An example for solar flares caused by magnetic field non-equilibrium

Using a photospheric magnetogram of the solar activity complex HR 16862, 16863, 16864 at the end of May 1980 as boundary data a sequence of three-dimensional force-free magnetic fields with spatially constant ( defined by the equation × B = B) is calculated, including numerical field-line tracing. The field is assumed not to be frozen-in and ¦¦, which is a measure of the magnetic free energy, is assumed to increase with time due to some dynamo mechanism. Variation of , starting from = 0, produces a catastrophe-like change of the topology of a field-line system corresponding to an arch filament system connecting the leading spot of HR 16863 with the trailing spot of HR 16862. This topological change is interpreted as causing a series of large homologous flares with synchronous flaring in the two spots. The catastrophe-like behaviour of the field topology is attributed to the nonlinear field-line equations.     

Force-free equilibrium at magnetic neutral points

It is shown that, at neutral points of force-free magnetic fields, the electric current density must vanish. This property is independent of whether the neutral points are isolated or (e.g.) fill lines or surfaces. One implication is the fact that in a cold pressureless plasma the formation of neutral current sheets cannot be adiabatically slow. The field-line topology in the neighbourhood of neutral points is discussed. At neutral points of force-free magnetic fields in general three constant- surfaces, defined by the equation ×B=B, with the same value of intersect orthogonally. If, during a time-development, the magnetic field gradient matrix B _i/x _j becomes singular at a neutral point, the field topology can change qualitatively — in general connected with the merger of two or more neutral points into one and/or the splitting up of one neutral point into several others. This can be interpreted as implying the transition from a quasi-static evolution to a dynamical state in which magnetic energy is released.     

Determination of constant α force-free solar magnetic fields from magnetograph data

At first it is shown that a magnetic field being force-free, i.e. satisfying × B = B, with = constant ( 0) in the whole exterior of the Sun cannot have a finite energy content and cannot be determined uniquely from only one magnetic field component given at the photosphere. Then the boundary value problem for a semi-infinite column of arbitrary cross section is solved by a Green's function method.     

The spectra of extended radio sources with a nonuniform magnetic field and hard injection of particles

On the basis of an analytical solution of the diffusion-type kinetic equation for electrons, electron distributions and radiation spectra have been found which result from a hard injection of particles in sources of the core halo type, characterized by spatially nonuniform magnetic fields and diffusion parameters. Such radio sources are shown to possess nonlinear radiation spectra containing universal (=0.5) and diffusion-controlled power-law sections shaped by synchrotron losses, spatial diffusion and radiation conditions of the electrons. The diffusion-controlled sections can be described by spectral indices 0.5<1, if the magnetic field decreases towards the source edge, and by <0.5 where the magnetic field increases.     

Vector magnetic field evolution,energy storage,and associated photospheric velocity shear within a flare-productive active region

The evolution of vector photospheric magnetic fields has been studied in concert with photospheric spot motions for a flare-productive active region. Over a three-day period (5–7 April, 1980), sheared photospheric velocity fields inferred from spot motions are compared both with changes in the orientation of transverse magnetic fields and with the flare history of the region. Rapid spot motions and high inferred velocity shear coincide with increased field alignment along the B _L= 0 line and with increased flare activity; a later decrease in velocity shear precedes a more relaxed magnetic configuration and decrease in flare activity. Crude energy estimates show that magnetic reconfiguration produced by the relative velocities of the spots could cause storage of 10³² erg day^–1, while the flares occurring during this time expended 10³¹ erg day^–1.Maps of vertical current density suggest that parallel (as contrasted with antiparallel) currents flow along the stressed magnetic loops. For the active region, a constant-, force-free magnetic field (J = B) at the photosphere is ruled out by the observations.Presently located at NASA/MSFC, Huntsville, Ala. 35812, U.S.A.     

Linear force-free fields in the lower corona

We have computed the surface Green's function for linear force-free magnetic fields, where × B = B and is a constant, for application to low coronal levels of the solar atmosphere. Boundary conditions are imposed on the normal component of B on two parallel planes which delineate the force-free volume. This procedure ensures that the magnetic field energy remains bounded, and that the field lines have a smooth behavior. A simple bipolar source distribution is treated and representative field line tracings are shown.     

