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.     

CME's,filament eruptions,and sheared low-lying magnetic loops in multipolar magnetic configuration

The finite element method was used to solve a partial differential equation (magnetostatic equation) for multipolar magnetic regions. It is found that the height of magnetic field lines above the magnetic neutral line of a central strong bipolar magnetic field decreases as the field lines' footpoints approach the neutral line and also with increased magnetic shear. Both the electric current density and plasma pressure in the sheared low-lying loops are high. We suggest that the sheared low-lying loops may store the energies of large coronal mass ejections (CMEs) and filament eruptions. In addition, it is found that a lower pressure area exists above the low-lying loops and that it is similar in morphology to a coronal cavity. Above the lower pressure area there is a higher pressure area, which may be the source of CMEs. In this area magnetic shear leads to magnetic reconnection, which may be the cause of high coronal temperature.     

Flare loops heated by thermal conduction

A flare observed with the Hard X-Ray Imaging Spectrometer (HXIS) was studied during its rise to maximum temperature and X-ray emission rate. Two proximate flare loops, of lengths 2.8 × 10⁹ cm and 1.1 × 10¹⁰ cm, rose to temperatures of 21.5 × 10⁶ K and 30 × 10⁶ K, respectively, in 30 s. Assuming equal heat flux F into each loop from a thermal source at the point where they met, we derive a simple relationship between temperature T and loop length , which gives a loop temperture ratio of 0.68, in close agreement with the observed ratio of 0.72. The observations imply that heating in each loop was maintained by a thermal flux of 5 × 10⁹ ergs cm^-2 s^-1. It is suggested that conductive heating adequately describes the rise and maximum phase emissions in the loops and that long flare loops reach higher temperatures than short loops during the impulsive phase because of an equipartition of energy between them at their point of interaction.     

Flare loops heating by the 0.1–1.0 MeV proton beams

The fast heating of coronal loops at the very beginning of solar flares is discussed as a first observable signature of downstreaming 0.1–1 MeV proton beams. We place emphasis on the produced by proton beams large-scale upward electric field, supporting beam-driven instability of the kinetic Alfvén waves (KAW). The considerable part of a beam kinetic energy may be converted into heat via intermediate KAW with heated region initially spreading from the top downward to footpoints of the loop-like coronal structures with velocity of about a few thousands km/s.     

Mass motions due to shock propagations along low-lying loops in the solar atmosphere

The formation of fibrils in low-lying loops is investigated by performing one-dimensional nonlinear hydrodynamic calculations. The loops have the height of 3000–5000 km and have an atmosphere extending from the photosphere to the corona. A shock wave is generated from a pressure pulse in the photosphere and it ejects the chromosphere-corona transition region along the loop, expanding the underlying chromosphere into the corona. This expanding chromospheric material in a loop is regarded as a fibril. The shock propagates in the corona and collides with another transition region where a reflected shock and a penetrating shock are generated. The effect of the reflected shock on the motion of the fibril is weak. The fibril shows a nearly ballistic motion as observations suggest, if it does not extend beyond the summit of the loop. The corona in the loop is compressed nearly adiabatically by the fibril, and the enhanced coronal pressure leads the fibril finally to a retracting motion even if the fibril goes beyond the summit of the loop.Contributions from the Kwasan and Hida Observatories, University of Kyoto, No. 261.     

The large-scale build-up of solar magnetic cycles

The purpose of the present article is to analyze the solar cycles from the point of view of the large-scale surface magnetic field (LSMF) polarity distributions. Using synoptic charts of the LSMF for the 1870–1991 time interval at maxima and minima and the spherical harmonic analysis of the polarity distributions, a connection between magnetic cycles has been found. The weight of the large-scale sectoral mode (m = 1) in the common LSMF polarity distribution at minima of the sunspot cycle is the source of sunspot activity at maxima after 16–18 years. The connections found suggest that surface LSMFs have a dual nature - the main source below the convective zone and a secondary source (sunspot production). The sunspot production has no visible influence on the LSMF cycles.     

