Hunting for open clusters in \textit{Gaia} DR2: the Galactic anticentre

The Gaia Data Release 2 (DR2) provided an unprecedented volume of precise astrometric and excellent photometric data. In terms of data mining the Gaia catalogue, machine learning methods have shown to be a powerful tool to, for instance, search for hitherto unknown stellar structures. Particularly, supervised and unsupervised learning methods combined together allow to significantly improve the detection of open clusters. We systematically scan Gaia DR2 in a region covering the Galactic anticentre and the Perseus arm (120<=l<=205 and -10<=b<=10), with the goal of populating this region with open clusters and fine tuning the methodology, proposed in arXiv:1805.03045v2 and successfully applied to TGAS data, adapting it to different density regions. Our methodology uses an unsupervised, density based, clustering algorithm, DBSCAN, that identifies over-densities in the five dimensional astrometric parameter space (l,b,\varpi,\mu_{\alpha^*},\mu_{\delta}) that may correspond to physical clusters. The over-densities are separated into physical clusters (open clusters) or random statistical clusters using an artificial neural network to recognise the isochrone pattern that open clusters show in a colour magnitude diagram. The method is able to recover more than 75% of the open clusters confirmed in the search area. Moreover, we are able to detect 58 open clusters unknown previous to Gaia DR2, which represent an increase of around 25% with respect to the already catalogued ones in this region. We find that the census of nearby open clusters is not complete. Different machine learning based methodologies for a blind search of open clusters are complementary to each other, with no single method being able to detect the 100% of the existing groups. Our methodology has shown to be a reliable tool for the automatic detection of open clusters, designed to be applied to the full Gaia DR2 catalogue.


Introduction
Popularity of machine learning (ML) techniques to analyse astronomical data is growing together with the volume of astronomical catalogues. The use of these techniques is mandatory to extract meaningful insight from big data sets such as the second data release of ESA's Gaia astrometric mission (Gaia DR2, Gaia Collaboration et al. 2016, which contains a volume of more than 550 GB 1 of data, including precise astrometry (Lindegren et al. 2018) and excellent photometry (Evans et al. 2018), among other products, for more than 1.3 × 10 9 sources down to magnitude G = 21 mag. This unprecedented volume of extremely precise data reveals unseen details in the structure of our galaxy.
Open clusters (OCs) are considered to be fundamental objects in our understanding of the structure and evolution of the Milky Way disc. The stars of an OC were born and move together, i.e. in terms of Gaia observables, they share common (l, b, , µ α * , µ δ ) and follow a specific pattern in a colourmagnitude diagram (CMD) (G, G BP , G RP ). The fact that they represent over-densities in the five dimensional astrometric space can be exploited by unsupervised learning algorithms to either characterise known OCs looking for new member stars (Gao 2018a,b;Cantat-Gaudin et al. 2018), or to detect new overdensities in the parameter space (Castro-Ginard et al. 2018; 1 https://www.cosmos.esa.int/web/gaia/dr2 Cantat-Gaudin et al. 2019). Supervised learning methods can help in determining whether or not a group of stars is an OC by identifying the isochrone pattern of its member stars in a CMD, due to the common age of its members. In the OC domain, Gaia DR2 represents a perfect scenario for the application of ML methods to both its detection and characterisation.
Our understanding of the OC population has dramatically changed with Gaia DR2. A pre-Gaia census of the OC population counted with around 3000 objects (Dias et al. 2002;Kharchenko et al. 2013;Froebrich et al. 2007;Schmeja et al. 2014;Scholz et al. 2015;Röser et al. 2016) compiled from heterogeneous data sources, making the characterisation of OC parameters a difficult task. After the publication of Gaia DR2, Cantat-Gaudin et al. (2018) revisited the OC population using a ML based unsupervised membership determination algorithm. This resulted in the compilation of an homogeneous OC catalogue of 1229 objects, including some serendipitously detected OCs and discarding some objects listed in previous catalogues. These well-determined members and mean astrometrical parameters from Gaia DR2 data, allowed the kinematical study of these objects (Soubiran et al. 2018) and the derivation of ages and physical parameters (Bossini et al. 2019). Additionally, the combination of ML techniques and Gaia DR2 data triggered the detection of new OCs. The discovery of nearby OCs (Castro-Ginard et al. 2018;Cantat-Gaudin et al. 2019), where the census Article number, page 1 of 8 arXiv:1905.06161v1 [astro-ph.GA] 15 May 2019 A&A proofs: manuscript no. manuscript was thought to be complete, showed the necessity to keep exploring the sky for new objects.
