The amplitude discrepancy between solar limb darkening and Doppler measurements in the five-minute range, suggests the possible existence of Earth's atmosphere oscillations. Recent aeronomical observations add strong evidence to this point of view. A possible explanation of the mysterious 160-min period is presented as a direct consequence. Short period oscillations are another one. Slight discrepancies between Doppler data and between those with theoretical calculations could be also explained in the same way.

We present a study of the effects of diffusion of helium and heavy elements from the convection zone into the radiative layer immediately below the convection zone, on the structure of the solar envelope. A comparison is made of the p-mode oscillation spectrum and the run of the speed of sound in a model with diffusion, in a standard model, and with observation.

A solar model which includes the plausible presence of a mild mixing in the solar inner radiative zone is presented. The mixing is supposed to result from the hydrodynamical instabilities which may occur in a differentially rotating medium leading then to turbulent diffusion. The model includes up-to-date input physics and takes into account the inhibition of the turbulent motions, due to molecular weight gradients (i.e. for Mr/M⊙ < 0.5). The properties of the model are compared to the standard model properties and to observational results: this turbulent diffusion mixing (TDM) improves the results on surface abundances of the light elements (7Li, 3He) and does not reduce the solar neutrino flux relative to the standard model. Moreover preliminary results show that this TDM weakly modifies the oscillation frequencies.

The influence of the modified treatment of subphotospheric convection, as recommended by Deupree (1979) and by Deupree and Varner (1980), on the frequencies of solar five-minute oscillations of degree 1 = 1–100 is studied. As compared with the results for a standard solar model, the convection theory modification has practically no effect on the frequencies near the low frequency edge of the observational interval (at ν ⋍ 2000 μHz), but causes a frequency decrease for high overtones; the effect is larger at larger frequencies. At ν ⋍ 4000 μHz the frequency decrease is about 4–6 μHz for all 1 ≤ 40 and about 8–10 μHz for 1 ⋍ 60–100. If, additionally, we use the dependence T(τ) according to Holweger and Müller (1974) instead of the HSRA model, the joint effect is 1.5–2 times larger. In this case the slope of the theoretical curves in “echelle diagrams” turns out to be in agreement with the observational one for 1 ≤ 20, but the frequencies themselves are approximately 10 μHz lower than those from observations.

Interesting joint constraints are placed on central solar conditions by the solar neutrino detection rate and the frequency separations of high-order, low-degree p-modes of pulsation. A new form of diagnostic diagram is introduced that illustrates the difficulty in standard theories of simultaneously satisfying these joint constraints. A model employing WIMPs (= weakly interacting massive particles) appears to be the only model extant capable of fitting both kinds of data. Unambiguous identification and fitting of g-modes can provide a further test of the WIMP model provided a certain caution is exercised.

The discrepancy between theoretical eigenfrequencies of standard solar models and the frequencies of solar modes of degree between 2 and 5 measured at Stanford is degree-independent for cyclic frequencies above about 2 mHz. Below that frequency the discrepancy for dotriacontapole modes diverges from that of the modes of lower degree. The differences between eigenfrequencies of a simple solar model containing a cloud of weakly interacting particles in its core and of one without do not reproduce this behaviour.

If at some radius r = rj there is a jump of the density and composition then a simple asymptotic formula can be derived which gives ω, the oscillation frequency for large degree modes (ℓ ≫ 1). Using relations of Gabriel and Scuflaire (1979) and taking into account the fact that the oscillation amplitude at R < rj or R > rj is equal to rℓ or r−ℓ multiplied by some functions only weakly dependent on ℓ, we obtain where g is the gravitational acceleration, and ρi(ρe) are the densities at the lover (upper) sides of the layer in question. The comparison with the exact ω-values considered below shows that the asymptotic values are larger by 13, 8.8, and 6 percents for ℓ equal to 5, 7, and 10, respectively. Because ω should be less than the maximum value of the Brunt - Väisälä frequency, we have for a finite thickness Δ of the jump layer and for finite ℓ that ℓ ≪ 2rj/Δ. We have performed numerical study of the above modes which may be called interior modes. The equilibrium model was similar to that studied by Vandakurov (1984 a,b) but now we assume that a small iron-like core (as in Rouse's (1983) model) is present. We assume the hydrogen content in the core to be large enough for convection to occur. Above the core, there are the inhomogeneous convectively neutral zone (rj ≤ r ≤ rj1), the homogeneous radiative zone (rj1 ≤ r ≤ ru), and the convective envelope (ru ≤ r ≤ R), whose structure have been taken from Spruit's (1974) paper.

Due to their efficient trapping in the outer layers such modes may reach observable amplitudes of the order of 1–10 m/s, even if their energies are as those of the “five minute” oscillations. The modes that are most likely to be seen correspond to the lowest radial orders.

The paper will be published in Acta Astronomica.