Electric fields in coronal magnetic loops

We analyze spectra taken with the 40 cm coronograph at Sacramento Peak Observatory, for evidence of Stark effect on Balmer lines formed in coronal magnetic structures. Several spectra taken near the apex of a bright post-flare loop prominence show significant broadening from H₁₀ to the limit of Balmer line visibility in these spectra, at about H₂₀ The most likely interpretation of the increasing width is Stark broadening, although unresolved blends of Balmer emissions with metallic lines could also contribute to the trend. Less significant broadening is seen in 3 other post-flare loops, and the data from 5 other active coronal condensations observed in this study show no broadening tendency at all, over this range of Balmer number. The trend clearly observed in one post-flare loop requires an ion density of n _i ? 2 × 10¹² cm^?3, if it is to be explained entirely as Stark effect caused by pressure broadening. But mean electron densities measured directly from the Thomson scattering at λ3875 in the same SPO spectra, yield n _e ? 3?7 × 10¹⁰ cm^?3 for the same condensations observed within that loop. Comparison of this evidence from electron scattering, with densities derived from emission measures and line-intensity ratios, argues against a volume filling factor small enough to reconcile the values of n _i and n _e derived in this study. This discrepancy leads us to suggest that the Stark effect observed in these loops, and possibly also in flares, could be caused by macroscopic electric fields, rather than by pressure broadening. The electric field required to explain the Stark broadening in the brightest post-flare loop observed here is approximately 170 V cm^?1. We suggest an origin for such an electric field and discuss its implications for coronal plasma dynamics.     

On build-up of magnetic energy in the solar atmosphere

The dynamic response of the solar atmosphere is examined with the use of self-consistent numerical solutions of the complete set of nonlinear, two-dimensional, hydromagnetic equations. Of particular interest are the magnetic energy build-up and the velocity field established by emerging flux at the base of an existing magnetic loop structure in a stationary atmosphere. For a plasma with a relatively low beta ( = 0.03) the magnetic energy build-up is approximately twice that of the kinetic energy, while the build-up in magnetic energy first exceeds but is eventually overtaken by the kinetic energy for a plasma with an intermediate beta ( = 3). The increased magnetic flux causes the plasma to flow upward near the loop center and downward near the loop edges for the low beta plasma. The plasma eventually flows downward throughout the lower portion of the loop carrying the magnetic field with it for the intermediate beta plasma. It is hypothesized that this latter case, and possibly the other case as well, may provide a reasonable simulation of the disappearance of prominences by flowing down into the chromosphere (a form of disparition brusque).The National Center for Atmospheric Research is sponsored by the National Science Foundation.Now at the School of Science and Engineering, The University of Alabama in Huntsville, Huntsville, Alabama 35807.     

Flare positions relative to photospheric magnetic fields

Of 21 flares of importance 1 or greater, observed on 15 days, all were found to lie adjacent to a neutral line in the longitudinal component of photospheric magnetic fields. In most of these cases, the flare consisted of two or more segments separated by the neutral line and located in areas of strong field and high-longitudinal field gradient. In some cases, the flare segments extended into areas of weak-magnetic field and low-field gradient, but maintained an orientation adjacent to a neutral line.Optical and magnetic field records of higher resolution were obtained on 6 July 1965. These observations reveal an excellent correlation between the size, shape, and intensity of the H fine structures and the longitudinal component of the photospheric magnetic fields, except in the vicinity of the neutral line. Sections of the neutral line are marked by long fibrils lying perpendicular to the neutral line or by small filaments lying along the neutral line.The development of a flare of importance 1 in this region appeared to be more precisely related to the neutral line than was found for the flares and magnetic fields observed with lower resolution. The two major segments of this flare lengthened in directions approximately parallel to the neutral line, while simultaneously drifting perpendicularly away from the neutral line. The initial rate of drift systematically varied from 1 to 12 km/sec at a series of positions approximately parallel to the neutral line and corresponding to increasing distance from strong fields. The rate of drift was also observed to decelerate throughout the life of the flare.     

Energy equilibrium in coronal magnetic loops -reinvestigated

Temperature distribution in cylindrically symmetric coronal magnetic loops has been reinvestigated under various conditions: (a) loop with the pressure varying along the radial distance, and (b) loop with constant pressure, for cooler apex loops and hotter apex loops. This work is reinvestigation of our previous work published inAstrophysics and Space Science (Chandra and Prasad, 1993b).     

Thermal equilibria of coronal magnetic loops

Equations of thermal equilibrium along coronal loops with footpoint temperatures of 2 × 10⁴ K are solved. Three fundamentally different categories of solution are found, namely hot loops with summit temperatures above about 4 × 10⁵ K, cool loops which are cooler than 8 × 10⁴ K along their whole length and hot-cool loops which have summit temperatures around 2 × 10⁴ K but much hotter parts at intermediate points between the summit and the footpoints. Hot loops correspond to the hot corona of the Sun. The cool loops are of relevance for fibrils, for the cool cores observed by Foukal and also for active-region prominences where the magnetic field is directed mainly along the prominence. Quiescent prominences consist of many cool threads inclined to the prominence axis, and each thread may be modelled as a hot-cool loop. In addition, it is possible for warm loops at intermediate summit temperatures (8 × 10⁴K to 4 × 10⁵ K) to exist, but the observed differential emission measure suggests that most of the plasma in the solar atmosphere is in either the hot phase or the cool phase. Thermal catastrophe may occur when the length or pressure of a loop is so small that the hot solution ceases to exist and there are only cool loop solutions. Many loops can be superimposed to form a coronal arcade which contains loops of several different types.     

