032 | 0.762 | 0.844 | -3.722 | 1.043 | 251 | 0.0200 | 11.0200 | 0.6000 | 0.0 | 0.54 | 0.0
56 | 3434 | 182.507 | 0.918 | 6.993 | 0.365 | 0.924 | 0.031 | 0.853 | 0.766 | -4.916 | 0.809 | 74 | 0.0080 | 12.3900 | 1.0000 | 0.4 | 0.51 | 0.0
57 | 3449 | 37.349 | 2.276 | 5.380 | 0.626 | 2.034 | 0.139 | 0.835 | 1.106 | -4.849 | 1.083 | 998 | 0.0080 | 8.2000 | 0.1800 | 1.2 | 0.49 | 0.7
58 | 3492 | 239.518 | 1.990 | 12.466 | 0.468 | 0.954 | 0.038 | -4.599 | 0.987 | 1.181 | 0.902 | 160 | 0.0010 | 11.0000 | 0.5800 | 0.5 | 0.46 | 0.7
59 | 3503 | 2.765 | 1.414 | 12.353 | 0.321 | 0.949 | 0.035 | -0.982 | 0.797 | -3.278 | 0.880 | 98 | 0.0080 | 10.5000 | 0.4500 | 1.3 | 0.54 | 0.0
60 | 3517 | 154.397 | 1.886 | 12.945 | 0.799 | 2.008 | 0.127 | -2.632 | 1.173 | -3.336 | 1.255 | 439 | 0.0200 | 9.0000 | 0.5500 | 0.0 | 0.55 | 0.0
61 | 3611 | 191.806 | 0.794 | -18.879 | 0.680 | 2.540 | 0.117 | 0.891 | 0.593 | -4.546 | 0.631 | 90 | 0.0080 | 9.0000 | 0.6000 | 0.0 | 0.55 | 0.0
62 | 3613 | 203.583 | 0.435 | -24.004 | 0.556 | 2.636 | 0.107 | 1.126 | 0.426 | -0.804 | 0.337 | 91 | 0.0080 | 6.3500 | 0.2000 | 0.0 | 0.54 | 0.0
63 | 3629 | 333.667 | 2.491 | -18.349 | 0.869 | 1.895 | 0.086 | -0.223 | 1.365 | -8.290 | 2.045 | 136 | 0.0010 | 8.3500 | 0.2000 | 0.6 | 0.53 | 0.0
64 | 3630 | 322.244 | 2.296 | -17.662 | 0.611 | 1.881 | 0.072 | -2.512 | 1.335 | -8.968 | 1.664 | 70 | 0.0080 | 9.5000 | 0.3800 | 0.9 | 0.54 | 0.0
65 | 3645 | 186.027 | 1.205 | -11.107 | 0.257 | 2.696 | 0.120 | 0.039 | 0.686 | -5.714 | 0.709 | 73 | 0.0200 | 8.3000 | 0.3200 | 0.3 | 0.44 | 0.0
66 | 3646 | 204.026 | 1.236 | -12.201 | 0.269 | 2.442 | 0.105 | -1.294 | 0.935 | -1.902 | 1.008 | 107 | 0.0040 | 7.0900 | 0.2000 | 0.0 | 0.52 | 0.0
67 | 3649 | 200.728 | 1.324 | -12.402 | 1.181 | 1.877 | 0.079 | 0.896 | 1.125 | -4.970 | 1.179 | 84 | 0.0200 | 9.0500 | 0.2600 | 1.1 | 0.44 | 0.0
68 | 3661 | 132.378 | 2.325 | -13.541 | 1.389 | 1.865 | 0.073 | 0.919 | 2.218 | -4.755 | 1.305 | 386 | 0.0100 | 8.5200 | 0.0600 | 2.9 | 0.47 | 0.0
69 | 3664 | 180.910 | 0.634 | -12.323 | 1.115 | 2.002 | 0.116 | 1.348 | 1.420 | -6.050 | 1.522 | 67 | 0.0040 | 8.2000 | 0.5000 | 0.2 | 0.52 | 0.0
70 | 3668 | 260.326 | 1.890 | -7.975 | 0.612 | 1.794 | 0.059 | -6.223 | 0.690 | 7.063 | 0.954 | 217 | 0.0200 | 8.9000 | 0.0100 | 0.2 | 0.36 | 0.0
71 | 3673 | 322.474 | 4.682 | -8.374 | 0.914 | 1.876 | 0.106 | -3.538 | 1.844 | -6.227 | 1.681 | 849 | 0.0300 | 8.6000 | 0.0100 | 0.3 | 0.51 | 0.0
72 | 3682 | 234.725 | 5.033 | -6.576 | 1.207 | 1.826 | 0.070 | -4.547 | 1.398 | 2.989 | 1.894 | 290 | 0.0100 | 9.1000 | 0.2400 | 0.6 | 0.45 | 0.0
73 | 3715 | 325.816 | 1.271 | 2.812 | 0.966 | 1.863 | 0.054 | -5.655 | 1.297 | -6.435 | 1.392 | 142 | 0.0300 | 8.9000 | 0.0500 | 0.4 | 0.47 | 0.0
74 | 3723 | 83.173 | 2.052 | 6.428 | 0.711 | 2.903 | 0.137 | 3.468 | 0.836 | 1.766 | 0.717 | 503 | 0.0080 | 7.3900 | 0.1050 | 0.0 | 0.48 | 0.0
75 | 3728 | 329.039 | 5.760 | 9.203 | 1.238 | 1.872 | 0.084 | -6.424 | 2.298 | -5.233 | 1.565 | 1260 | 0.0100 | 8.7600 | 0.1100 | 0.5 | 0.53 | 0.0
76 | 3732 | 63.094 | 1.590 | 4.935 | 0.499 | 1.886 | 0.061 | 0.792 | 1.087 | -2.900 | 1.550 | 71 | 0.0300 | 10.7931 | 0.7000 | 0.0 | 0.31 | 0.0
77 | 3737 | 306.166 | 7.076 | 12.106 | 0.479 | 1.875 | 0.060 | -12.042 | 1.777 | -2.801 | 2.040 | 104 | 0.0001 | 9.5000 | 0.8000 | 0.0 | 0.48 | 0.0
78 | 3749 | 310.208 | 4.242 | 11.992 | 0.762 | 1.887 | 0.061 | -12.021 | 1.830 | -3.862 | 1.386 | 104 | 0.0300 | 10.0000 | 0.4500 | 0.3 | 0.49 | 0.0
79 | 3755 | 54.403 | 0.836 | 17.142 | 0.575 | 2.810 | 0.145 | -0.147 | 1.163 | -5.460 | 0.898 | 200 | 0.0200 | 8.0000 | 0.2000 | 0.0 | 0.47 | 0.0
80 | 3759 | 138.326 | 1.395 | 11.615 | 0.777 | 1.890 | 0.089 | -1.238 | 1.425 | -1.246 | 1.663 | 96 | 0.0080 | 8.5500 | 0.4000 | 0.6 | 0.42 | 0.0
81 | 3783 | 256.616 | 2.702 | 12.670 | 0.557 | 3.848 | 0.126 | -20.561 | 1.316 | 15.861 | 1.607 | 59 | 0.0040 | 8.0000 | 0.5200 | 0.2 | 0.23 | 0.0
82 | 3785 | 48.633 | 3.613 | 20.382 | 0.577 | 3.553 | 0.128 | -1.400 | 1.090 | -7.091 | 1.731 | 98 | 0.0040 | 7.1000 | 0.3000 | 0.0 | 0.47 | 0.0

