Stability and equilibrium of emerged magnetic flux

We analyse stability and equilibrium of a unipolar large-scale magnetic field pervading a plane horizontal subphotospheric layer with the possible implications for sunspots in mind. Eddy diffusivity is applied to account for the effects of the small-scale convective turbulence. Diffusivity quenching by magnetic field results in a secondary large-scale instability. A linear stability analysis is performed to define the marginal stability boundary in parametric space and the unstable mode structure. The nonlinear dynamics of the unstable modes are followed numerically. The original state of a uniform vertical magnetic field is transformed via the instability into the nonlinear dynamical equilibrium with a highly intermittant distribution of the magnetic field. Magnetic flux is concentrated in a relatively small area surrounded by an almost field-free region. The role of the fluid motion in the hydromagnetic equilibrium is emphasized. Although the relevance of the instability to the process of sunspot formation is rather questionable, the resulting equilibrium structures are similar to mature spots in their thermal and magnetic properties. Also, the simulated flow structure agrees with helioseismic tomography results.     

Rayleigh-Taylor instability of a two-fluid layer under a general rotation field and a horizontal magnetic field

In this paper the Rayleigh-Taylor instability (RTI) of a two-fluid layer system under the simultaneous action of a general rotation field and a horizontal magnetic field is presented. An approximate and an exact solution of the eigenvalue equation are calculated. These solutions are important not only to understand more deeply the physical problem but also to determine the correct numerical solutions. Numerical calculations are done for an unstable density stratification in the cases of horizontal magnetic field parallel and perpendicular to the horizontal component of the angular velocity. For an adverse density stratification, it is shown that in comparison to previous works, the horizontal magnetic field creates new angular areas (of the angle of propagation of the perturbation) at which the perturbation is stable and propagates as traveling waves. It is also shown that the vertical component of the angular velocity has a destabilizing effect because it works to eliminate the stable angular areas.     

A model of ‘disparitions brusques’ (sudden disappearance of eruptive prominences) as an instability driven by mhd waves

A model of ‘disparitions brusques’ (sudden disappearence of eruptive prominences) is discussed based on the Kippenhahn ans Schlüter configuration. It is shown that Kippenhahn and Schlüter's current sheet is very weakly unstable against magnetic reconnecting modes during the lifetime of quiescent prominences. Disturbances in the form of fast magnetosonic waves originating from nearby active regions or the changes of whole magnetic configuration due to newly emerged magnetic flux may trigger a rapid growing instability associated with magnetic field reconnection. This instability gives rise to disruptions of quiescent prominences and also generates high energy particles.     

Waves in the sunspot penumbra

The stability of a plane-parallel polytropic fluid layer in the presence of a uniform horizontal magnetic field is investigated to explore the possibility of identifying the running penumbral waves and the penumbral filaments with different types of instabilities.     

Hydrodynamic instability of convectively unstable atmospheres in shear flow

Results are presented concerning the interaction between regions of convectively unstable fluid, bounded above and below by stable fluid, with a basic horizontal flow field, sheared in a vertical direction. The analysis is conveniently based on the definition of the mechanical energy flux associated with wave motion in a stratified compressible fluid, and enables bounds to be placed on the real and complex phase velocities of overstable modes, in addition to some general results on the net upward wave energy flux. It is shown that purely exponentially growing modes (with horizontal wavevectors spanwise to the shear) do not exist. A known sufficient condition for the stability of stable atmospheres is reproduced here with an interesting modification, and details of energy-flux discontinuities at certain singular points of the equations are given. The work is relevant to any astrophysical and geophysical situations in which convectively unstable regions and shear flows are likely to be together present, but the special motivation here is that of describing some aspects of the interaction between supergranular flow and granular convection.     

