M. J. Hagyard

A quantitative study relating observed shear in photospheric magnetic fields to repeated flaring

In this paper we present a quantitative evaluation of the shear in the magnetic field along the neutral line in an active region during an epoch of flare activity. We define shear as the angular difference in the photosphere between the potential magnetic field, which fits the boundary conditions imposed by the observed line-of-sight field, and the observed magnetic field. For the active region studied, this angular difference (shear) is non-uniform along the neutral line with maxima occurring at the locations of repeated flare onsets. We suggest that continued magnetic evolution causes the fields maximum shear to exceed a critical value of shear, resulting in a flare around the site of maximum shear. Evidently, the field at the site of the flare must relax to a state of shear somewhat below the critical value (but still far from potential), with subsequent evolution returning the field to the critical threshold. We draw this inference because several flares occurred at sites of maximum photospheric shear which were persistent in location.

Transformation of vector magnetograms and the problems associated with the effects of perspective and the azimuthal ambiguity

Off-center vector magnetograms which use all three components of the measured field provide the maximum information content from the photospheric field and can provide the most consistent potential field independent of the viewing angle by defining the normal component of the field. The required transformations of the magnetic field vector and the geometric mapping of the observed field in the image plane into the heliographic plane have been described. Here we discuss the total transformation of specific vector magnetograms to detail the problems and procedures that one should be aware of in analyzing observational magnetograms. The effect of the 180-deg ambiguity of the observed transverse field is considered as well as the effect of curvature of the photosphere. Specific results for active regions AR 2684 (23 September, 1980) and AR 4474 (26 April, 1984) from the Marshall Space Flight Center Vector Magnetograph are described which point to the need for the heliographic projection in determining the field structure of an active region.

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 BL= 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-α, force-free magnetic field (J = αB) at the photosphere is ruled out by the observations.

The observed characteristics of flare energy release. I - Magnetic structure at the energy release site

It is shown that flaring activity as seen in X-rays usually encompasses two or more interacting magnetic bipoles within an active region. Soft and hard X-ray spatiotemporal evolution is considered as well as the time dependence of the thermal energy content in different magnetic bipoles participating in the flare, the hardness and impulsivity of the hard X-ray emission, and the relationship between the X-ray behavior and the strength and observable shear of the magnetic field. It is found that the basic structure of a flare usually consists of an initiating closed bipole plus one or more adjacent closed bipoles impacted against it. 119 references.

The MSFC vector magnetograph

The NASA/Marshall Space Flight Centers solar vector magnetograph system is described; this sytem allows measurements of all components of the Suns photospheric magnetic field over a 5 × 5 or 2.0 × 2.0 arc min square field-of-view with an optimum time resolution of ∼ 100 s and an optimum signal-to-noise of ∼ 1600. The basic system components are described, including the optics, detector, digital system and associated electronics. Automatic sequencing and control functions are outlined as well as manual selections of system parameters which afford unique system flexibility. Results of system calibration and performance are presented, including linearity, dynamic range, uniformity, spatial and spectral resolutions, signal-to-noise, electro-optical retardation and polarization calibration. Scientific investigations which utilize the unique characteristics of the instrument are described and typical results are presented.

On the numerical computation of nonlinear force-free magnetic fields

An algorithm has been developed to extrapolate nonlinear force-free magnetic fields from the photosphere, given the proper boundary conditions. This paper presents the results of this work, describing the mathematical formalism that was developed, the numerical techniques employed, and comments on the stability criteria and accuracy developed for these numerical schemes. An analytical solution is used for a benchmark test; the results show that the computational accuracy for the case of a nonlinear force-free magnetic field was on the order of a few percent (less than 5 percent). This newly developed scheme was applied to analyze a solar vector magnetogram, and the results were compared with the results deduced from the classical potential field method. The comparison shows that additional physical features of the vector magnetogram were revealed in the nonlinear force-free case. 41 refs.