Effects of Hall current on hydromagnetic free-convective flow through a porous medium

An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c _p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H ₀ applied magnetic field - H magnetic field intensity - (j _x , j _y , j _z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n _e electron number density - P Prandtl number - q velocity vector - (T, T _w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U ₀ uniform velocity - v ₀ suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - _e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - _e charge density - electrical conductivity - _e electron collision time     

Coronal magnetic field equilibrium with discrete flux sources

A model of the equilibrium structure of the coronal magnetic field is developed, taking account of the fact that field lines are rooted in the photosphere, where field is concentrated into isolated flux tubes. The field is force-free, described by ×B = B, with constant; this field has special physical significance, being the state of mininum energy after small-scale reconnections, and is also mathematically convenient in that the principle of superposition can be used to construct complex geometries. First a model of a single loop is presented, with a flux source and sink pair at the photosphere; both point flux tubes and finite radius flux tubes are considered. Then more complex topologies with multiple sources and sinks are investigated. It is shown that significant topology changes arise for different values of, indicating the possibility that there can be energy changes through magnetic reconnection if the field evolves ideally and then relaxes to a linear state.     

Evolution of helically twisted prominence structures of March 11, 1979

Helical structures are generally associated with many eruptive solar prominences. Thus, study of their evolution in the solar atmosphere assumes importance. We present a study of a flare-associated erupting prominence of March 11, 1979, with conspicuous helically twisted structure, observed in H line center. We have attempted to understand the role played by twisted force-free magnetic fields in this event. In the analysis, we have assumed that the helical structures visible in H outline the field lines in which prominence tubes are embedded. Untwisting of observed prominence tubes and later, formation of open prominence structures provide evidence of restructuring of the magnetic field configuration over the active region during the course of prominence eruption. Temporal evolution of the force-free parameter is obtained for two main prominence tubes observed to be intertwined in a rope-like structure. Axial electric currents associated with the prominence tubes are estimated to be of the order of 10¹¹ A which decreased with time. Correspondingly, it is estimated that the rate of energy release was 10²⁸ erg s^–1 during the prominence eruption.     

Flare build-up in preflare magnetic loops and nonlinear force-free magnetic fields

In this paper, we extend B. C. Low's study on nonlinear force-free magnetic fields. Based on Low's mathematical method, a revised boundary-value problem of the two-dimensional nonlinear force-free magnetic field is solved analytically. The solution shows that higher magnetic loops evolve towards preflare loops when the gradient of longitudinal magnetic field at the photospheric level and the angle (shear) included between the magnetic field line and magnetic neutral line increase with time. The density, temperature and the current density are higher in the preflare loops than in the high-lying magnetic loops. We believe it is the loops that provide conditions for the eruption of the flare.The original has been published in the Acta Astronomica Sinica 21 (1980), 152, in Chinese. The present paper completes the discussion and revises some of the preliminary results.     

Material ejecta in a disturbed solar filament

H observations, using the Multichannel Subtractive Double Pass (MSDP) spectrograph operating on the Meudon Solar Tower, have been made of an active region filament which undergoes a disparition brusque. The period of observation was from 10 45 to 13 30 UT on 22 June, 1981. Velocity and intensity fluctuations in H were measured. The proper motions of ejecta were followed allowing their trajectories and vector velocities to be determined. To model the dynamics of ejecta several models using thermal or magnetic driving forces are compared. The most promising model explains the motion as the consequence of magnetic stresses acting on an isolated magnetized plasmoïd in a diverging flux tube.     

Calculation of force-free magnetic field with non-constant α

A numerical method is developed for solving the force-free magnetic field equation, × B = B, with spatially-varying . The boundary conditions required are the distribution of B _n (viz. normal component of the field on the photosphere) as well as the value of in the region of positive (or negative) B _n . Examples of calculations are presented for a simple model of a solar bipolar magnetic region. It is found that the field configuration and the energy stored in the field depend crucially on the distribution of . The present method can be applied to a more complex configuration observed on the Sun by making use of actual magnetic field measurements.On leave of absence from Department of Astronomy, University of Tokyo.     

MODELING OF SOLAR AND INTERPLANETARY MAGNETIC FIELDS

A brief historical review of solar and interplanetary magnetic field modeling and analysis is presented. The modeling was initiated with the routine observation of longitudinal magnetograms and the application of current free potential magnetic fields for its interpretation. Almost simultaneously, the development of detailed H observation motivated the constant-, force-free magnetic field analysis. Subsequent development of transverse magnetograms leads not only to further refinements of the analysis and modeling but also to many physically meaningful interpretations of the observations. In this review, historical development is traced with the emphasis placed on the yet unanswered questions.     

The relations between chromospheric features and photospheric magnetic fields

High resolution photographic magnetograms are compared with H filtergrams (both on- and off - band) for a wide variety of solar features. It is verified that H filaments overlie neutral lines or bands and that H plages always occur at magnetic field clumps. However, the brightness of H plages bear no relation to magnetic field strength or polarity, and the direction of the magnetic field with respect to threads and filaments remains obscure. Counter-examples can be found for virtually every rule that has been formulated so far.Basic questions about the usefulness and final research goal of filtergrams and magnetograms are raised. It is shown that neither filtergram or magnetogram alone is capable of furnishing a unique solution. It is suggested that the proper direction for research is to use magnetograms, together with (as yet unspecified) additional sources of data, to understand H structures.     