The structure of coronal magnetic loops

We present here a model, based on observations, for the magnetic-field equilibrium of a cool coronal loop. The pressure structure, taken from the Harvard/Skylab EUV data, is used to modify the usual force-free-field form in quasi-cylindrical symmetry. The resulting field, which has the same direction but different strength, is calculated and its variation displayed. Finally, localized interchange stability is evaluated and discussed, as the first step in a subsequent complete magnetohydrodynamic-stability analysis.     

The structure of coronal magnetic loops

We present the second part of a complete theory for the plasma and field structure of a cool coronal arch, corresponding to those observed in the EUV from Skylab. The global magneto-hydrodynamic (MHD) stability of a previously described equilibrium-loop model is evaluated, and compared with that of an unmodified ambient force-free field. The influence of the photospheric boundary condition is also evaluated, producing a specification of stability limits which depend on the relative field and plasma pressures and scale widths. The resulting restrictions on the allowable field configuration of a coronal loop are then compared with observed values. The implications of this general method for deducing small-scale coronal magnetic-field structure from the measured plasma profile of an emissive feature are also described.     

Flares and separatrices between magnetic loops

Time sequences of vector magnetograms of Hauirou and Big Bear Solar Observatories have provided us the opportunity to identify the individual magnetic loops and athe separatrices between them.

Based on the continuous observatin of vector magnetic field of NOAA 7469 from 4 to 12 April 1993, for the first time, the authors have identified the magnetic loop systems and relevant separatrices for such an active region. The observational signature ofthe cross-section of separatrices on the photosphere is as follows:

1. (1) High degree of magnetic shear at or close to the separatrices;

2. (2) Steep gradient of line-of-sight magnetic field ( 0.1 G/km) crossing the neutral line.

3. (3) Flux cancellation from both sides of the separatrices. At this point the transverse field partly changes its alignment.

During the observed period, flare activity took place repeatedly in the vicinity of the separatrices.     

A new expression for cylindrically-symmetric magnetic fields in coronal magnetic loops

We present a set of cylindrically-symmetric force-free magnetic fields with non-constant scalar function scalar. We found that the kink instability of the fields can be suppressed by reducing the length of the flux tube. By using the pressure profile in coronal magnetic loops obtained on the basis of the observational data, and by neglecting the effect of gravity, these force-free fields ars modified to non-force-free ones. For the plasma of finite conductivity the time and space dependent magnetic fields are obtained, and the ohmic dissipation per unit volume per second is calculated. For the magnetic fields, presented in the investigation, it is also found that, due to the large electrical conductivity of the plasma, the ohmic dissipation is negligable in comparison to the conduction and the radiation loss. Hence, for the energy equilibrium in a coronal loop, the contribution of ohmic dissipation is insignificant.     

Stability of siphon flow in coronal magnetic loops

Plasma siphon flow with velocities up to 100 km/s have been observed in coronal magnetic loops. We discuss the stability of this siphon flow using slab and cylinder models. We calculate numerically the dispersion relation and obtain the rate of growth of instability and the frequency of perturbing waves. Our main conclusions are that magnetic field is a stabilizing factor and that flow velocity is a de-stabilizing factor. We discuss the question whether stationary, high-velocity siphon flow can exist in coronal magnetic loops.     

Evolution of energetic protons in twisted magnetic loops

We study the evolution of an ensemble of energetic (1 GeV) protons in a twisted force-free magnetic loop. The protons are followed with a bounce-average method and they are subjected to collisions with ambient gas and pitch-angle scattering by plasrma turbulence in the loop. The proton loss is initially by drift and later by scattering into the loss cone. Gamma rays are produced by pion decays resulting from nuclear reactions of these lost protons. It is found that in order to have long-lasting protons, one of the following scenarios should hold: (1) For small loops (of length 2 × 10⁹ cm), the twist angle should be about 2 and the turbulence level below 10^–8 erg cm^–3. (2) For large loops ( 10¹⁰ cm), the turbulence level should be below 10^–6 erg cm^–3. These set the conditions for testing the trapping picture as a viable explanation for the observed eight-hour gamma-ray emission.     

A study of magnetic energy build-up based on vector magnetograms

Solar Physics - Vector magnetograms taken at the Okayama Astrophysical Observatory are studied. A sequence of procedures applied to the data for analysis are explained, and their validity is...     

A study of magnetic energy build-up based on vector magnetograms

Vector magnetograms taken at the Okayama Astrophysical Observatory are studied. A sequence of procedures applied to the data for analysis are explained, and their validity is studied by examining the global magnetic force balance.