In Castro-Ginard et al. (2018) (hereafter CG18) we presented a method for the automatic detection of OCs in the Gaia data. The method consists in the application of an unsupervised clustering algorithm, DBSCAN, that looks for over-densities in the astrometric five-dimensional space (l, b, , µ α * , µ δ ). Once the over-densities are detected, we classify them into either random statistical over-densities or real OCs by identifying the isochrone pattern of OC member stars in a CMD using an artificial neural network (ANN). The method has proved to be successful in the detection of OCs in the TGAS data (Lindegren et al. 2016;Michalik et al. 2015), that were later validated in the Gaia DR2 data. In this paper, we apply the methodology to a region of the sky around the Galactic anticentre with the aim of increasing our knowledge of the OC population in that region and fine tuning the methodology for its planned future application in an all sky blind search.
The paper is organised as follows. Section 2 briefly describes the methodology used, which is discussed in detail in CG18. The data-set used for the detection is described in Sect. 3. The proposal of new OCs and some comments on the results found are in Sect. 4. Finally, concluding remarks are summarised in Sect. 5.

Methodology
This section briefly describes the methodology used in CG18, where our approach to detect OCs in the Gaia DR2 data is explained in detail. The method consists in three parts: a preprocessing step, where the data is prepared to be exploited; the use of a density based clustering algorithm, DBSCAN (Ester et al. 1996), to look for over-densities in the 5-dimensional astrometric data; and a classification of the resulting clusters into real OCs and random statistical clusters using an ANN (Hinton 1989) to recognise the isochrone pattern of the cluster member stars in a CMD.
In the preprocessing step, the sky area of study is divided into smaller regions: rectangles of size L × L deg. The reason for that is to compute a representative averaged star density of the region where to search for over-densities. In each rectangle, the parameters (l, b, , µ α * , µ δ ), used to perform the clustering analysis, are standardised (re-scaled to have zero mean and variance one) to avoid a preferred dimension and to balance the importance of each dimension on the clustering process.
The detection of statistical clusters is done using the DBSCAN 2 algorithm, which is a density based algorithm that uses the notion of distance between stars to define close stars as a cluster. The statistical distance between two stars is computed as the euclidean distance in the standardised five dimensional parameter space. The reasons for the choice of DBSCAN are twofold. Firstly, it is able to detect arbitrarily shaped clusters so it accounts, for instance, for the effects of the projection of a cluster location into a two dimensional sky (l and b). Secondly, it requires only two input parameters: minPts, the minimum number of stars to consider them as a cluster; and , the radius of the hyper-sphere where to search for these minPts stars. The parameter is automatically computed in each rectangle using the fact that the distance between neighbours in a cluster is smaller than that between field stars (see Sect. 2.2 of CG18).
The values for the parameters (L, minPts) are set using Gaia DR2-like simulated data (see Sect. 3 of CG18), where in this 2 Algorithm from the scikit-learn python package (Pedregosa et al. 2011)  . The reddest the pixel, the better performance of the algorithm in terms of OC detection. Parameters selected, considered to be optimal for OC detection, are inside the black lines.
