Dynamical Equilibrium Models of Astrophysical Objects

We derive the dynamical equilibrium equations for an adiabatically and polytropically expanding or contracting gas flow with radial and zonal velocity components that represent a deep self-similar modification of the equations of the Lane–Emden theory for stellar polytropes. The models are classified by dynamical equilibrium parameter. We have ascertained an important role of the zonal flow in the establishment of dynamical equilibrium that determines the structure and evolution of stars. Based on the derived equations, we develop a new nonlinear theory of stellar pulsations and construct the period–luminosity relation for them. For the Sun the theory gives the explanation of the 11-year activity cycle as radial–zonal pulsations of its structure in dynamical equilibrium. We present a numerical analysis of the temperature and density distributions in stars in comparison with the data on the Sun. The explanation of the temperature maximum in the solar corona as an element of the dynamically equilibrium stellar structure is proposed within these models.