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Astron. Astrophys. 342, 854-862 (1999)

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4. Analyses

4.1. 2D singular points in the observed transverse field

We take the vector magnetogram observed at 01:44UT on October 27 as an example for determining singular points in the observed transverse field. We make use of Eq. (1) to calculate Poincaré index of singular points from the transverse field. The distributions of computed singular points are shown in Fig. 1, in which figures (a) and (b) are obtained from the raw data, while figures (c) and (d) from the data treated with the lowpass filter technique in the cases, [FORMULA]=10 and 5. The singular points with [FORMULA] are marked by the symbol, `[FORMULA]', and those with [FORMULA] are marked by `[FORMULA]'. For the raw data, a large number of candidate points are presented, we thus have to tell apart which are real singular points.

[FIGURE] Fig. 1a-d. Illustration of the procedures to determine 2D singular points, defined by the Poincaré index, in the observed transverse field taken at 01:44UT on October 27, 1991 in Active Region NOAA 7321. The singular points with [FORMULA] are marked by the symbol `[FORMULA]' and those with [FORMULA] are marked by `[FORMULA]'. a , b  The cases for the raw data. In b  the false points due to the measurement noise are excluded. c , d  The cases for the filtered data with [FORMULA]=10 and 5. The 2D field lines are traced from the transverse field directions; specifically, in c those with the grey color approach to their corresponding lanes which demarcate the 2D cells. In each case the solid (dashed) contours show the longitudinal field (isocontours of [FORMULA] 500, 1500, 2500 G), and the thick solid lines indicate magnetic neutral lines. The field of view is [FORMULA][FORMULA].

To start with, we neglect candidates in the weak-field region, where the average strength of the observed transverse field is lower than 2[FORMULA] (see Fig. 1b). Secondly, we apply the lowpass filter technique to exclude the candidates in the rest, dubiously attributed to the small-scale structures or the noise fluctuation. Thirdly, we confirm the final ones by the 2D field-line pattern, which are traced from the directions of the filtered observed transverse field. Fig. 1c shows that all singular points are well correlated with special field-line patterns; those with [FORMULA] correspond to convergence patterns, while those with [FORMULA] saddle patterns.

In this way, we then obtain the distributions of 2D singular points in the observed transverse fields, taken at 01:44UT and 04:12UT on Oct. 27 (Fig. 2). For both cases, there are six nodes (C1, C2, [FORMULA], and C6) and three saddles (P1, P2, and P3), which are linked by the magnetic lanes demarcating different 2D cells. All cells can be divided into two classes, L and H, based on the difference in the 2D magnetic connectivity patterns. For L cells 2D field lines connect two nodes located in opposite polarity regions, while for H cells 2D field lines converge at a node. This classification will be explained in Sect. 4.3.

[FIGURE] Fig. 2a and b. The 2D singular points derived from the observed transverse fields in the photosphere. The magnetogram in a was taken at 01:44UT, and the data were filtered with the cutoff frequency [FORMULA]=10. The magnetogram in b was taken at 04:12UT, and the data were filtered with [FORMULA]=20. `[FORMULA]' indicates the location of the node points and `[FORMULA]' that of the saddle points. The bold curves linking these singular points are called the magnetic lanes, which demarcate 2D magnetic cells of the different field-line connectivities.

4.2. Comparison with the inferred linear force-free fields

In the previous studies (Wang & Wang 1996; Wang 1997), 2D singular points and magnetic lanes are computed from extrapolated transverse fields based on a specific model such as potential or force-free field model. In this section, we compare these 2D singular features in the computed field with those in the observed field.

Using the Fourier Transform Method on a linear force-free field model (Nakagawa & Raadu 1972; Alissandrakis 1981), we compute transverse fields in the photospheric plane for four cases, [FORMULA] =0, 0.03, 0.06, and 0.09 in units of 0.69Mm-1. The boundary condition takes as the longitudinal magnetic field at 01:44UT. The way to determine singular points and other features is the same as in Sect. 4.1. For all cases, the lowpass filtering takes the cutoff frequency, [FORMULA]=10.

Fig. 3 shows that the 2D topology of the computed field, compared with that of the observed field, is distinctly different. For example, in the observed field, the saddle P3 separates the emerging pole C3 from the main pole C2, while in the computed field P3 disappears, which results in the cells L2 and L3 merging into one cell, L23. In 2D magnetic connectivity patterns, the nodes C1, C4 and C6 are linked to the node C3 in the observed field, while those are linked to the node C2 in the computed field for the cases [FORMULA]=0 and 0.03.

[FIGURE] Fig. 3a-d. The 2D singular points derived from the linear force-free field model, in which the observed longitudinal field at 01:44UT was taken as the boundary condition on the photospheric surface. a  [FORMULA]=0; b  [FORMULA]=0.03; c  [FORMULA]=0.06; d  [FORMULA]=0.09. The unit of [FORMULA] is 0.69 Mm-1. All symbols are the same as those in Fig. 2.

We can evaluate the force-free factor, [FORMULA], for the field in 2D cells, from comparisons with 2D magnetic connectivity patterns of the computed fields. The cells H1 and H2 in the main bipole are almost potential ([FORMULA]=0). The cells H3, H5 and L4 are of 0[FORMULA]0.03. Specially, the cells L1, L2, L3 and H4, associated with the drasticly emerging flux, indicate much strong shear ([FORMULA]0.09).