case we added the errors 3 at the time of Gaia DR2. Several combinations of optimal parameters (L, minPts) were selected in order to assess for the resulting performance of the algorithm, in this case we chose 28 pairs of (L, minPts). Figure 1 shows the pairs of parameters explored and the chosen combination inside the black lines, whose values range within L ∈ [9 • , 13 • ] and minPts ∈ [8, 15]. The selection of these parameters was made trying to find a balance between low noise and good efficiency, defined as the false positive -true positive ratio for the noise and false negative -true positive for the efficiency. After the clustering process, the resulting clusters can be either real OCs or random statistical clusters. This two types can be differentiated by the pattern followed by the cluster member stars on a CMD. The classification into real OCs or random statistical clusters is done with an ANN 2 , which is able to identify the characteristic shape of isochrones in CMDs corresponding to real OCs. To train the ANN we used CMDs from OCs from the most homogeneous OC catalogue to date (see details in Cantat-Gaudin et al. 2018), which also has the advantage of being compiled from Gaia DR2 data so it is representative of the OCs we expect to detect, and with similar photometric errors. The training set consists in a sample of 1229 real OCs. In addition we used data augmentation techniques so the volume of the training set was increased by randomly selecting member stars to create a set of sub-clusters from each of these catalogued OCs. On the negative identification side, we used CMDs from random field 3 Implementation provided by PyGaia package: https://github.com/agabrown/PyGaia stars on the same field that those 1229 OCs to avoid location biases.
As a last step, and to ensure the selection only of newly detected OCs, we remove the already catalogued OCs. We improved this step with respect to CG18 thanks to the compilation of the catalogue by Cantat-Gaudin et al. (2018). In this case, not only positional arguments were use in order to match a found OC with a catalogued one. An OC was considered to be already catalogued if the mean parameters (l, b, , µ α * , µ δ ) of its members was compatible within 2σ of those mean parameters of the catalogued OC in Cantat-Gaudin et al. (2018). We did not make a cross-identification with other catalogues such as Dias et al. (2002); Kharchenko et al. (2013); Bica et al. (2019) and others, due to the in-homogeneous data sources they are compiled from.

Data
The Gaia catalogue, in its second data release (Gaia DR2, Gaia Collaboration et al. 2018), provides precise five-dimensional astrometric data (positions, parallax and proper motions) together with magnitudes in three photometric broad bands (G, G BP and G RP ) for more than 1.3 billion sources up to G = 21 mag. In this work, we focused in a region located at the disc (b ∈ [−10 • , 10 • ]) near the Galactic anticentre (l ∈ [120 • , 205 • ]) down to magnitude G = 17 mag, where we find a total of 8 715 057 sources with mean standard uncertainties of 0.07 mas for the parallax and 0.1 mas·yr −1 for proper motions.
The reason we fixed the search region in the Galactic disc is because the expectation to find OCs decreases at higher altitudes. For instance, around 93% of the OCs catalogued in Cantat-Gaudin et al. (2018) are at |b| < 10 • , and around 99% are located at |b| < 20 • ; similar numbers are found in the catalogues of Dias et al. (2002) and Kharchenko et al. (2013) with 96% and 94% of the OCs located at |b| < 20 • . Moreover, initially the search region was as wide as |b| < 40 • but an exploratory analysis of the results of our method showed that the detection of clusters tend to be less reliable at |b| > 10 • . This effect is shown in Fig. 2, the clusters at |b| > 10 • are detected less number of times within the 28 pairs of (L, minPts) explored than those located at the disc, decreasing the reliability of the candidate. In addition, clusters detected outside the disc increase in size with Galactic latitude, so with decreasing stellar density. Since there is no physical reason for this and although we cannot discard that some of those detected clusters may be real, we interpret that the determination of the parameter for such low density regions is not accurate and therefore we decided to limit the final search region to the disc, defined as |b| < 10 • .
The reason for the choice of the region near the Galactic anticentre is twofold. On the computational side, the limited volume of data due to the manageable density of stars in the anticentre direction facilitates its analysis while keeping the richness of the data up to G = 17 mag. On the astrophysical side, more distant objects can be reached due to the moderate extinction caused by interstellar dust, compared to the Galactic centre direction. The search region also covers the area recently studied by Cantat-Gaudin et al. (2019) with Gaia DR2 data, where they find 41 new clusters and notice that the region l ∈ [140 • , 160 • ] seems to be devoid of OCs.