An analysis of photospheric vector magnetograms, Hα images and soft X-ray images in a superactive region NOAA 7321

Based on the photospheric vector magnetograms taken at Huairou Solar Observing Station (HSOS), H images taken at Hiraiso Solar Terrestrial Research Center of Communication Research Laboratory, soft X-ray images taken by Yohkoh and an extrapolation method, the magnetic field structures and some active phenomena of the active region AR 7321 around 04:12 UT on 27 October 1992 are analyzed in this paper. A divergence of the transverse magnetic field, located at a newly formed spot, was found. At least four highly sheared magnetic field systems separately spread from this divergence to four other sites around this divergence. Vertical current concentrations are upward in this region and downward in the other four sites, and the corresponding H bright patches and soft X-ray bright loops coincide with these structures, confirming the existence of these four systems. The extrapolated magnetic force lines reconstructed by the Boundary Element Method (BEM), force-free field assumption, and boundary condition of observed photospheric vector magnetic field, coincide in space with the H bright patches and soft X-ray bright loops, showing that this extrapolation method is very effective and suggesting that the H bright patches and soft X-ray bright loops in this case represent the magnetic field structures in the upper atmosphere of the Sun.The bright structures in the H images and the soft X-ray images have a close correlation with the non-potential characteristics of the magnetic fields.     

On the reconstruction of the nonlinear force-free coronal magnetic field from boundary data

Using a simple model in which the corona is represented by the half-space domain = {z > 0} and the photosphere by the boundary plane = {z = 0}, we discuss some important aspects of the general problem of the reconstruction of the magnetic field B in a small isolated coronal region from the values of the vector B¦ measured by a magnetograph over its whole basis. Assuming B to be force-free in : (i) we derive a series of relations which must be necessarily satisfied by the boundary field B¦ , and then by the magnetograph data if the force-free assumption is actually correct; (ii) we show how to extract directly from the measured B¦ some useful informations about the energy of B in and the topological structure of its field lines; (iii) we present a critical discussion of the two methods which have been proposed so far for computing effectively B in from B¦ .     

Study of alpha component dynamics in the solar wind using the Prognoz satellite

The analysis of solar wind He⁺⁺ and H⁺ ion distribution functions, collected over five months by the satellite Prognoz 1, shows that these are in general maxwellian but that often tails appear at higher speeds. The existing relation V-T, the observation of ratios of T/Tp 3.83 and V/Vp 1.035 give evidence of preferential He⁺⁺ ion heating and acceleration. The criteria for heating by dissipation of hydromagnetic waves proposed by Barnes and Hung (1973) are tested experimentally. Finally, multifluid models are likely to predict certain observations such as dependence of the velocity ratio V/Vp on the solar wind flux.     

Observations of chromospheric lines from OSO-8

The line profiles of L, Ca ii K and Mg iik were measured with the spectrometer of the Laboratoire de Physique Stellaire et Planétaire on board of OSO-8. The results of these measurements are presented.Mitteilungen aus dem Kiepenheuer-Institut Nr. 181.     

Метагалактические протоны сверхвысоких энергий

, . 2.7°- . . . E3×10¹⁹ (1.6) .     

On the value of 'αAR' from vector magnetograph data

This investigation centers upon the quantifying magnetic twist by the parameter , commonly defined as (×B_h)_z/B_z=₀J_z/B_z, and its derivation from vector magnetograph data. This parameter can be evaluated at each spatial point where the vector B is measured, but one may also calculate a single value of to describe the active region as a whole, here called '_AR'. We test three methods to calculate such a parameter, examine the influence of data noise on the results, and discuss the limitations associated with assigning such a quantity. The three methods discussed are (1) to parameterize the distribution of (x,y) using moments of its distribution, (2) to determine the slope of the function J_z(x,y)=_ARB_z(x,y) using a least-squares fit and (3) to determine the value of for which the horizontal field from a constant- force-free solution most closely matches the observed horizontal magnetic field. The results are qualitatively encouraging: between methods, the resulting value of the _ARparameter is often consistent to within the uncertainties, even though the resulting _ARcan differ in magnitude, and in some cases in sign as well. The worst discrepancies occur when a minimal noise threshold is adopted for the data. When the calculations are restricted to detections of 3 or better, there is, in fact, fair quantitative agreement between the three methods. Still, direct comparison of different active regions using disparate methods must be carried out with caution. The discrepancies, agreements, and overall robustness of the different methods are discussed. The effects of instrumental limitations (spatial resolution and a restricted field-of-view) on an active-region _AR, and quantifying the validity of _AR, are addressed in Paper II (Leka, 1999).