On the convective instability of finitely conducting viscous model chromosphere

The convective stability of a simple model chromosphere, consisting of protons, electrons and hydrogen atoms in the ground state, has been studied in the presence of a vertically upward uniform magnetic field to include the effects of FLR, Hall-currents, finite conductivity and ionization. The ionization in the chromosphere is collisional and the recombination is radiative. It is found that the Schwarzchild criterion should necessarily be satisfied for the stability together with the condition thatv > 2v ₀, where is kinematic viscosity andv ₀ is gyroviscosity. Some special cases have also been investigated.     

A model of a penumbral chromosphere

A semi-empirical model of a penumbral chromosphere is presented which represents a specific region of the penumbra located approximately one-fourth the distance outward from the umbra-penumbra interface. The model is based on simultaneous observations of high-resolution spectra of Caii K, H, and 8498 made over a sunspot penumbra (SPO 5007) with the Echelle Spectrograph at the Vacuum Tower Telescope at Sacramento Peak Observatory on 18 December, 1979.Spectral profiles were calculated using a non-LTE line formation procedure with various chromospheric models where the optimum model is determined by matching the synthesized profiles with the observational features. The best fit yields a model with overlying column mass m ₀ of 8 × 10^–6 g cm^–2 which also agrees with the observed K₃/H₃ intensity ratio of 1.22.This work was supported by the US-Republic of Korea Cooperative Science Program (K-53).     

Convective instability in a compressible atmosphere

The degree of convective instability as expressed by the growth rate of linear modes, is calculated for a plane parallel polytropic atmosphere in the presence of radiative damping, without using Boussinesq approximation. A comparison with the results based on the Boussinesq approximation reveals that the use of the Boussinesq approximation leads to an overestimation of the radiative damping. The computation of as a function of the horizontal wave number yields a wavelength of maximal instability under a variety of conditions. For reasonable choices of physical parameters appropriate to the solar atmosphere, the fastest growing wavelengths turn out to be in the range 600–1200 km, and their e-folding times are in the range 200–2000 s.NAS-NRC Senior Research Associate on leave of absence from the Tate Institute of Fundamental Research, Bombay.     

Convective instability of thin flux tubes

The stability of magnetic flux tubes embedded vertically in a convection zone is investigated. For thin tubes, the dominant instability is of the convective type, i.e. it is driven by buoyancy forces associated with displacements along the tube. The stability is determined by = 8P/B ²; if _c the tube is convectively stable, otherwise it is unstable, where the critical value _c depends on the stratification of the convection zone. For a solar convection zone model, _c = 1.83, corresponding to a magnetic field strength of 1350 G at the surface of the Sun. It is concluded that the flux tubes making up the small scale field of the Sun are probably hydrodynamically stable.In tubes with > _c, the instability is expected to transform the tube either into a state of vanishing surface field strength (in the case of an upward flow), or one with a field strength higher than the original value (if the instability sets in as a downward flow). Following Parker, we suggest that this effect is related to the concentrated nature of the observed solar fields.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Small-scale Langmuir wave instability in preflare chromosphere of solar active region

Necessary conditions have been investigated for the appearance of instability of high-frequency electron Langmuir waves in plasma of solar chromosphere near the foot-point of loop structure. We have considered the earliest stage of a flare process in solar active region. At the chromospheric part of current circuit of a flare loop such instability can appear and develop as the result of combined action of large-scale electric field, Landau damping and collisional processes in preflare plasma. We have investigated the process of instability development for two possible scenarios: (a) when preflare loop plasma has a classical Coulomb conductivity and (b) when anomalous resistance appears due to saturation of Bernstein turbulence. The growth rates of instability have been obtained and analyzed in detail. It has been assumed in the process of calculation that preflare plasma can be described by the FAL model of the solar atmosphere, which takes into account the process of helium diffusion. It has been shown that Langmuir wave instability can appear in its marginal form in the area under investigation either in the presence of Coulomb conductivity or in the presence of saturated Bernstein turbulence. Existence of instability with the growth rate, which changes its sign, proves the principal possibility of generation of nondamping Langmuir waves with small amplitudes.     