On large-scale solar convection

We examine the effects of rotation about a vertical axis on thermal convection with a simple model in which an inviscid, incompressible fluid of zero thermal conductivity and electrical resistivity is contained in a thin annulus of rectangular cross-section. The initial steady state assumed is one of no motion relative to the rotating frame with constant (unstable) vertical temperature gradient and uniform toroidal magnetic field. Small periodic disturbances are then introduced and the linearized perturbation equations solved. We also determine the second-order mean circulations and magnetic fields that are forced by non-zero Reynolds and thermal stresses and magnetic field transports.The solutions have several properties which are relevant to large-scale solar phenomena if giant long-lived convection cells exist on the sun. In particular, the convective cells are tilted in latitude in the same sense as bipolar magnetic regions, and induce vertical magnetic fields with the same tilt. They transport momentum across latitude circles through Reynolds stresses and induced meridional circulations thus setting up a differential rotation. Cells which grow slowly compared to the rotation rate and have comparable dimensions in latitude and longitude transport momentum toward the equator. The cells also form a poloidal magnetic field from initial toroidal field, in a manner similar to that put forth by Parker.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Rotating self-gravitating fluid spheroid with a magnetic field

The equilibrium of a self-gravitating fluid spheroid is examined in the presence of a rotation and a poloidal magnetic field. It is shown that ‘true equilibrium’ allows only rigid rotation for a spheroid of a small eccentricity.     

Larmor radius effects on the instability of a rotating layer of a self-gravitating plasma

The instability of a stratified layer of a self-gravitating plasma has been studied to include jointly the effects of viscosity, Coriolis forces and the finite Larmor radius (FLR). For a plasma permeated by a uniform horizontal magnetic field, the stability analysis has been carried out for a transverse mode of wave propagation. The solution has been obtained through variational methods for the case when the direction of axis of rotation is along the magnetic field. The analysis for the case when the direction of rotation is transverse to the magnetic field has also been considered and the solutions for this case have been obtained through integral approach. The dispersion relations have been derived in both the cases and solved numerically. It is found that both the viscous and FLR effects have a stabilizing influence on the growth rate of the unstable mode of disturbance. Coriolis forces are found to have stabilizing influence for small wave numbers and destabilizing for large wave numbers.     

The instability of a stratified layer of rotating and conducting self-gravitating fluid

Instability of a horizontal rotating layer of a self-gravitating electrically conducting fluid has been studied to simultaneously, include the effects of Hall currents and magnetic resistivity. The prevailing magnetic field is uniform and acts along the vertical direction along which the fluid has a one-dimensional density gradient. The solution has been obtained through the variational methods. The dispersion relation obtained has been solved numerically and it is found that Hall currents as well as magnetic resistivity have a destabilizing influence. Coriolis forces, however, have a stabilizing influence.     

Azimuthal convective rolls and the subsurface magnetic field

The continual emergence of magnetic flux in solar active regions suggests that a substantial reservoir of flux is present somewhere beneath the photosphere. It has been proposed that this flux could be stored in an azimuthal field of order 3000 G residing in the lower portion of the convection zone. Such a field may be large enough to substantially influence the dynamics of the convection: linear stability analyses indicate that donut-like convective rolls having azimuthal symmetry might then be preferred to banana cells aligned with the rotation axis. Observational detections of such azimuthal rolls have been claimed.The problem of pattern selection by convection in the presence of rotation and a horizontal magnetic field is examined here in a model system consisting of a planar Boussinesq fluid layer. Nonlinear solutions are obtained numerically. It is found that solutions consisting solely of donut cells can exist even at parameter values at which linear theory suggests that banana cells should be preferred instead. However, when the horizontal field decays below a critical value, banana cells may then grow. This leads to the destruction of the horizontal field and a permanent transition to banana cells.     

Electron cyclotron maser emission from solar flares

Energetic electrons, with energies 10–100 keV, accelerated during the impulsive phase of solar flares, sometimes encounter increasing magnetic fields as they stream towards the chromosphere. A consequence of the conservation of their magnetic moment is that the electrons with large initial pitch angle will be reflected at different heights from the atmosphere. Energetic electrons reflected below the transition zone will lose most of their energy to collisions and will never return to the corona. Thus, electrons reflected above the transition zone form a loss-cone velocity distribution which can be unstable to Electron Cyclotron Maser (ECM). The interaction of quasi-perpendicular shocks with the ambient coronal plasma will form a ‘ring’ or ‘hollow beam’ velocity distribution upstream of the shock. ‘Ring’ velocity distributions are also unstable to the ECM instability. A review of the recent results on the theory of ECM will be presented. We will focus our discussion on the questions: (a) What are the characteristics of the linear growth rate of the ECM during solar flares? (b) How does the ECM saturate and what is its efficiency? (c) How does the ECM generated radiation modify the flare environment? Finally we will review the outstanding questions in the theory of ECM and we will relate the theoretical predictions to current observations.     