  * •

Note: For each cluster, seven parameters, i.e., distance modulus $(m-M)$,
color excess $E(V-I)$, young stellar age $t$, age spread $t_{sp}$ , binary
fraction $f_{bin}$ and rotating star fraction $f_{rot}$, are determined. The
$n_{member}$ means the total number of member star in each cluster.

##  5 Conclusions

In this work, we presented an improved method-based HDBSCAN algorithm,
e-HDBSCAN, for open cluster hunting. This method uses only the astrometric
measurements from Gaia eDR3 to blind search for clusters. This technique
consists of three steps described in Section 3, which agrees with most other
works. When we apply this method to the data of Gaia eDR3, 3787 potential OCs
are found, of which 83 are newly detected. It suggests that e-HDBSCAN is more
effective than DBSCAN in searching for Galactic OCs. In addition, the
fundamental parameters of newly detected clusters are determined by fitting
CMDs with the ASPS model. Besides distance modulus, colour excess, age ,
metallicity and the fractions of binary stars and rotating stars are obtained
in this work. Although e-HDBSCAN found some new OCs, further confirmation is
needed. For example, these OC candidates can be confirmed with radial
velocities if their member stars are available in Gaia DR3.

The results are summarised as follows:

  1. 1.

In the work, our method achieves promising results and suggests that the
proposed three-step clustering method (e-HDBSCAN) is efficient in star cluster
searches.

  2. 2.

More than half of the newly discovered OCs are young clusters (age $<$
0.5Gyr), and most of them are metal-poor ( metallicity Z $<$ 0.03).

  3. 3.

Although more than 3,000 OCs have been reported so far, the search for Gaia
disk clusters needs to continue, especially with the release of updated Gaia
data.

  4. 4.

It is of great interest to try different methods to search for OCs since
different methods have their own merits and shortcomings.

###### Acknowledgements.

This work is supported by the National SKA Program of China No 2020SKA0110300,
Joint Research Fund in Astronomy (U1831204) under cooperative agreement
between the National Natural Science Foundation of China (NSFC) and the
Chinese Academy of Sciences (CAS), the National Key Research and Development
Program of China (2018YFA0404603), the National Natural Science Foundation of
China (Nos. 11863002) the National Natural Science Foundation of China (Nos.
11961141001). The authors acknowledge that this work has been supported by the
Yunnan Academician Workstation of Wang Jingxiu (No. 202005AF150025), China
Manned Space Project with NO.CMS-CSST-2021-A08 and Sino-German Cooperation
Project (No. GZ 1284). This work has made use of data from the European Space
Agency (ESA) mission Gaia https://www.cosmos.esa.int/gaia, processed by the
Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

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