Observed nonpotential magnetic fields and the inferred flow of electric currents at a location of repeated flaring

We have analyzed the vector magnetic field of an active region at a location of repeated flaring to determine the nature of the currents flowing in the areas where the flares initiated. The component of electric current density crossing the photosphere along the line-of-sight was derived from the observed transverse component of the magnetic field. The maximum concentrations of these currents occurred exactly at the sites of flare initiation and where the photospheric field was sheared the most. The calculated distribution of current density at the flare sites suggested that currents were flowing out of an area of positive magnetic polarity and across the magnetic inversion line into two areas of negative polarity. This interpretation was reinforced by a calculation of the source field, the magnetic field produced in the photosphere by the electric currents above the photosphere. In the vicinity of the flare sites, the calculated source field exhibited three particular characteristics: (1) maximum magnitudes at the sites of flare initiation, (2) a rotational direction where the vertical current density was concentrated, and (3) a fairly constant angular orientation with the magnetic inversion line. The source field was thus very similar to the field produced by two arcades of currents crossing the inversion line at the locations of greatest magnetic shear with orientations of about 60° to the inversion line. With this orientation, the inferred arcades would be aligned with the observed chromospheric fibrils seen in the Hα data so that the currents were field-aligned above the photosphere. The field thus exhibited a vertical gradient of magnetic shear with the shear decreasing upward from the photosphere. We estimated the currents in the two arcades by matching the source field derived from observations with that produced by a model of parallel loops of currents. We found that the loops of the model would each have a radius of 4500 km, a separation of 1830 km, and carry a current of 0.15 × 1012 A. Values of vertical current densities and source fields appearing in the umbrae of the two large sunspots away from the flare sites were shown to lie at or below the level of uncertainty in the data. The main source of this uncertainty lay in the method by which the 180° ambiguity in the azimuth of the transverse field is resolved in umbral areas. We thus concluded that these quantities in large umbrae should be treated with a healthy skepticism. Finally, we found that the source field at the flare sites was produced almost entirely by the angular difference between the observed and potential field and not by the difference in field intensity.

Relationship between magnetic field evolution and flaring sites in AR 6659 in June 1991

During the international campaign of June 1991, the active region AR 6659 produced six very large, long-duration flares (X10/12) during its passage across the solar disk. We present the characteristics of four of them (June 4, 6, 9, 15). Precise measurements of the spot motions from Debrecen and Tokyo white-light pictures are used to understand the fragmentation of the main sunspot group with time. This fragmentation leads to a continuous restructuring of the magnetic field pattern while rapid changes are evidenced due to fast new flux emergence (magnetograms of MFSC, Huairou). The first process leads to a shearing of the field lines along which there is energy storage; the second one is the trigger which causes the release of energy by creating a complex topology. We conjecture that these two processes with different time scales are relevant to the production of flares.

Evolutionary and flare-associated magnetic shear variations observed in a complex, flare-productive active region

Evolution of nonpotential structures in a complex, flare-productive active region NOAA AR 6555 has been studied during the period March 23–26, 1991, using a quantitative description of the degree of magnetic shear at both local and regional scales. Distinct shear evolution in four subareas of AR 6555 is inferred from daily variation of their shear indices. Subareas which showed significant evolution in their overall magnetic structure are found to be most active. Hα flare ribbons mostly formed bordering, andnot within, areas of large shear and expanded over areas of lower shear.Magnetic shear changes are also detected during several flares, including a major X4.7/4B flare. Out of the 14 events for which temporally contiguous magnetograms were available, a decrease, or dip, in area-averaged shear index around flare onset time followed by an increase was observed in eight cases. There were two events with increase, three events with continuous decrease, and one event with no change in the shear index during the flare.

Measurement and interpretation of magnetic shear in solar active regions

Abstract In this paper we summarize and synthesize the results on the role of magnetic shear in the flare process that have been derived from the series of Flare Buildup Study Workshops in the Solar Maximum Analysis program. With emphasis on observations, we discuss the mechanisms that seem to produce the sheared magnetic configurations observed in flaring active regions. The spatial and temporal correlations of this shear with the onset of solar flares are determined from quantitative analyses of measurements of the vector magnetic field. The question of why some areas of sheared magnetic fields are the sites of flares and others are not is investigated observationally. We conclude by synthesizing these findings with current theoretical models of stressed magnetic fields that lead to the eruption of a flare.