Results
The method described in Sect. 2 is applied to the Gaia DR2 data, focused in a region around the anticentre, i.e. 120 • ≤ l ≤ 205 • ; The grey-scale represents how many times each cluster is found within the pairs of (L, minPts) explored. High latitude clusters are detected fewer times and are larger in size.
and in the disc, −10 • ≤ b ≤ 10 • . This results in the detection of 58 OCs that were unknown previous to Gaia DR2, which represent an increase of ∼ 25% with respect to the reference catalogue.

Determination of a detection
We can assess the detection criteria by comparing the detected and non-detected OCs from the existing catalogues. In our region of search, Cantat-Gaudin et al. (2018) report 240 OCs of which we are able to recover 182, i.e. ∼ 76% of the already known OCs. The reason for the non-detection of the remaining ∼ 24% OCs is related to the contrast of the OC with respect to the field, as seen by the DBSCAN algorithm. Figure 3 shows a distribution of the parameter computed for each of the 240 OCs, including both the detected (blue dots) and non-detected OCs (red dots), for L = 13 • and minPts = 9. The computation of the parameter, as explained in Sect. 2.2 of CG18, is done via a data-driven approach so for the interpretation of the parameter not just the physical properties of the OCs (or the field) have to be taken into account but the whole data-set used instead. In this case, the key factor that enables the detection of the OC is the OC-field contrast in terms of compactness. We see from Fig. 3 that only clusters with low values of (high contrast) are detected. This is confirmed by the fact that the reapplication of the method detects most of the undetected OCs when increasing the contrast with respect to the field by localising the search area to a cone search centred at the targeted OC, instead of the large rectangle.

Proposal of new OCs
The application of our method to the described data-set leads to an initial list of 496 OC candidates. The Monte Carlo type analysis (application of the method for several optimal pairs of parameters) allows us to assess the reliability of these detections by the number of times each cluster was found. In order to clean the initial list from false positives, we manually inspect each of the OC candidates and try to re-detect the candidate in a smaller field (cone search around the centre of the targeted OC) where the OC-field contrast is higher. This re-detection was done using again the DBSCAN algorithm in a cone search region centred in the targeted OC 4 . The decision on the proposal of the candidate as an OC is made based on the reliability of the candidate and its re-detection.
After this manual step, 58 of these 496 are validated and proposed as OCs. The reason for the validation of only these 58 OCs is related to the low complexity of the ANN's architecture used, which is so due to the low volume of training data available (based on Gaia DR2 data only). This can give false positive identifications, i.e. wrong identification, by the ANN, of a stellar structure as an OC. In our manual validation step we have been conservative, tending to accept as OCs those groups without a sparse distribution in the sky, with the larger compactness in proper motions and parallax and with the better defined sequences in the CMD. This step may have introduced a strong bias in the selection and rejected true clusters. With the improved proper motions and parallaxes of Gaia DR3 and a more populated training data-set, one will be able to repeat the analysis to fainter magnitudes and this will allow to have less dubious cases. Even though the method is devised to require the minimal user intervention, this is an important step as the exploitation of the Gaia data in terms of blind search for stellar structures is at its initial stages, so a robust OCs catalogue needs to be built to reliably train an automatic detection procedure.
A final list of 58 OCs is proposed, divided in class A OCs and class B depending on the reliability of the candidate. Positions (α, δ) and (l, b) together with mean parameters ( , µ α * , µ δ ) and mean V rad when available can be found in Table 1 for each of the new OCs, which also includes the computed apparent size of the OC and its estimated distance with one sigma (asymmetric) confidence interval. A list of the detected members for all the reported OCs is available in Table 2

Comments on the detected OCs
The newly found OCs are distributed along the Galactic anticentre direction as shown in Fig. 4, where green crosses represent OCs found in this work, blue triangles are the already catalogued OCs in Cantat-Gaudin et al. (2018) and yellow boxes are the OCs in Cantat-Gaudin et al. (2019). It is worth noting that in a region around l ∼ 140 • the density of OCs decreases in terms of both catalogued clusters and newly detected ones. This confirms the findings in Cantat-Gaudin et al. (2019) that this region seems to be devoid of OCs. The low OC density is better seen in Fig. 5, where an X-Y projection is shown with the Sun at (0, 0), and it seems to be pointing in the direction of the Perseus arm (Local and Perseus arms follow the model of Reid et al. (2014)). This region of relatively lower density was first reported as a lack of OB stars in the Gaia DR2 data, and dubbed Gulf of Camelopardalis 6 .