Convective instability in the solar envelope

The characteristics of the most unstable fundamental mode and the first harmonic excited in the convection zone of a variety of solar envelope models are shown to be in reasonable agreement with the observed features of granulation and supergranulation. On leave of absence from Government Digvijai College, Rajnandgaon 491441     

Suppression of the kink instability for magnetic flux ropes in the chromosphere

Energy storage in chromospheric flux ropes is discussed, in the context of solar flares. The structure is represented by a cylindrically symmetric magnetic field of finite length. The field is assumed to be approximately force-free. The stability of the field to a kink perturbation is investigated. Flux ropes are rooted in dense photospheric material. So the ends of the field lines are taken to be fixed on rigid boundaries for all perturbations. An energy perturbation method is used and the boundary conditions give a stabilizing effect. It is shown that for a moderate degree of twisting the fields are stable to a kink perturbation. Thus energy can be stored in cylindrical fields prior to release in a solar flare.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Convective instability in the martian middle atmosphere

Dry convective instabilities in Mars’s middle atmosphere are detected and mapped using temperature retrievals from Mars Climate Sounder observations spanning 1.5 martian years. The instabilities are moderately frequent in the winter extratropics. The frequency and strength of middle atmospheric convective instability in the northern extratropics is significantly higher in MY 28 than in MY 29. This may have coupled with changes to the northern hemisphere mid-latitude and tropical middle atmospheric temperatures and contributed to the development of the 2007 global dust storm. We interpret these instabilities to be the result of gravity waves saturating within regions of low stability created by the thermal tides. Gravity wave saturation in the winter extratropics has been proposed to provide the momentum lacking in general circulation models to produce the strong dynamically-maintained temperature maximum at 1-2 Pa over the winter pole, so these observations could be a partial control on modeling experiments.     

Convective instability and overstability in the sunspot umbra

Convective instability and overstability of a plane-parallel medium in the presence of a uniform vertical magnetic field is studied. We take into account both the effect of penetration of disturbances into sub-adiabatically stratified semi-infinite upper and lower layers, and the effect of thermal damping of disturbances introduced by the compressibility of the medium. If the degree of super-adiabaticity in temperature stratification in the middle layer is relatively large compared with that of sub-adiabaticity in the upper and lower layers, the range of physical conditions in which overstable convection occurs is very narrow. However, if it is not the case the range is rather wide. In the normal sunspot umbra, only disturbances with selected sizes in vertical dimension will be able to become overstable. The overstable convection might be a cause of some dynamical features (such as dots) in the sunspot umbra, but will not be the main contributor for transporting mechanical energy in the sunspot region.     

A model of the inhomogeneous chromosphere of the sun

A new model is proposed for the solar chromosphere, which is assumed to be an instable inhomogeneous formation, consisting of numerous elements (filaments), each with different temperature and density. Fluctuations of the magnetic field may give rise to chromospheric turbulence and may also cause the chromospheric inhomogeneities.The chromosphere is suggested to consist of four discrete groups of filaments: (1) metallic filaments where the conditions for the emission of lines of neutral metals are optimal, (2) hydrogenic elements, with optimum conditions for the emission of the Balmer series of hydrogen, (3) helium filaments, with optimum conditions for the appearence of the neutral helium lines, (4) the subcoronal filaments, representing a transition from chromospheric to coronal formations.The metallic filaments may be further subdivided, first into filaments where the emission arises from scattering of photospheric radiation - these emit lines of neutral metals and of some metallic ions (CaII, SrII, and others), and further into filaments where the emission is farther from LTE conditions; the latter filaments are characterized by a somewhat higher electron temperature and by an electron density at least exceeding that of the other elements by an order of 10. Computations of the optimum conditions for the emission of the neutral helium lines were made with the aid of new tables of Sobolev. The helium filaments in the low chromosphere have lower temperatures and are denser than those in the upper chromosphere; for a part they may also be considered as hydrogen filaments. The derivation of the physical parameters of the subcoronal filaments was based on data on the Heii4686 chromospheric line emission and also on rocket observations of the ultraviolet solar spectrum. In order to evaluate the relative distribution of the various filaments between heights of 0 and 5000 km, data on the radio emission of the Sun at 8 mm are also used. Characteristics of the proposed model of the chromosphere are given in Table III and Figure 1.     

