Multi-colour photometry and Gaia EDR3 astrometry of two couples of binary clusters (NGC 5617 and Trumpler 22) and (NGC 3293 and NGC 3324).

This paper presents a comprehensive analysis of two pairs of binary clusters (NGC 5617 and Trumpler 22) and (NGC 3293 and NGC 3324) located in the fourth quadrant of our Galaxy. For this purpose we use different data taken from VVV survey, WISE, VPHAS, APASS, GLIMPSE along with Gaia EDR3 astrometric data. We identified 584, 429, 692 and 273 most probable cluster members with membership probability higher than $80 \%$ towards the region of clusters NGC 5617, Trumpler 22, NGC 3293 and NGC 3324. We estimated the value of $R=\frac{A_{V}}{E(B-V)}$ as ∼ 3.1 for clusters NGC 5617 and Trumpler 22, which indicates normal extinction law. The value of R ∼3.8 and ∼1.9 represent the abnormal extinction law towards the clusters NGC 3293 and NGC 3324. Our Kinematical analysis show that all these clusters have circular orbits. Ages are found to be 90 ± 10 and 12 ± 3 Myr for the cluster pairs (NGC 5617 and Trumpler 22) and (NGC 3293 and NGC 3324), respectively. The distances of 2.43 ± 0.08, 2.64 ± 0.07, 2.59 ± 0.1 and 2.80 ± 0.2 kpc estimated using parallax are alike to the values calculated by using the distance modulus. We have also identified 18 and 44 young stellar object candidates present in NGC 5617 and Trumpler 22, respectively. Mass function slopes are found to be in fair agreement with the Salpeter’s value. The dynamical study of these objects shows a lack of faint stars in their inner regions, which leads to the mass-segregation effect. Our study indicates that NGC 5617 and Trumpler 22 are dynamically relaxed but the other pair of clusters are not. Orbital alongwith the physical parameters show that the clusters in both pairs are physically connected.

Consensus Function Based on Clusters Clustering and Iterative Fusion of Base Clusters

In clustering ensemble, it is desired to combine several clustering outputs in order to create better results than the output results of the basic individual clustering methods in terms of consistency, robustness and performance. In this research, we want to present a clustering ensemble method with a new aggregation function. The proposed method is named Robust Clustering Ensemble based on Iterative Fusion of Base Clusters (RCEIFBC). This method takes into account the two similarity criteria: (a) one of them is the cluster-cluster similarity and (b) the other one is the object-cluster similarity. The proposed method has two steps and has been done on the binary cluster representation of the given ensemble. Indeed, before doing any step, the primary partitions are converted into a binary cluster representation where the primary ensemble has been broken into a number of primary binary clusters. The first step is to combine the primary binary clusters with the highest cluster-cluster similarity. This phase will be replicated as long as our desired candidate clusters are ready. The second step is to improve the merged clusters by assigning the data points to the merged clusters. The performance and robustness of the proposed method have been evaluated over different machine learning datasets. The experimentation indicates the effectiveness of the proposed method comparing to the state-of-the-art clustering methods in terms of performance and robustness.

Formation History of Binary Clusters in the Large Magellanic Cloud

Global history of star or cluster formation in the Large Magellanic Cloud (LMC) has been the center of interest in several studies as it is thought to be influenced by tidal interaction with the Small Magellanic Cloud and even the Milky Way. This study focus on the formation history of the LMC in relation with the context of binary star clusters population, the apparent binary fraction (e.g., percentage of cluster pairs) in different epoch were calculated and analyzed. From the established distributions, it can be deduced that the binary clusters tend to be young (∽ 100 Myr) while their locations coincide with the locations of star forming complexes. There is an indication that the binary fraction increases as the rise of star formation rate in the last millions years. In the LMC, the increase of binary fraction at age ∽ 100 Myr can be associated to the last episode of close encounter with the Small Magellanic Cloud at ∽ 150 Myr ago. This observational evidence supports the theory of binary cluster formation through the fission of molecular cloud where the encounter between galaxies enhanced the clouds velocity dispersion which in turn increased the probability of cloud-cloud collisions that produce binary clusters.