Seismology of the solar convection zone

An attempt is made to infer the structure of the solar convection zone from observedp-mode frequencies of solar oscillations. The differential asymptotic inversion technique is used to find the sound speed in the solar envelope. It is found that envelope models which use the Canuto-Mazzitelli (CM) formulation for calculating the convective flux give significantly better agreement with observations than models constructed using the mixing length formalism. This inference can be drawn from both the scaled frequency differences and the sound speed difference. The sound speed in the CM envelope model is within 0.2% of that in the Sun except in the region withr > 0.99R _⊙. The envelope models are extended below the convection zone, to find some evidence for the gravitational settling of helium beneath the base of the convection zone. It turns out that for models with a steep composition gradient below the convection zone, the convection zone depth has to be increased by about 6 Mm in order to get agreement with helioseismic observations.     

Thallium in the solar atmosphere

Umbral spectra are shown to contain an absorption feature attributable to the Tl i transition 6p ² P°_3/2–7s ² S _1/2 at 5350 Å. Analysis of the umbral spectrum suggests a solar abundance in the 0.72< log N(Tl)T<1.10 on the standard scale log N(H) = 12.00. Unidentified blends limit the accuracy of the abundance determination.     

The rotation of the solar atmosphere

A model of the solar atmosphere is presented in which we discuss the conservation of angular momentum for the two basic states in which the solar gas can be: namely, either confined by closed field lines or outflowing along open magnetic field lines. It can be shown that the boundary conditions are in general different for these two cases. From this we obtain the results that in the closed configuration the gas can corotate at the solar surface with the magnetic field lines and its angular velocity will then increase with height, whereas for a gas flowing along an open field line the angular velocity will decrease. An exception to the latter case can be found where the open magnetic field lines are strongly nonradial and where the density is a slowly varying function of radius. In such regions the angular velocity may initially increase with height, reach a maximum and then decrease.Kitt Peak National Observatory Contribution No. 439.Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Models of the open solar atmosphere

McWhirter et al. (1975) have presented a standard model for the transition region and inner corona that matches with the Harvard Smithsonian Reference Atmosphere. They assume an open field line configuration and solve numerically the equations of energy and hydrostatic equilibrum. The purpose of the present paper is to generalise their model for the temperature and density as functions of height in several ways and, in particular, to determine the temperature maxium and its location. The effect of varying the following characteristics of the model is determined:

1. Boundary conditions on temperature and density;
2. magnitude of the heating;
3. form of the heating term;
4. divergence of the field lines;
5. presence of subsonic flows, either upward or downward.

If the heating is localised at great altitudes, it tends to produce a narrower and larger temperature maximum at a greater altitude than a uniform heating and even more so than a heating proportional to density. For fixed base conditions, an increase in heating or field line divergence or downflow decreases the coronal temperature and reduces the height of the temperature maximum, while a steady upflow has the opposite effects. A maximum possible upflow was found, beyond which a catastrophe occurs so that no steady hot solution exists.     

Lithium depletion in the solar atmosphere

Using a complete non-local convection theory, we carried out the theoretical calculations of ⁷Li depletion of the solar convective envelope models with different convective parameters c₁ and c₂, and got a model of the solar convection zone consistent with the observed ⁷Li abundance and the depth of the solar convection zone determined by helioseismic techniques. The overshooting distance of effective non-local convective mixing of ⁷Li is very extensive, which is about 1.07H_P or 0.09R. However, the super-radiative temperature zone is much narrower, and it is only 0.20H_P or 0.016R.     

Ion-acoustic waves in the solar atmosphere

A model for ion-acoustic waves in the solar atmosphere is presented. In the limit of strongly magnetized plasma this model leads to the Zakharov-Kuznetsov equation which possesses a flat solitary wave solution. An initial-value problem for this equation is solved numerically to show a transition of the flat solitary waves into spherical solitary waves. The paper suggests further developments of an ion-acoustic wave theory that may improve our knowledge of ion-acoustic waves and lead to the possibility of their being detected in the solar atmosphere.     