The 2D topology of the observed field bears more characters than those the constant-[FORMULA] field can interpret, which is related to the evolution of magnetic fluxes with different origins. So this offers more chances approaching the real singular structures favorable to the energy release in the flares.

4.3. The 3D modeling field

Since field lines close to a separator or separatrix, which initially close to one another, separate widely in a distance (Démoulin et al. 1996), we can locate intersections of separatrices by tracing these field lines.

Fig. 4 shows the connectivity patterns of 3D field lines in the computed fields in the cases, [FORMULA]=0 and [FORMULA]=0.06. Some special field lines, highlighted in thick solid style, are seen discontinuous at the saddles where they are separated widely. We suppose that the loci of their starting points, portrayed by the dashed lines, represent the intersections of separatrices in the photosphere. For both cases, these intersections are in good agreement with portions of the 2D magnetic lanes in the places close to the saddles. In some places, however, such as region A, they are shown divergent. Fig. 5 shows a side view of these special 3D field lines. The `cavity' structures around the saddles suggest the associated nulls beneath the photosphere.

[FIGURE] Fig. 4a and b. The top view of 3D field-line connectivity patterns extrapolated from the linear force-free field models with different values of [FORMULA]. a  [FORMULA]=0 and b  [FORMULA]=0.06. The special field lines separating widely near the saddles are drawn in the boldface, the starting points of these lines depict the intersections of separatrices with the photosphere (the dashed lines). In the down-left of the panel a , the arrow indicates the view angles in Figs. 5a and 5b.

[FIGURE] Fig. 5a and b. The side view of the special field lines related to saddle points. a  [FORMULA]=0 and b  [FORMULA]=0.06. The view angle, [FORMULA], is [FORMULA] with respect to y-axis (see the arrow in Fig. 4a).

Since the magnetic connectivities involved in the lanes separating L cell from H cell show no discontinuity (Fig. 4), these lanes do not seem related to separatrices. Fig. 6, however, shows that such lanes demarcate two kinds of magnetic loops different in height and shape. The low loops are confined only in a L cell, while the high ones have long span between H cells. Table 2 lists height and the average ratio between height and horizontal extension of low and high loops.

[FIGURE] Fig. 6a and b. The side view of magnetic loops. a  [FORMULA]=0 and b  [FORMULA]=0.06. The view angle, [FORMULA], is [FORMULA].


Table 2. Comparisons between two kinds of magnetic loops in the height ([FORMULA]) and the average ratio between height and horizontal extension ([FORMULA]/[FORMULA]) for the cases, [FORMULA]=0 and 0.06.

Moreover, the alignments of the low loops coincide well with those of transverse field components on the photospheric surface (Fig. 4). This may account for the validity of the way we explore the field topology in the low atmosphere in terms of connectivity patterns of the 2D field lines in the photosphere.

4.4. The heating of flaring loops

A 1N/M1.1 flare occurred at 01:44UT on October 27. Based on a comprehensive study of the magnetic configuration from the coordinated observations, Wang et al. (1998) found that the event originated from the interaction between two strongly sheared loops.

Fig. 7 shows several flaring loops in SXR are spatially related to the 2D singular features, and all the bright kernels in H[FORMULA] are located on the footpoints of these loops. The triggering of this flare was on the top (D) of a small loop, but further energy release took place along the loop, especially at its foot regions of A and B (Wang et al. 1998), which may be involved in the separatrices.

[FIGURE] Fig. 7a and b. The coalignment of SXR images (gray map), taken by Yohkoh SXT from the filter Al.1, with 2D singular points in the observed transverse field. a  The comparison among SXR features, singular points and H[FORMULA] flare kernels at 01:55:26UT (plotted with thick black contours). b  The comparison between SXR features and singular points. The white, dashed lines in a and b indicate magnetic neutral lines.

Fig. 8 shows a series of small events associated with these singular structures, providing the additional evidence. At 01:28:13UT and 02:33:27UT, a glowing streak was just lying along segment P1P3 of the magnetic lanes (Figs. 8a and 8c). At 01:44:33UT, 02:53:15UT and 03:12:13UT, the SXR emissions disclose the intermittent interaction of two loops at region A (Figs. 8b8d and 8e). In Fig. 8f the asterisk (*) marks the position of bright point A in Fig. 8e, which was identified as the interaction site.

[FIGURE] Fig. 8a-f. The SXR images taken at 01:00UT-05:00UT on Oct. 27 by Yohkoh SXT from the filter Al.1. The field of view is [FORMULA]. In order to illustrate clearly the structures at different times, the SXR images are not shown in the same grey scale.

This fact may account for a puzzle in Qiu et al. (1997) who found the mixed thermal and nonthermal features of coronal plasma at region A at the onset of the 1N/M1.1 flare. We conjecture that the nonthermal component came from the depositing of nonthermal electrons produced at region D, while the thermal component due to the local heating by reconnection (Fig. 7a or Fig. 8b).

The last example to show the heating of flaring loops involved in the separatrices is illustrated in Fig. 8c. A set of bright loops, commonly connecting an emitting SXR locus (G), are coincided with the magnetic lane (P2P3). The reconnection may contribute to the heating process and injected hot plasma into the field loops.

Our results agree with those of Parnell, Priest, and Golub (1994) as they show that X-ray bright loops can be considered as being reconnected magnetic loops, and support the viewpoint that magnetic reconnection represents an elementary heating source in various coronal phenomena (Priest, Parnell, & Martin 1994; Mandrini et al. 1997).

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© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999