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Chapter 9 The solar seismical oscillations 9.1 The spectrum of solar seismic oscillations The measurements [9] show that the Sun surface is subjected to a seismic vibration. The most intensive oscillations have the period about five minutes and the wave length about 10 4 km or about hundredth part of the Sun radius. Their spectrum obtained by BISON collaboration is shown in Fig.9.1. It is supposed, that these oscillations are a superposition of a big number of different modes of resonant acoustic vibrations, and that acoustic waves propagate in different trajectories in the interior of the Sun and they have multiple reflection from surface. With these reflections trajectories of same waves can be closed and as a result standing waves are forming. Specific features of spherical body oscillations are described by the expansion in series on spherical functions. These oscillations can have a different number of wave lengths on the radius of a sphere (n) and a different number of wave lengths on its surface which is determined by the l-th spherical harmonic. It is accepted to describe the sunny surface oscillation spectrum as the expansion in series [8]: ν nlm ≃ ∆ν 0(n + l + ɛ0) − l(l + 1)D0 + m∆νrot. (9.1) 2 Where the last item is describing the effect of the Sun rotation and is small. The main contribution is given by the first item which creates a large splitting in the spectrum (Fig.9.1) △ν = ν n+1,l − ν n,l . (9.2) 67
Figure 9.1: (a) The power spectrum of solar oscillation obtained by means of Doppler velocity measurement in light integrated over the solar disk. The data were obtained from the BISON network [9]. (b) An expanded view of a part of frequency range. 68
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Boris V.Vasiliev ASTROPHYSICS and a
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5 The main parameters of star 29 5.
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theories of stars that are not purs
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But plasma is an electrically polar
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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
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Page 23 and 24: 3.2 The equilibrium of a nucleus in
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Page 27 and 28: As a result, the electric force app
Page 29 and 30: and in accordance with Eq.(4.11), t
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: N -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0
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
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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
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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
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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
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[52] Semeniuk I. Apsidal motion in
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[75] Andersen J. and Gimenes A. Abs
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