Wave reflections in the solar atmosphere

The small phase-lag between velocities observed at different chromospheric levels is interpreted as being due to acoustic waves reflected by the very hot atmospheric layers of the chromosphere-corona transition zone. We consider first an isothermal slab, then a realistic solar atmospheric model and calculate weighting functions for velocities in Ca ii lines. It is shown that taking into account these functions and integrating over horizontal wave numbers leads to a good agreement with previous observations (Mein, 1977) in the case of 8498 and 8542 Ca ii lines. For the K line, the less good agreement shows that magnetoacoustic waves become important in the upper chromospheric layers.     

Velocity fields in the solar atmosphere

Observations of velocity fields in the solar atmosphere made with the Mount Wilson solar magnetograph are analyzed. These observations, which were made with very high velocity sensitivity, cover nearly 250 hours and were made with apertures of several sizes and at various parts of the solar disk, and in strong and weak magnetic fields. The amplitudes of the 300-sec oscillations are about 25% weaker in regions where the magnetic field is greater than 80 gauss than where the field is less than 10 gauss. No difference in the frequencies of the oscillations could be found between strong-field and field-free regions. It is suggested that the oscillations occur only where the field is absent and the lower amplitude in a strong field represents the fraction of the magnetograph aperture occupied by a magnetic field. The element sizes for the 300-sec oscillations are probably at least 5–10 arc seconds.Observations made simultaneously with two lines formed at different depths in the solar atmosphere showed small phase differences in the 5-min oscillations. The upper level showed shorter period oscillations when the lower level oscillations underwent phase changes.A short period oscillation is found superposed on the 300-sec oscillation. These SPOs come in bursts that last for a minute or two and have average amplitudes that fall in the range 0.05–0.10 km/sec peak to peak. All attempts to explain them as instrumental or seeing effects have failed. Their periods fall in the range 1–5 seconds. The horizontal scale of these oscillations is smaller than that of the 300-sec oscillations, and the SPOs are more nearly isotropic oscillations than are these around 300 seconds. They do not represent a high-frequency tail of the latter. These observations did not have a digitizing interval short enough to analyze the SPOs for power spectra, but it is clear from the tracings that they are not a nearly monochromatic oscillation as are the longer waves. The amplitudes of the SPOs in the solar atmosphere must be very large and they contribute greatly to the non-radiative energy flux. It is suggested that they represent a large microturbulence line-broadening effect.     

Magnetohydrostatic structures in the solar atmosphere

Separable two-dimensional solutions to the isothermal magnetohydrostatic equations are presented which include the effect of gravity. Examples of three types of linear solution are given in which photospheric magnetic fields are prescribed and the field topologies are discussed. In addition, a new nonlinear solution is discussed. The functional form of the pressure distribution is restricted by the separable assumption. An analysis suggests that these are the only separable analytical solutions.     

Temperature waves in the solar atmosphere

The properties of five-minute temperature waves in the photosphere are investigated. The phase and amplitude relations of temperature and acoustic waves are deduced. It is expected that the five-minute oscillations represent a mixture of acoustic and temperature waves. The temperature waves are generated due to linear interaction with acoustic waves.It is well known that concurrent with the acoustic waves, temperature or heat waves can appear in the case of nonadiabatic disturbances (Landau and Lifshitz, 1959). The temperature waves are dissipative damped waves. Propagation of nonadiabatic hydrodynamic waves in a stratified medium have been considered by Zhugzdha (1983). If stratification of heat exchange exists, a linear interaction of hydrodynamic and temperature waves arises. The temperature waves must be present in the solar atmosphere.     

Ambipolar diffusion in the solar atmosphere

The process of non-linear ambipolar diffusion in the region overlying the solar surface can be an effective mechanism for producing sharp magnetic structures and current sheets. These may be the sites responsible for the occurrence of connectivity of magnetic field lines, and the subsequent explosive input of energy for heating of some of the features in the atmosphere of the Sun..     

Non-divergent oscillations in the solar atmosphere

Non-divergent oscillations having the form of deep water waves are shown to form normal modes or free oscillations of the solar atmosphere under two approximations: the chromosphere-coronal interface behaves like a free surface, and the density scale height is sufficiently large in the convective zone. These modes show the temporal and spatial characteristics of the 300 second chromospheric oscillations.     

