ALBERT

Notes: Abstract The magnetic shear at a point within an active region field configuration can be defined (Hagyard et al., 1984b) as the difference in angle between the observed photospheric transverse field and that of a reference potential field calculated using the observed line-of-sight field as a boundary condition. Using analytic models for non-potential (but force-free) fields representative of preflaring active regions, we calculate the degree of magnetic shear along the magnetic neutral line that such fields would exhibit, as a function of the location and orientation of the active region on the solar disk. We find that, except for regions close to disk center, the position of the inferred neutral line (zero line-of-sight field) is significantly different from the actual neutral line (zero radial field), and that the calculated reference potential field also varies significantly with the position of the region. Thus the inferred degree of shear can vary significantly with the position and orientation of the region, due to (a) straightforward geometric projection effects, (b) the shift of the inferred neutral line relative to its true position, and (c) variations in the reference potential field. The significance of these results for flare prediction is considered.

Notes: Abstract By using two spacecraft equipped with multi-bandpass X-ray telescopes, it is possible to obtain direct 3-dimensional morphology of coronal structures which is essential for understanding the energetics and dynamics of the solar atmosphere. X-ray observations taken only in orbit about the Earth are inadequate to fully resolve the 3-dimensional nature of the solar corona. These Earth-orbit observations produce 2-dimensional images and an appropriate model must be included to derive the 3-dimensional structures from the line-of-sight information. Stereoscopic observations from space will remove this limitation and are needed if we are to improve our knowledge of the 3-dimensional morphology of the corona. Several important points regarding a stereoscopic mission are investigated and illustrated using model coronal flux tubes and image-rendering techniques. Synthesized images are formed by integrating the emission from volume elements along the line-of-sight path through a 3-dimensional volume in which a set of model flux tubes are located. The flux tubes are defined by (1) a plasma model defining the emissivity for a specific density, temperature, and pressure distribution, and (2) a magnetic field model from which a set of field lines are selected to define the geometry of the flux tubes. The field lines are used to define the flux-tube volume by assuming an initial base radius and conservation of flux. An effective instrumental spectral-response function is folded into the integration. Analysis of pairs of these synthesized images with various angular perspectives are used to investigate the effect of angular separation on mission objectives. The resulting images and analysis provide guidelines for developing a stereoscopic mission. Our study produced four important results, namely: (1) An angular separation of ∼ 30 degrees maximizes the scientific return by direct triangulation analysis because of the tradeoff between increased line-of-sight resolution of position and decreased recognition of individual loop structures arising from the overlapping of multiple loops with increasing angular separation. (2) The analysis benefits from the use of time-differential images to select flux tubes from the collection of numerous overlapping systems by selecting only recently heated or cooled flux tubes. (3) An analysis needs to be developed for algebraic reconstruction techniques applying a priori information, specific to the solar coronal structures, i.e., flux-tube continuity, maximum emission strength, non-negative emission, previous history, and maximum gradients of emission. (4) An analysis strategy combining triangulation, modeling techniques, and algebraic restoration is necessary to derive a complete understanding of the 3-dimensional morphology of the magnetic field. In the same way that helioseismology is classical viewing of the Sun with a tailored set of analysis tools for probing the interior of the Sun, heliostereoscopy is classical viewing of the X-ray emitting corona and requires a tailored set of analysis tools to deduce the true 3-dimensional structure of the corona.

Notes: Abstract A method is presented for constructing the coronal magnetic field from photospheric magnetograms and observed coronal loops. A set of magnetic field lines generated from magnetogram data is parameterized and then deformed by varying the parameterized values. The coronal flux tubes associated with this field are adjusted until the correlation between the field lines and the observed coronal loops is maximized. A mathematical formulation is described which ensures that (i) the normal component of the photospheric field remains unchanged, (ii) the field is given in the entire corona over an active region, (iii) the field remains divergence-free, and (iv) electric currents are introduced into the field. It is demonstrated that a parameterization of a potential field, comprising a radial stretching of the field, can provide a match for a simple bipolar active region, AR 7999, which crossed the central meridian on 1996 November 26. The result is a non-force-free magnetic field with the Lorentz force being of the order of 10−5.5 g cm s−2 resulting from an electric current density of 0.079 μA m−2. Calculations show that the plasma beta becomes larger than unity at a relatively low height of ∼0.25 r⊙ supporting the non-force-free conclusion. The presence of such strong non-radial currents requires large transverse pressure gradients to maintain a magnetostatic atmosphere, required by the relatively persistent nature of the coronal structures observed in AR 7999. This scheme is an important tool in generating a magnetic field solution consistent with the coronal flux tube observations and the observed photospheric magnetic field.

