Description of the scenario for the development of proto galaxies with small angular momentum through cascade fragmentation with the formation of proto clusters and proto stars based on graph theory - Mailybaev, A.T.; Zakhozhay, V.A.; Alimgazinova, N.Sh.; Demesinova, A.M.; Sagyntayeva, U.Zh.; Manapbayeva, A.B.; Kuratova, A.K.; Naurzbaeva, A.Zh.; Kyzgarina, M.T. (Recent Contributions to Physics, 2020)
The process of proto galaxies development is considered in the period of Universe cooling, when their masses are equal to the Jeans values. As a result of further cooling, the proto systems are subjected to the cascade fragmentation mechanism under which the more and more new smaller fragments are formed. Primary fragments are future galaxies (the upper limit of the mass of fragments falls within the mass range of galaxies), the ancestors of future star clusters, stars and sub stars form in the secondary fragmentation wave. In order to describe cascade fragmentation in proto systems with an extremely small angular momentum, a directed graph is constructed based on a general idea about the evolution of stellar systems. Star formation efficiency evaluations are carried out for proto systems, which determined by power-law mass spectra and the probabilities of key events are calculated. The fractional contents of the substance leaving for the formation of a new generation of stars and sub stars are calculated, depending on the μ-th star formation cycle (for its total number N). The dependence of the mass fraction transferred from the proto system to the system is presented in graphical form as a function of the fragments number N. Four options of the evolution of stellar systems such as galaxies are obtained, which are described by mass spectra with different exponents at the first and second stages of evolution. It is shown that, depending on the evolutionary scenario determined by the combination of mass spectra at the first and second stages of evolution, galaxies at the final stage of evolution may have different populations. According to one of the scenarios, galaxies should contain stellar composition limited by the masses of dwarf stars (≤ 0.8 M⊙). For the calculated maximum value Nmax ≈ 70 and the time of one fragmentation cycle, which occurs during one-star star formation in stellar clusters of galaxies ~ 107 years, it is expected that the time of complete gas depletion in stellar systems such as elliptical galaxies will be ~ 7•109 years. Considering that the characteristic time for the beginning of the formation of galaxies is ≈ 12•109 years, the obtained result explains satisfactorily the absence of star formation in elliptical galaxies over the past 5 billion years. Further development of research in this direction shows that it possible to understand the causes of differences in the composition of populations of various types of galaxies.