Stellar Models

distributions of the temperature, density, and pressure of the matter in stars of a given mass and chemical composition calculated on the basis of various theoretical assumptions. The construction of stellar models is based on the concept of a gaseous star in equilibrium whose state is determined by mechanical equilibrium (between the force of gravity and the force of gas pressure), on the one hand, and by thermal equilibrium (between energy generation and dissipation), on the other.

Characteristic parameters of stellar models are the absorption coefficient, the mode of energy transport, the equation of state of stellar matter, and the mode of energy generation. The values of these parameters are determined from the theory of the internal structure of stars. Distinctions are made between homogeneous and inhomogeneous stellar models (according to chemical composition) and simple and complex multiphase stellar models (according to the equation of state and mode of energy transport). The simplest models are those of stars of the main sequence of the Hertzsprung-Russell diagram: stars located in its upper part consist of a convective core (including 0.30–0.15 of the star’s mass; energy transport in it is carried out by means of convection) and a radiative layer, or shell. All the energy is generated in the convective core as a result of nuclear reactions involving the transformation of hydrogen into helium. The larger the star’s mass, the larger the dimensions and mass of the convective core. Stars in the lower part of the main sequence, on the contrary, consist of an outer convective shell and a core in radiative equilibrium, in the center of which the hydrogen is burned out. The temperature at the center of hot blue stars is about 30 million degrees and the density about 2 g/cm³; at the center of the sun the temperature is about 15 million degrees and the density about 100 g/cm³; at the center of red dwarfs the temperature is about 10 million degrees and the density about 1,000 g/cm³.

With the passage of time, the chemical composition of the core changes because of nuclear transformations, and the initially homogeneous stellar model becomes ever more inhomogeneous. With the exhaustion of the hydrogen reserves in a star, reactions that build heavier nuclei from helium are possible if the temperature and density in its interior increase significantly as a result of the contraction of the star. The increase in density leads to a change in the equation of state in the central regions of the stellar model (to degeneracy of the gas). Models of stars in late stages of development (red giants) are the most complex. They consist of several alternately convective and radiative zones of different chemical composition and two or three layers of energy sources (with different nuclear reactions). Some zones or the central core can be found in a state of contraction or expansion. The model of a white dwarf consists almost totally of degenerate gas. Computers are used in the calculations of stellar models and in tracing the evolution of stars.