Our strategy to detect OCs rely in the OC-field contrast, being able to detect those OCs with the highest contrast. This may result in a detection bias towards the more compact objects. Figure 6 shows the radius of the detected OC as a function of its distance, which is computed as 1/  given the low parallax relative error (σ ∼ 0.04 mas corresponding to 3 − 16% in parallax relative error). The size range of the objects found is increasing with distance, limiting our detection to very compact objects in a close neighbourhood. The mean size of the detected OCs is σ l , σ b ∼ 0.08 • corresponding to an apparent size of θ ∼ 0.11 • . Our detection limit seems to be at a cluster apparent size of θ = 0.2 • .
In terms of estimated distance, we find 7 new OCs within 1 kpc (being the closest one at around 645 pc) and 31 within 1.8 kpc, to be added to the 23 of Castro-Ginard et al. (2018) and the 31 of Cantat-Gaudin et al. (2019) found in that distance range, further supporting the claim that more objects are yet to be discovered in this volume, specially with the combination of the excellent Gaia data and ML algorithms in future all sky searches. This challenges the statement that the OC census is complete up to 1.8 kpc (Kharchenko et al. 2013;Matsunaga et al. 2018;Piskunov et al. 2018).
From the kinematical point of view, the reported OCs have a mean dispersion of µ α * , µ δ ∼ 0.2 mas·yr −1 , computed from the found member stars. This corresponds to a mean tangential velocity dispersion of ∼ 2.2 km·s −1 . Only 35 of the 58 reported OCs have a radial velocity measurement available in Gaia DR2, with 14 of them having more than 2 measurements (N V rad > 2). The large σ V rad for 6 of them may indicate the presence of binaries or non-members. Cross-matching with external surveys dedicated to radial velocity estimation, such as APOGEE (Majewski et al. 2017), does not add information (only one star was found in common between the two catalogues). The little information on radial velocities difficulties the characterisation of OC members free of contamination from field stars.
The photometric information is included when deciding if a CMD matches a real OC or not. This is done using an ANN trained with CMDs from the 1229 OCs in Cantat-Gaudin et al.
(2018) (see Sect. 2), so the expected isochrone patterns are similar to those present in the training set. The ages of the reference clusters used in the training span from 40 Myr to 1.5 Gyr, so objects accepted by the ANN are in that age range. No estimation of photometric derived quantities is done here, only to mention that 28 of the 58 reported OCs have stars evolved beyond the main sequence, representing the oldest population of the found clusters. In Fig. 7 few examples of detected OCs are shown, 4 class A and 1 class B, showing different ages. Together with the Table 1: List of the proposed OCs ordered by increasing l. The parameters shown are the mean (and standard deviation) for the (N) members found also including the computed apparent size (θ) and estimated distance (d) with one sigma confidence interval, radial velocity is included when available and it is computed with N V rad members. The name follows the numeration started in CG18.