Motivated by recent interest in the possibility of a long range gravitation-like force we have considered the effects a deviation from the Newtonian force law would have on the solar normal mode spectrum. Observations of low order and degree modes provide the most interesting limits to possible new physics. The constraint from solar oscillation observations is distinct from other planetary data in that it provides an integral bound on force law deviations on spatial scales between roughly 2×104 km and planetary scales. This limit is −0.02 ≤ δG/G ≤ 0.3 and is presently limited by systematic differences between the low-l observations and uncertainty in the solar model.

Asymptotic properties of low degree gravity modes and their relation to the stratification of the model through the Brunt-Väissälä frequency are discussed for a solar type model and for a 10 M⊙ model. For the solar model, taking into account the quasiadiabaticity of the solar convection zone, it is shown that two global constraints on the deep interior of the solar model can be derived from a set of g-modes periods in the observed range. However modes with large periods, i.e. larger than those up to now observed, are required to obtain informations on the stratification just below the convection zone. For the 10 M⊙ model, the preliminary results show that the existence of a layer with a large mean molecular weight gradient destroys the equidistance of the periods of gravity modes of a given degree and that some informations on the properties of this layer can be obtained from the analysis of the g-modes periods.

We have analysed and attempted to classify the acoustic ray patterns in stars whose equilibrium figure is globally deformed. We discuss here the effect of distortions of ellipsoidal and pear-shaped structure. Under ellipsoidal symmetry all ray patterns remain ‘regular’. For arbitrarily small pear-shaped deformations our numerical results indicate the occurrence of ‘chaotic’ ray patterns arising out of the unstable longest diameter ray. These chaotic rays cover the whole configuration space.

We describe how remote sensing problems can be reformulated within the framework of optimization theory. This reformulation allows any prior knowledge about the solution to be naturally incorporated into the solution process. The inversion problem then reduces to a search for the global extremum in the possible presence of local extrema. Two algorithms are presented that can be used to solve this global optimization problem, and their application to the helioseismology inverse problem is detailed.

By using the quantization rule based on the WKB asymptotic method, we present an integral equation to infer the form of the acoustic potential of a fixed ℓ as a function of the acoustic length. Since we analyze the acoustic potential itself by taking account of some factors other than the sound velocity and we can analyze the radial modes by this scheme as well as nonradial modes, this method improves the accuracy and effectiveness of the inverse problem to infer the internal structure of the Sun, in particular, the deep interior of the Sun.

The asymptotic inversion technique is developed, including independent determination of the sound speed profile and frequency dependence of the effective phase shift. Numerical results are presented.

The purpose of this investigation is to estimate how well the structure of the solar core might be inferred by inverting g-mode frequencies.

Delache and Scherrer (1983), Isaak et al. (1984), Severny et al. (1984) reported detection and identification of solar g modes. Although the results seem not to be complete it is helpful to invert the available data in order to understand what new information on the structure of the solar core can be obtained from g-mode frequencies.

Solar gravity modes can be used to probe the stratification below the convection zone. An asymptotic formula for high-order gravity-mode frequencies has been obtained in terms of a stratification parameter β. The domain of validity of this formula is investigated by least-squares regression of frequencies obtained from a theoretical model. Random noise is introduced to simulate real observations. An estimate is made of the critical noise-level above Which β cannot be inferred.

An overshoot region near the base of the solar convection zone may be the region where intense magnetic fields are stored during the solar cycle (Spiegel and Weiss, 1980; Schmitt and Rosner, 1983; Pidatella and Stix, 1986). In this report we study the possible influence of such a field on the frequencies of the solar five-minute oscillations.

Magnetic fields contribute to the splitting of the degeneracy of modes of like order and degree. The splitting is estimated for some simple hypothetical toroidal magnetic field configurations in the sun, and the results are compared with previous asymptotic estimates. Splitting by a field confined to a thin layer at the base of the convection zone is found not to agree with recent measurements.

Both analytical and numerical studies of the effect of a magnetic field at the base of the convection zone on p-modes are presented. It is argued that the recently reported changes in the low degree p-mode frequencies, from 1980 to 1984, may result from corresponding changes in the magnetic field strength. A lower limit of some 5 × 105–106 gauss is implied for the field strength at the base of the convection zone.

The overshoot layer in stellar convection zones is slightly subadiabatic and can be considered as a stable region for storage of magnetic flux. Belvedere, Pidatella and Stix (1986) estimated the size of the overshoot layer and computed the magnetic field strength, beyond which toroidal flux tubes become unstable to buoyancy, for a number of main sequence spectral types ranging from F5 to K0. Here we estimate the relative frequency perturbation of high order acoustic modes due to the presence of a non-oblique axisymmetric magnetic field in the overshoot layer. We find that increases with the advancing spectral type, the predicted frequency splitting being large enough to be detected by observations, at least for the Sun.

We conclude that magnetic field induced frequency splitting of high order acoustic modes may well be due to a toroidal field of relatively moderate strength just beneath the bottom of the convection zone.