- Text
- Plasma,
- Density,
- Electron,
- Equilibrium,
- Binary,
- Radius,
- Stellar,
- Eclipsing,
- Parameters,
- Equation,
- ÑÐ¸Ð·Ð¸ÐºÐ¾ÑÐµÑ Ð½Ð¸Ðº.ÑÑ

Book Boris V. Vasiliev Astrophysics

In the absence of the gravitation, the equilibrium state of ideal gas in some volume comes with the pressure equalization, i.e. with the equalization of its temperature T and its density n. This equilibrium state is characterized by the equalization of the chemical potential of the gas µ (Eq.(2.8)). 4.4 The radial dependence of density and temperature of substance inside a star atmosphere For the equilibrium system, where different parts have different temperatures, the following relation of the chemical potential of particles to its temperature holds ([12],25): µ kT = const (4.9) As thermodynamic (statistical) part of chemical potential of monoatomic ideal gas is [12],45: [ ( ) n 2π 2 3/2 ] µ T = kT ln , (4.10) 2 mkT we can conclude that at the equilibrium n ∼ T 3/2 . (4.11) In external fields the chemical potential of a gas [12]25 is equal to µ = µ T + E potential (4.12) where E potential is the potential energy of particles in the external field. Therefore in addition to fulfillment of condition Eq. (4.11), in a field with Coulomb potential, the equilibrium needs a fulfillment of the condition − GMrγ rkT r + P2 r 2kT r = const (4.13) (where m is the particle mass, M r is the mass of a star inside a sphere with radius r, P r and T r are the polarization and the temperature on its surface. As on the core surface, the left part of Eq.(4.13) vanishes, in the atmosphere M r ∼ rkT r. (4.14) Supposing that a decreasing of temperature inside the atmosphere is a power function with the exponent x, its value on a radius r can be written as ( ) x R⋆ T r = T ⋆ (4.15) r 27

and in accordance with Eq.(4.11), the density ( ) 3x/2 R⋆ n r = n ⋆ . (4.16) r Setting the powers of r in the right and the left parts of the condition Eq.(4.14) equal, one can obtain x = 4. Thus, at using power dependencies for the description of radial dependencies of density and temperature, we obtain ( ) 6 R⋆ n r = n ⋆ (4.17) r and ( ) 4 R⋆ T r = T ⋆ . (4.18) r 4.5 The mass of the star atmosphere and the full mass of a star After integration of Eq.(4.17), we can obtain the mass of the star atmosphere ∫ R0 ( ) [ 6 R⋆ M A = 4π (A/Z)m pn ⋆ r 2 dr = 4π ( ) ] 3 R⋆ r 3 (A/Z)mpn⋆R⋆3 1 − R 0 R ⋆ (4.19) It is equal to its core mass (to R3 ⋆ ≈ 10 −3 ), where R R 3 0 is radius of a star. 0 Thus, the full mass of a star M = M A + M ⋆ ≈ 2M ⋆ (4.20) 28

- Page 3 and 4: Boris V.Vasiliev ASTROPHYSICS and a
- Page 5 and 6: 4
- Page 7 and 8: 5 The main parameters of star 29 5.
- Page 9 and 10: 8
- Page 11 and 12: theories of stars that are not purs
- Page 13 and 14: But plasma is an electrically polar
- Page 15 and 16: can be described by definite ration
- Page 17 and 18: But even at so high temperatures, a
- Page 19 and 20: 2.2 The energy-preferable state of
- Page 21 and 22: 20
- Page 23 and 24: 3.2 The equilibrium of a nucleus in
- Page 25 and 26: 24
- Page 27: As a result, the electric force app
- Page 31 and 32: The total kinetic energy of plasma
- Page 33 and 34: we obtain η = 20 = 6.67, (5.24) 3
- Page 35 and 36: 40 N 35 30 10 9 8 7 6 5 4 3 2 1 A/Z
- Page 37 and 38: One can show it easily, that in thi
- Page 39 and 40: 2.10 log (TR/R o T o ) 1.55 1.00 me
- Page 41 and 42: averaged temperature and averaged p
- Page 43 and 44: log R/R o 1.5 1.3 1.1 0.9 measured
- Page 45 and 46: The Table(6.2). The relations of ma
- Page 47 and 48: The Table(6.2)(continuation). N Sta
- Page 49 and 50: The Table(6.2)(continuation). N Sta
- Page 51 and 52: log T/T o 1.0 0.9 0.8 0.7 0.6 measu
- Page 53 and 54: Figure 6.4: The schematic of the st
- Page 55 and 56: 54
- Page 57 and 58: Simultaneously, the torque of a bal
- Page 59 and 60: At taking into account above obtain
- Page 61 and 62: 60
- Page 63 and 64: of periastron rotation of close bin
- Page 65 and 66: 8.3 The angular velocity of the aps
- Page 67 and 68: N -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0
- Page 69 and 70: Figure 9.1: (a) The power spectrum
- Page 71 and 72: Figure 9.2: (a) The measured power
- Page 73 and 74: 9.3 The basic elastic oscillation o
- Page 75 and 76: 9.5 The spectrum of solar core osci
- Page 77 and 78: star mass spectrum. At first, we ca
- Page 79 and 80:
where ˜ λ C = m ec is the Compto

- Page 81 and 82:
This energy is many orders of magni

- Page 83 and 84:
82

- Page 85 and 86:
Figure 11.1: The steady states of s

- Page 87 and 88:
It opens a way to estimate the mass

- Page 89 and 90:
N 10 9 8 7 6 5 4 3 2 1 0 1.0 1.1 1.

- Page 91 and 92:
This makes it possible to estimate

- Page 93 and 94:
to p F ≈ mc, its energy and press

- Page 95 and 96:
94

- Page 97 and 98:
approach to the separation of the E

- Page 99 and 100:
is evident as soon as in this proce

- Page 101 and 102:
Figure 12.1: The dependence of the

- Page 103 and 104:
Figure 12.2: a) The external radius

- Page 105 and 106:
104

- Page 107 and 108:
It gives a possibility to conclude

- Page 109 and 110:
This allows us to explain the obser

- Page 111 and 112:
[14] Landau L.D. and Lifshits E.M.:

- Page 113 and 114:
N Name of star U P M 1 /M ⊙ M 2 /

- Page 115 and 116:
[9] Gemenez A. and Clausen J.V., Fo

- Page 117 and 118:
[30] Hill G. and Holmgern D.E. Stud

- Page 119 and 120:
[52] Semeniuk I. Apsidal motion in

- Page 121:
[75] Andersen J. and Gimenes A. Abs