Velocity oscillations in the solar atmosphere

From a series of long duration continuous Doppler records of selected spectral lines, characteristics of solar velocity oscillations have been studied. Statistical distribution of the durations of the bursts of oscillations has been estimated. From the nature of distortion of the waveforms of the oscillation, the presence of disturbing impulses has been speculated. Constancy and homogeneity of the oscillations have been examined from detailed spectral density plots. Duration indices for the oscillations at different heights in the solar atmosphere have been derived by estimating mean spectral densities of characteristic oscillation amplitudes during several individual bursts and comparing them with corresponding spectral densities from long records. The variation among experimental results has been explained as due to the limitations of the power spectral analysis method on short records.     

Electric fields in the solar atmosphere

The gross-structure of the force-free currents in the solar atmosphere and their possible dynamics have been discussed as caused by quasi short-circuited electric fields, generated by the motion of the solar magnetic features.     

Isotopes of magnesium in the solar atmosphere

We have analysed MgH A ² -X ²(0.0), (1.1), (2.2), (0.1) and (1.2) absorption bands in a sunspot spectrum. By two different methods, which are almost independent of the estimated value of the correction for stray light, we have determined the solar isotopic ratios of magnesium. These ratios are equal to the terrestrial ones - ²⁴Mg²⁵Mg²⁶Mg = 801010.     

The coarse structure of the solar atmosphere

Observations of the quiet sun at wavelengths from 3 Å to 75 cm show (with two exceptions: the Ovi line at 1032 Å and possibly the continuum at 1.2 mm) either no limb brightening or less than had been supposed. On the other hand, the brightness temperature is observed to increase with wavelength in the millimeter and centimeter range. If this increase is due to greater visibility of hot overlying material, that material ought to be evident at the limb at shorter wavelengths, resulting in limb brightening. The only possible explanation for the absence of limb brightening at almost all wavelengths is that the emitting surface is rough at all wavelengths, with a scale of roughness approximately equal to the scale height at each temperature. Contradictions with existing models, along with the additional observations required for an improved model are discussed.     

A model of the quiet solar atmosphere

The solar atmosphere may be divided into a number of isolated active components and a quiet residue. On the largest scale the latter is dominated by a general dipole magnetic field of strength 1–2 G; its observable components are flux concentrations in supergranule boundary regions (SBRs), spicules, mottles and polar plumes. The velocity field in the SBRs is discussed. There are continuous gas streaming motions up and down between the photosphere and the corona; spicules may be mainly downward moving gas.A unifying model is developed of these various components, as well as the heating mechanism of the whole quiet atmosphere. Highly ordered velocity fields of the cell, together with a gravitational wave, cause a vertical magnetic force tube to collapse below a critical level; the result is an upward eruption of a vortex ring at the Alfvén velocity. The complex mass velocity pattern may explain spicules, mottles and plumes, as well as unobservable streaming motions.The quiet atmosphere is divided into regions above SBRs and those above the inner parts of the cells. Hydromagnetic eruptions from the former may account for the entire heat requirement of the atmosphere. The model atmosphere has a chromosphere-corona transition layer which bulges upwards above the SBRs and so conforms with EUV data. The energy and mass balances in this solar atmosphere are considered, and it is also shown to be consistent with the radio data.     

A new resonance in the solar atmosphere

We consider a horizontally stratified isothermal model of the solar atmosphere, with vertical and uniform B ₀, and v _A ² v _s ² . The equations of motion are linearized about a background which is in hydrostatic equilibrium. A homogeneous wave equation results for the motions perpendicular to B ₀; this wave equation is similar to the equation for the MHD fast mode. On the other hand, the equation for the parallel motions is inhomogeneous, containing driving terms which arise from the presence of the fast mode; the homogeneous form of this equation is identical to the equation describing vertically-propagating gravity-modified acoustic waves. We demonstrate that a resonance can exist between the (driving) fast wave and the (driven) gravity-modified acoustic wave, in such a way that very large parallel velocities can be driven by small perpendicular velocities. Applications of this resonance to solar spicules, jets, and other phenomena are discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.