The Bilderberg model of the photosphere and low chromosphere

From 17 through 21 April 1967, an international study week was held in the Bilderberg near Arnhem, Netherlands, with the aim of obtaining an internationally acceptable model of the solar photosphere and low chromosphere. It was found that such a model, based on observed intensities and center-to-limb observations of the solar continuous spectrum, could indeed be established. This model, henceforth called the Bilderberg Continuum Atmosphere (BCA), is shown in Table I, which gives the temperature, gas and electron pressures, and other data as functions of the continuous optical depth at 5000 Å between 5000 = 10^–7 and 25. The model is characterized by a flat temperature minimum of 4600 °K between 5000 10^–2 to 10^–4. The model is homogeneous, and in hydrostatic equilibrium. A hydrogen-helium ratio of 10 has been assumed.Much divergence remains in the interpretation of line-profile observations with regard to the establishment of a photospheric model (Section 4). It proved to be as yet impossible to obtain reliable information on the variation with depth of the following functions: temperature fluctuations, turbulence velocities, convective velocities, and vibrational velocity amplitudes (Section 5). Provisionally, it is assumed that _macro = 2 km/sec and _micro = 1 km/sec, isotropic and independent of depth.     

A numerical model of a solar flare based on electron beam heating of the chromosphere

There are two parts to this paper. In the first we calculate the hydrodynamic response of the solar atmosphere to the injection of an intense beam of electrons in a numerical simulation of a solar flare. In the second we predict the spectroscopic consequences of the hydrodynamic behaviour calculated in the first part. The hydrodynamics is predicted by solving the equations of conservation of mass, momentum, and energy. The latter is expressed as two temperature equations; one for the electrons and the other for the neutral atoms and positive ions of hydrogen. The equations are solved in one dimension and the geometric form is of a semi-circular loop having its ends in the photosphere. The results show how the loop is filled at supersonic speed with plasma at temperatures characteristic of flares. At the same time a compression wave is predicted to propagate down towards the photosphere. After the heating pulse stops, the plasma that has risen into the loop, starts to decay and return to the condition it was in before the pulse started. In predicting the spectrum that would be emitted by such a plasma calcium was chosen for illustration. The first and main part of this calculation was setting up and solving the time-dependent equations of ionization/recombination. In order to provide a standard for comparison the same ionization and recombination rate coefficients are used to predict the steady-state distribution of populations of ionization stages. This is then compared with the distribution found from the time-dependent solution and shows that there is a negligibly small time lag predicted by the time-dependent result. However the more significant comparisons to make are between the temperatures of the peak abundances of the various ions under the assumptions of steady-state and time-dependent ionization. For the particular circumstances chosen here the temperature differences are predicted to be in the neighbourhood of 10% or less and in view of the overall accuracy of the atomic data are not significant. It would appear therefore that the much simpler assumption of steady-state ionization balance leads to results of acceptable accuracy for the particular case considered.     

The chromosphere above a sunspot umbra

Spectra of several strong lines of sunspots have been obtained with the Echelle spectrograph at the Vacuum Tower Telescope, Sacramento Peak Observatory. With a variety of model atmospheres, Ca ii H, K, and 18498 line profiles were calculated using a non-LTE line formation procedure.In the present study we examined only a specific part of the sunspot umbra which is thought to be coolest over the spot. An optimum model representing such a region is presented and its physical properties are discussed.This work has been supported by the U.S. - Republic of Korea Cooperative Science Program (K-24).     

The galloping chromosphere

Solar Physics - Oscillating velocity fields can be observed on Hα filtergrams as a shifting pattern of intensity fluctuations known as ‘the galloping chromosphere’. The...     

