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Book Boris V. Vasiliev Astrophysics

The small splitting of

The small splitting of spectrum (Fig.9.1) depends on the difference δν l = ν n,l − ν n−1,l+2 ≈ (4l + 6)D 0. (9.3) A satisfactory agreement of these estimations and measurement data can be obtained at [8] ∆ν 0 = 120 µHz, ɛ 0 = 1.2, D 0 = 1.5 µHz, ∆ν rot = 1µHz. (9.4) To obtain these values of parameters ∆ν 0, ɛ 0 D 0 from theoretical models is not possible. There are a lot of qualitative and quantitative assumptions used at a model construction and a direct calculation of spectral frequencies transforms into a unresolved complicated problem. Thus, the current interpretation of the measuring spectrum by the spherical harmonic analysis does not make it clear. It gives no hint to an answer to the question: why oscillations close to hundredth harmonics are really excited and there are no waves near fundamental harmonic? The measured spectra have a very high resolution (see Fig.(9.1)). It means that an oscillating system has high quality. At this condition, the system must have oscillation on a fundamental frequency. Some peculiar mechanism must exist to force a system to oscillate on a high harmonic. The current explanation does not clarify it. It is important, that now the solar oscillations are measured by means of two different methods. The solar oscillation spectra which was obtained on program ”BISON”, is shown on Fig.(9.1)). It has a very high resolution, but (accordingly to the Liouville’s theorem) it was obtained with some loss of luminosity, and as a result not all lines are well statistically worked. Another spectrum was obtained in the program ”SOHO/GOLF”. Conversely, it is not characterized by high resolution, instead it gives information about general character of the solar oscillation spectrum (Fig.9.2)). The existence of this spectrum requires to change the view at all problems of solar oscillations. The theoretical explanation of this spectrum must give answers at least to four questions : 1.Why does the whole spectrum consist from a large number of equidistant spectral lines? 2.Why does the central frequency of this spectrum F is approximately equal to ≈ 3.23 mHz? 3. Why does this spectrum splitting f is approximately equal to 67.5 µHz? 4. Why does the intensity of spectral lines decrease from the central line to the periphery? The answers to these questions can be obtained if we take into account electric polarization of a solar core. The description of measured spectra by means of spherical analysis does not make clear of the physical meaning of this procedure. The reason of difficulties lies in attempt to consider the oscillations of a Sun as a whole. At existing dividing of a star into core and atmosphere, it is easy to understand that the core oscillation must form a 69

Figure 9.2: (a) The measured power spectrum of solar oscillation. The data were obtained from the SOHO/GOLF measurement [19]. (b) The calculated spectrum described by Eq.(9.26) at < Z >= 3.4 and A/Z = 5. 70

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