The generalized polytropic model for the Sun-like stars

Abstract

The Eddington method based on simultaneous consideration of gas and light pressures with a homogeneous сhemical composition of stellar matter was generalized for the case of model with a spatially inhomogeneous chemical composition. As a result, it was obtained the equation of state, which is expressed by a generalized polytrope with index n=3. As an example, it was solved the equilibrium equation for the Sun both using the standard polytropic equation of state and generalized polytrope. The coordinate dependence of the Sun characteristics was calculated within two models. Obtained results are compared with the results of numerical calculations for the Sun based on the system of Schwarzschild equations for the standard model. It was shown that the standard polytropic model is applicable only for the Sun of zero-age. The Sun characteristics calculated with help of generalized equation of state are close to the results of numerical calculations based on Schwarzschild equations. It was concluded that the standard polytropic model is applicable for the stars of zero-age main sequence, and the generalized model – for the stars of finite age, in which thermonuclear reactions have already created a significant spatially inhomogeneity of chemical composition inside of the core.