Spectroscopic investigation of the chromosphere

The cloud model employed in the analysis of chromospheric contrast profiles is subject to two criticisms. The source function in the cloud may not be varied independently of the Doppler width in the case of Hα and the radiative coupling between the cloud and the underlying atmosphere cannot be ignored. These criticisms are investigated quantitatively with two simple extreme models. It is found that by taking account of both effects the cloud model may be reinstated. Observed chromospheric features may be understood in terms of clouds of varying parameters embedded in the uppermost regions of a generally undisturbed homogeneous atmosphere. The variable cloud parameters are the optical thickness, the Doppler width, the bulk velocity and the angular size viewed from the line forming regions of the underlying atmosphere. Without multidimensional models the distribution of these parameters in chromospheric features observed at supergranulation boundaries for instance cannot be determined. General considerations however allow the interpretation of plagettes as simply low-lying mottles and allow the chromospheric velocity distribution derived by the original cloud model analysis to be upheld.     

The mystery of the chromosphere

We discuss many aspects of the solar chromosphere from an observational point of view, and show that most existing models are in direct contradiction to radio and eclipse measurements. We plead for attention to the actual observed radio temperatures and density gradients, as well as images of the chromosphere. We find that the chromosphere is not in hydrostatic equilibrium and suggest that the support is due to the tangled intranetwork fields.Dedicated to Cornelis de Jager     

Oscillations of the upper chromosphere

Variations of intensity and wavelength in several UV lines have been observed with the SUMER spectroheliometer onboard SOHO, and they have been analysed to obtain oscillation spectra and phase differences between lines of different ions. Lines intensities of neutral or singly ionized atoms (with temperature of formation 30000 K) exhibit an increase of oscillatory power between 2.5 and 7 mHz, which may be considered as the signature of p modes. Lines of highly ionized elements (with a temperature of formation 50000 K) yield power spectra which are continuously decreasing with frequency. Brightness variations of the continuum at different wavelengths between 1000 and 1400 Å present oscillations in the same frequency range. Thus, p modes seem to be efficiently stopped by the transition region. No clear evidence is found for the existence of a chromospheric oscillation mode. Phase comparisons between lines formed at different altitudes (in particular Sii and Siii) indicate that these lines oscillate in phase, within the precision of the measurements.     

Spectral investigation of the chromosphere

Highly resolved H spectra and filtergrams obtained at the Fraunhofer Observatory on Capri were analysed by a method whose principles have been described before. As a result the tentative conclusion of our previous work has been confirmed: The mottles of the chromospheric fine structure are clouds superimposed on the low chromosphere. Furthermore, it is proposed that the latter is identical with the interior of the supergranular cells whose spatial averages lend themselves to an interpretation in terms of a spherically symmetric model. On the other hand, we present evidence that the boundary regions which are formed by the mottles of the fine structure pattern and which constitute the upper chromosphere are not adequately described by spatial averages. Instead, the properties of the individual structural elements should be taken into account by an appropriate theory, if only in a statistical fashion. Some of these properties, viz. source function, optical thickness, Doppler width and velocity, were measured for a large number of elements. On the basis of indirect evidence we suggest that the spicules seen on limb photographs of chromospheric lines are identical with the elements of the supergranule boundary structure.Mitteilung aus dem Fraunhofer Institut Nr. 116.     

Spectral investigation of the chromosphere

The results of the analysis of 16 H spectra taken with high spatial resolution are presented. The properties of the line profile in the boundary regions of supergranular cells (SGB) are described by the statistical distribution functions and correlation coefficients of four parameters which determine the shape of a suitable fitting curve. Although some of the line profile properties of both H and H in the SGB can be interpreted in terms of a model which was recently proposed by Durrant (1975) the agreement between that theory and our observations is not entirely satisfactory.Mitteilungen aus dem Fraunhofer Institut Nr. 137.     

High-resolution photography of the solar chromosphere

High-resolution filtergrams of a sunspot and its surroundings, taken at seven wavelengths in H with the aid of a computer-controlled 1/8 Å filter, have been used to derive the contrast of ten sunspot superpenumbra fibrils as functions of wavelength. The observed contrast profiles are compared with profiles calculated on the basis of three theoretical models, namely, Beckers' (1964) cloud model, Athay's (1970) velocity model, and a pure Doppler shift model. However, none of these models in their present form account for all the observed profiles.Arguments are presented which suggest that, in addition to line-of-sight velocity, the height of a moving chromospheric structure relative to the region over which the H line is formed plays a decisive role in shaping the observed profile. Improvements to existing theoretical treatments are suggested.The nature of the fibril velocity field is discussed briefly.