Abstract
This article discusses the problems of origin and evolution and issues of numerical modeling of spherical systems, such as clusters of galaxies, globular clusters or E0 galaxies, characterized by massiveness and relatively old age, including up to 1000 bodies. First, observational data on galaxy clusters and their results are analyzed, including using a numerical method. Methods for numerical modeling of the evolution of spherical systems are studied. Two models are analyzed: the first is spherically homogeneous, with an isotropic distribution, and the second is with a particle distribution obeying the Plummer model. Changes in the position of bodies in the system and the distribution of velocities for different moments of time were obtained for each individual model. The calculation results are presented in the form of graphs. In the first model, at an early stage of evolution, the system collapses: a dense core is formed in the center, and a shell is formed around it. It is shown that over time the concentration of the nucleus decreases and it begins to stretch and the size of the system begins to increase. In this case, the distribution of bodies in the system obeys the Gaussian distribution and remains unchanged until the end of evolution. The second model also shows that at an early stage of evolution, the system collapses: then the system contracts and a compacted core forms in the center. The difference between the second model and the first is that a dense halo appears around the nucleus. It is found that sometimes in the early stages of evolution the system is slightly elongated and then tends to a spherical shape. It is also discovered that when solving the modeling of spherical systems, the choice of initial conditions plays an important role