Photometric Analysis of the Open Star Clusters IC 1442, King 21, and Trumpler 7 using TOPCAT Tools with Machine Learning Techniques and ASteCA

This study presents the results of the analysis of three open star clusters — IC 1442, King 21, and Trumpler 7 — using data from Gaia DR3 combined with Machine Learning techniques and TOPCAT tools. The identified cluster members are 208 for IC 1442, 133 for King 21, and 319 for Trumpler 7. From the derived density profiles, we determined each cluster’s structural parameters, such as cluster radii. The estimated distances from the Sun are 2785.599 pc, 2502.302 pc, and 1478.923 pc, respectively, while the logarithmic ages are log(age) = 7.40 yr, 7.60 yr, and 7.80 yr. Assuming solar metallicity, the average stellar masses are ⟨m⟩ = 1.824 ± 0.860 M⊙, 2.689 ± 2.006 M⊙, and 1.089 ± 0.526 M⊙ for the respective clusters. All clusters are dynamically relaxed, as indicated by relaxation times smaller than their ages. The analysis, conducted using the ASTeCA package, focuses on the structure and evolution of stellar clusters through modules for cluster structure, membership determination, synthetic cluster generation, parameter fitting, and studies of stellar masses and binaries.