Notes: Abstract The potential magnetic field from a finite planar boundary is extrapolated into the upper hemisphere using information from all three magnetic field components. The method determines, first, the transverse field associated with the observed normal magnetic intensity. Then by subtraction, the method determines the associated transverse magnetic field observed in the interior (i.e., in the field of view) of the magnetogram which is due to the normal flux exterior to the field of view of the magnetogram. Inverting this information gives an approximation to the exterior normal flux. The combination of the observed normal flux of the interior and the approximation of the exterior normal flux is employed to calculate the potential field. The formulation of the problem results in an ill-posed integral inversion problem in which a regularized solution is obtained using the singular value decomposition (SVD) technique in conjunction with an appropriate Tikhonov-Phillips filter. The technique can be applied to correcting potential field calculations which are influenced by out-of-view fluxes, e.g., for a high spatial resolution vector magnetogram with a small field of view in which there is no supporting exterior data. The problem studied is also important in providing a regularized solution of the Cauchy potential problem. The method provides a much larger range of convergence than the method of Gary and Musielak (1992), and, in fact, is stable in the total upper hemisphere.

Notes: Abstract An X-ray or EUV image of the corona or chromosphere is a 2D representation of an extended 3D complex for which a general inversion process is impossible. A specific model must be incorporated in order to understand the full 3D structure. We approach this problem by modeling a set of optically-thin 3D plasma flux tubes which we render these as synthetic images. The resulting images allow the interpretation of the X-ray/EUV observations to obtain information on (1) the 3D structure of X-ray images, i.e., the geometric structure of the flux tubes, and on (2) the internal structure using specific plasma characteristics, i.e., the physical structure of the flux tubes. The data-analysis technique uses magnetograms to characterize photospheric magnetic fields and extrapolation techniques to form the field lines. Using a new set of software tools, we have generated 3D flux tube structures around these field lines and integrated the plasma emission along the line of sight to obtain a rendered image. A set of individual flux-tube images is selected by a non-negative least-squares technique to provide a match with an observed X-ray image. The scheme minimizes the squares of the differences between the synthesized image and the observed image with a non-negative constraint on the coefficients of the brightness of the individual flux-tube loops. The derived images are used to determine the specific photospheric foot points and physical data, i.e., scaling laws for densities and loop lengths. The development has led to computer efficient integration and display software that is compatible for comparison with observations (e.g., Yohkoh SXT data, NIXT, or EIT). This analysis is important in determining directly the magnetic field configuration, which provides the structure of coronal loops, and indirectly the electric currents or waves, which provide the energy for the heating of the plasma. We have used very simple assumptions (i.e., potential magnetic fields and isothermal corona) to provide an initial test of the techniques before complex models are introduced. We have separated the physical and geometric contributions of the emission for a set of flux tubes and concentrated, in this initial study, on the geometric contributions by making approximations to the physical contributions. The initial results are consistent with the scaling laws derived from the Yohkoh SXT data.

Notes: Abstract The high-resolution Hα images observed during the decay phase of a long-duration flare on 23 March 1991 are used to study the three-dimensional magnetic field configuration of the active region NOAA 6555. Whereas all the large flares in NOAA 6555 occurred at the location of high magnetic shear and flux emergence, this long-duration flare was observed in the region of low magnetic shear at the photosphere. The Hα loops activity started soon after the maximum phase of the flare. There were a few long loop at the initial phase of the activity. Some of these were sheared in the chromosphere at an angle of about 45° to the east-west axis. Gradually, an increasing number of shorter loops, oriented along the east-west axis, started appearing. The chromospheric Dopplergrams show blue shifts at the end points of the loops. By using different magnetic field models, we have extrapolated the photospheric magnetograms to chromospheric heights. The magnetic field lines computed by using the potential field model correspond to most of the observed Hα loops. The height of the Hα loops were derived by comparing them with the computed field lines. From the temporal evolution of the Hα loop activity, we derive the negative rate of appearance of Hα features as a function of height. It is found that the field lines oriented along one of the neutral lines were sheared and low lying. The higher field lines were mostly potential. The paper also outlines a possible scenario for describing the post-flare stage of the observed long-duration flare.

Notes: Abstract The observational difficulties of obtaining the magnetic field distribution in the chromosphere and corona of the Sun has led to methods of extending photospheric magnetic measurements into the solar atmosphere by mathematical procedures. A new approach to this problem presented here is that a constant alpha force-free field can be uniquely determined from the tangential components of the measured photospheric flux alone. The vector magnetographs now provide measurements of both the solar photospheric tangential and the longitudinal magnetic field. This paper presents derivations for the computation of the solar magnetic field from these type of measurements. The fields considered are assumed to be a constant alpha force-free fields or equivalent, producing vanishing Lorentz forces. Consequently, magnetic field lines and currents are related by a constant and hence show an identical distribution. The magnetic field above simple solar regions are described from the solution of the field equations.

Notes: Abstract We investigate a potential field calculation for off disk-center vector magnetograms that uses all the three components of the measured field. There is neither any need for interpolation of grid points between the image plane and the heliographic plane nor for an extension or a truncation to a heliographic rectangle. Hence, the method provides the maximum information content from the photospheric field as well as the most consistent potential field independent of the viewing angle. The introduction of polarimetric noise produces a less tolerant extrapolation procedure than using the line-of-sight extrapolation, but the resultant standard deviation is still small enough for the practical utility of this method.