Matches with other catalogues
The candidates have been cross-matched with known catalogues of OCs (Dias et al. 2002;Kharchenko et al. 2013). These catalogues contain around 2000 and 3000 known stellar structures, respectively. However, some of these structures have been recently found not to be real OCs ( as σ 2 l + σ 2 b ) as a function of distance for each of the reported 58 OCs. Dotted lines represent the limiting cluster apparent size and the mean apparent size, θ = 0.2 • and θ ∼ 0.11 • , respectively. data sources, making the identification of an OC less reliable beyond positional arguments. We consider an OC to be positionally matched to a catalogued one if their centres lie within a circle of radius r = 0.5 • . We find 17 candidates which centres are identified with one object either from Dias et al. (2002) or Kharchenko et al. (2013), however none of the identifications are compatible in the rest of the astrometric mean parameters ( , µ α * , µ δ ), with the closest pair differing by ∼ 8σ in at least one parameter. However, we find UBC 84 near the association Cas OB1, to which it may be related due to the extended region of an association.
A recent list of 10 978 star clusters, associations and candidates in the Milky Way has been published by Bica et al. (2019). Our list of candidates was cross-matched and only UBC 90 and UBC 44 are near one entry in the catalogue, Teutsch 20 and Patchick 12 respectively. Teutsch 20 and Patchick 12 are not listed in any of the other studied catalogues. Moreover, the quoted distance for Teutsch 20 is 2.54 ± 0.05 kpc (Guo et al. 2018) and we find UBC 90 at 2.94 kpc, not being compatible within errors. For the case of Patchick 12, we found no record of its mean astrometric parameters in the literature. Leftmost plots show the position of the OC in (α, δ). Inner left plots show (µ α * , µ δ ) distribution whilst inner right plots show the distribution in ( , µ α * ). Rightmost plots show the CMD of each OC. The plotted OCs are, from top to bottom: UBC 54, UBC 56, UBC 57, UBC 79 and UBC 90. The first four clusters are class A and the last one is a class B cluster (see Table 1).
As said before, Cantat-Gaudin et al. (2019) recently found 41 OCs located in roughly the same area of the sky, exploring the data of Gaia DR2. We find 21 OCs in common, that share the five astrometric parameters (see Table 1). The other 20 OCs were not detected in our blind search, but we were able to recover them by increasing the OC-field contrast when running DBSCAN in a cone search centred in the targeted OC. This shows that ML methods are complementary to each other, with none of the explored methods being able to detect the 100% of the existing structures.

Conclusions
We use the methodology described in CG18 to systematically explore the Gaia DR2 archive to search for unknown OCs in the anticentre direction. The method is a fully automated data mining task consisting in an unsupervised clustering algorithm, DB-SCAN, to find groups of stars that share common (l, b, , µ α * , µ δ ) and decide whether or not they are real OCs based on an isochrone pattern recognition in the CMD using an ANN.
We can assess the overall performance in terms of the detection of already existing OCs. In this case, the method is able to find more than 75% of the confirmed OCs in the search region. Most of the remaining ∼ 24% of the clusters not found are recovered when the search is focused in the targeted OC. This suggests that our method works better for the OCs which OC-field contrast is high, and may be biased towards the most compact objects when the distance decreases.
The application of the whole methodology leads to the report of 58 new OCs in a region covering the Galactic anticentre and the Perseus arm in the Gaia DR2 data (120 • ≤ l ≤ 205 • and −10 • ≤ b ≤ 10 • ), which represents an increase of around 25% with respect to the OCs catalogued in this area. Moreover, 32 of the detected OCs are closer than 2 kpc, suggesting that there may be more groups to be detected in this volume.
The density of OCs decreases in a region near l ∼ 140 • . Very few OCs are found in this region, including already catalogued OCs and the newly reported. This region has been named as the Gulf of Camelopardalis, and it reveals a complex structure of the second Galactic quadrant whose mapping was only recently made possible by Gaia DR2 data, and still deserves further study.
The application of our methodology in the search regions shows that the census of OCs may not be complete. Moreover, other similar methodologies exploring the same region are able to find more groups not detected in our method, while they missed some groups detected here. We conclude that a blind search using a single detection method could not recover all the existing stellar structures and that different ML algorithms for this purpose are complementary to each other.
The design of the whole methodology, requiring minimal manual intervention, makes possible its application to a big data set such as the whole Gaia DR2. The planned future exploitation of the Gaia archive in terms of blind search of OCs would represent a huge increase to the known OC population.