Effectively massive photons within Abelian Higgs galaxies

We demonstrate that photons emitted by spiral galaxies become effectively massive, if the latter are treated as macroscopic Abelian Higgs topological solitons. The rest mass of a photon is shown to be proportional to the squared amplitude of the Higgs field distribution representing a ‘background’ static cylindrically symmetric magnetic vorto-source (-sink). Because the amplitude increases in a monotonous fashion from zero at the center of a spiral to a fixed non-zero value at its outer boundary, the rest mass (group velocity) of photons emitted at shorter distances from the galaxy' s center is smaller (greater) when compared to that of photons originating at larger distances. A rough estimate shows that for a spiral with a diameter of 60 kpc the maximum attainable mass of photon is of the order of 10⁻⁶⁰ g.     

Hydromagnetic stability of a stratified parallel flow varying in two directions

The stability of a stratified parallel flow varying in two directions of an incompressible conducting fluid permeated by a uniform aligned magnetic field is investigated. Complex wave speed of an unstable mode lies in the upper half of a semi-circle whose diameter decreases with increasing magnetic field. It is also found that a strong enough magnetic field can completely stabilize flows with unstable density stratification.     

Day-side ionospheric conductivities at Mars

We present estimates of the day-side ionospheric conductivities at Mars based on magnetic field measurements by Mars Global Surveyor (MGS) at altitudes down to ∼100 km during aerobraking orbits early in the mission. At Mars, the so-called ionospheric dynamo region, where plasma/neutral collisions permit electric currents perpendicular to the magnetic field, lies between 100 and 250 km altitude. We find that the ionosphere is highly conductive in this region, as expected, with peak Pedersen and Hall conductivities of 0.1-1.5 S/m depending on the solar illumination and induced magnetospheric conditions. Furthermore, we find a consistent double peak pattern in the altitude profile of the day-side Pedersen conductivity, similar to that on Titan found by Rosenqvist et al. (2009). A high altitude peak, located between 180 and 200 km, is equivalent to the terrestrial peak in the lower F-layer. A second and typically much stronger layer of Pedersen conductivity is observed between 120 and 130 km, which is below the Hall conductivity peak at about 130-140 km. In this altitude region, MGS finds a sharp decrease in induced magnetic field strength at the inner magnetospheric boundary, while the day-side electron density is known to remain high as far down as 100 km. We find that such Titan-like behaviour of the Pedersen conductivity is only observed under regions of strongly draped magnetospheric field-lines, and negligible crustal magnetic anomalies below the spacecraft. Above regions of strong crustal magnetic anomalies, the Pedersen conductivity profile becomes more Earth-like with one strong Pedersen peak above the Hall conductivity peak. Here, both conductivities are 1-2 orders of magnitude smaller than the above only weakly magnetised crustal regions, depending on the strength of the crustal anomaly field at ionospheric altitudes. This nature of the Pedersen conductivity together with the structured distribution of crustal anomalies all over the planet should give rise to strong conductivity gradients around such anomalies. Day-side ionospheric conductivities on Mars (in regions away from the crustal magnetic anomalies) and Titan seem to behave in a very similar manner when horizontally draped magnetic field-lines partially magnetise a sunlit ionosphere. Therefore, it appears that a similar double peak structure of strong Pedersen conductivity could be a more general feature of non-magnetised bodies with ionised upper atmospheres, and thus should be expected to occur also at other non-magnetised terrestrial planets like Venus or other planetary bodies within the host planet magnetospheres.     

Magnetic resistivity and Hall currents effects on the stability of a self-gravitating plasma of varying density in variable magnetic field

The effect of Hall currents have been studied on the instability of a stratified layer of a self-gravitating finitely conducting plasma of varying density. It is assumed that the plasma is permeated by a variable horizontal magnetic field stratified vertically. The stability analysis has been carried out for longitudinal mode of wave propagation. The solution has been obtained through integral equation approach. The dispersion relation has been derived and solved numerically. It is found that both the Hall currents and finite conductivity have a destabilizing influence on the growth rate of the unstable mode of disturbance.     

