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Book Boris V. Vasiliev Astrophysics

Chapter 4 The internal

Chapter 4 The internal structure of a star It was shown above that the state with the constant density is energetically favorable for a plasma at a very high temperature. The plasma in the central region of a star can possess by this property . The calculation made below shows that the mass of central region of a star with the constant density - the star core - is equal to 1/2 of the full star mass. Its radius is approximately equal to 1/10 of radius of a star, i.e. the core with high density take approximately 1/1000 part of the full volume of a star. The other half of a stellar matter is distributed over the region placed above the core. It has a relatively small density and it could be called as a star atmosphere. 4.1 The plasma equilibrium in the star core In this case, the equilibrium condition (Eq.(3.3)) for the energetically favorable state of plasma with the steady density n s = const is achieved at P = √ Gγ ⋆r, (4.1) Here the mass density is γ ⋆ ≈ A mpn⋆. The polarized state of the plasma can be Z described by a state with an electric charge at the density and the electric field applied to a cell is ˜ϱ = 1 3 divP = √ Gγ ⋆, (4.2) Ẽ = g √ G . (4.3) 25

As a result, the electric force applied to the cell will fully balance the gravity action γg + ˜ϱẼ = 0 (4.4) at the zero pressure gradient ∇P = 0. (4.5) 4.2 The main parameters of a star core (in order of values) At known density n ⋆ of plasma into a core and its equilibrium temperature T ⋆, it is possible to estimate the mass M ⋆ of a star core and its radius R ⋆. In accordance with the virial theorem 1 , the kinetic energy of particles composing the steady system must be approximately equal to its potential energy with opposite sign: GM 2 ⋆ R ⋆ ≈ kT ⋆N ⋆. (4.6) Where N ⋆ = 4π 3 R3 ⋆n ⋆ is full number of particle into the star core. With using determinations derived above (2.18) and (2.22) derived before, we obtain M ⋆ ≈ M Ch (4.7) (A/Z) 2 ( where M Ch = c Gm 2 p ) 3/2 mp is the Chandrasekhar mass. The radius of the core is approximately equal ( c R ⋆ ≈ Gm 2 p ) 1/2 a B Z(A/Z) . (4.8) where A and Z are the mass and the charge number of atomic nuclei the plasma consisting of. 4.3 The equilibrium state of the plasma inside the star atmosphere The star core is characterized by the constant mass density, the charge density, the temperature and the pressure. At a temperature typical for a star core, the plasma can be considered as ideal gas, as interactions between its particles are small in comparison with kT ⋆. In atmosphere, near surface of a star, the temperature is approximately by 3 ÷ 4 orders smaller. But the plasma density is lower. Accordingly, interparticle interaction is lower too and we can continue to consider this plasma as ideal gas. 1 Below we shell use this theorem in its more exact formulation. 26

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