Evidence for a small, high-Z, iron-like solar core
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Radial and nonradial oscillation equations without and with the gravitation perturbation (with and without the Cowling approximation, CA) are solved numerically using the profile from a more accurate high-Z core (HZC) solar model. This more accurate HZC model was generated with the CRAY X-MP/48 supercomputer at the San Diego Supercomputer Center. Frequencies of oscillation in the five-min band (5MB) and frequencies with period near 160 min are presented in tables and plotted in echelle diagrams. The model was generated by integrating the stellar structure equations from the center to he surface, as done in Rouse (1964), using a maximum space step, Δ;x m = 5 × 10−4, decreasing to 10−6 in the hydrogenionization zone just below the photosphere. Two subsets of space mesh points are used to calculate the oscillation frequencies, viz., one with a maximum space step of 5 × 10−3, decreasing to 10−6 with a total of 621 points (mesh 5I) and the other with a maximum space step of 2 × 10−3, with a total of 867 points (mesh 5J).
With the surface boundary condition applied at x = 1.0, the l − 1 degree nonradial frequencies with CA and the l-degree frequencies without CA are in very good agreement with the frequency spacings for observed frequencies of oscillation labeled l = 1 to 5, but with the l − 1 frequencies with CA about ≲ 10 μHz or so less than the observations and the l frequencies without CA about ≳ 10 μHz or so greater than the observations. And for the Duvall and Harvey (1983) observations labeled l = 10 and l = 20, the l = 9 and l = 19 nonradial solutions with CA agree to about ≲ 5 μHz or less with the observations. Considering from the two preceeding papers in this series that increasing the density in the outer envelope and photosphere will increase the 5MB frequencies and applying the outer boundary condition at x > 1.0 will decrease the 5MB frequencies, the net affects of such changes could move one or the other set of frequencies closer to the observations — or require a slightly different model structure to obtain accurate agreements with the values of the observed frequencies throughout the 5MB.
In either case, it is concluded that the first-order, radially-symmetric structure of the model outside the HZC is close to the structure of the real Sun. This is of fundamental importance because a real gas adiabatic temperature gradient (Rouse, 1964, 1971) is used in the outer convective region without free parameters.
Other aspects of agreements and differences between radial and nonradial solutions, with CA and without CA are discussed. In particular, the l = 4, 6, 8, and 9 g-mode solutions with CA indicate that the observed 160.01 min period may be a common l-mode period of oscillation. More research is proposed.
KeywordsAdiabatic Temperature Surface Boundary Condition Solar Model Outer Envelope Gravitation Perturbation
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