Analysis and results of cooperative magnetographic measurements. I. Correction,comparison and discussion of measurements

On June 24, 1983 cooperative magnetographic measurements were made with the vectormagnetographs of the Sayan Observatory (Irkutsk) and the Potsdam Solar Observatory “Einsteinturm” and with the longitudinal magnetograph of the Ondrejov Observatory. Additionally, the maximum field strengths in the sunspot were measured with the photographic method. Using the photographically measured field strengths as reference values we provide a method to eliminate the influences of stray light in a time series of vectormagnetograms. A comparison of nearly simultaneous magnetograms shows a good correspondence in general. The deviations of the zero points as well as the scales are comparable with the results of other authors. Regarding the magnetic field distribution the magnetograms reflect a substantial nonsymmetric structure in the spot under study. The magnetic field lines tend to concentrate into several flux tube clusters. In one region of the penumbra we find a magnetic field with nearly longitudinal character in close neighbourhood of a strong, nearly horizontal flux tube bundle. This indicates a strong nonradial horizontal field gradient in the penumbra.     

Rayleigh–Taylor instability in an ionized medium

We study the linear theory of the magnetized Rayleigh–Taylor instability in a system consisting of ions and neutrals. Both components are affected by a uniform vertical gravitational field. We consider ions and neutrals as two separate fluid systems that can exchange momentum through collisions. However, ions have a direct interaction with the magnetic field lines but neutrals are not affected by the field directly. The equations of our two-fluid model are linearized and by applying a set of proper boundary conditions, a general dispersion relation is derived for our two superposed fluids separated by a horizontal boundary. We found two unstable modes for a range of wavenumbers. It seems that one of the unstable modes corresponds to the ions and the other one is for the neutrals. Both modes are reduced with increasing particle collision rate and ionization fraction. We show that if the two-fluid nature is considered, the RT instability would not be suppressed and we also show that the growth time of the perturbations increases. As an example, we apply our analysis to the Local Clouds which seem to have arisen because of the RT instability. Assuming that the clouds are partially ionized, we find that the growth rate of these clouds increases in comparison to the fully ionized case.     

Drag-driven instability of a dust layer in a magnetized protoplanetary disc

We study drag-driven instability in a protoplanetary disc consisting of a layer of single-sized dust particles which are coupled to the magnetized gas aerodynamically and the particle-to-gas feedback is included. We find a dispersion relation for axisymmetric linear disturbances and growth rate of the unstable modes are calculated numerically. While the secular gravitational instability in the absence of particle-togas feedback predicts the dust layer is unstable, magnetic fields significantly amplify the instability if the Toomre parameter for the gas component is fixed. We also show that even a weak magnetic field is able to amplify the instability more or less irrespective of the dust-gas coupling.     

Perturbations of a twisted solar coronal loop: The relation between surface waves and instabilities

The spectrum of propagating waves and instabilities on a current-carrying, zero gas pressure, twisted magnetic flux loop is analysed for several models of the magnetic field structure. A surface wave mode of the fast Alfvén wave is found to exist, with damping of the wave when Alfvén resonance absorption occurs. If the loop is surrounded by a uniform, purely axial magnetic field, then the surface wave is always stable. If the loop is surrounded by a nonuniform field which is continuous with the loop's field, then the surface wave may connect to the unstable external kink mode.     

The Rayleigh Taylor instability of superposed partially-ionized plasmas

The Rayleigh-Taylor instability of the plane interface separating two superposed, partiallyionized, viscous plasmas of different densities has been studied to include the effects of finite Larmor radius. The solution of the relevant linearized perturbation equations has been developed by the Normal mode technique, taking the prevalent magnetic field to be uniform and horizontal. The potentially unstable case of a dense fluid superimposed on a lighter one has been considered. It is found that neutral gas friction, viscosity as well as finite Larmor radius all have stabilizing influence.On leave of absence from Department of Mathematics, University of Jodhpur, India.