4 Relationship of flare occurrence to current helicity

4.1 Current helicity and flare kernels in AR 6233

Active region 6233 was a flare-productive region which was located near the disk center (N13, W04) on August 30, 1990. Observations of this region, including a study of the morphological relationship between vertical electric currents and chromospheric flare phenomena, can be found in Wang et al. (1996) (also see de La Beaujardière et al. 1993); while the correlation of its magnetic separatrices with flare manifestations has been studied by Mandrini et al. (1995).

  

Figure 1: a) A photospheric image of NOAA Active Region 6233 on 30 August 1990. b, c) H$_{\beta}$ filtergrams of this region at 01:58 UT and 04:34 UT on the same day. The dark patches are sunspots, while the bright patches are flare kernels. North is at the top, and West is to the right

In this section we discuss how the distribution of current helicity in AR 6233 changes in the areas where flares occurred. To illustrate its general configuration, a photospheric image of the active region is shown in Fig. 1a; while Figs. 1b and 1c are H$_{\beta}$ filtergrams of two flares to be discussed, a SN/M1.2 flare at 01:58 UT and a SN/M1.0 flare at 04:34 UT on August 30.

  

Figure 2: Time sequence of the distribution of current helicity density in NOAA Active Region 6233 on 30 August 1990. The solid (dotted) contours correspond to positive (negative) current helicity of 0.07, 0.12, 0.20, and 0.40 G2 m-1. The bold contours represent two flares occurred at 01:58 UT and 04:34 UT respectively

Figure 2 shows a time sequence of the distribution of current helicity from 00:57 UT to 06:28 UT on the day. Note that only significant current helicity densities ($\geq 10$$\sigma_{h_{\rm c}}$) are displayed in Fig. 2. Thus, any little changes shown are thought to be due to a true change of current helicity itself rather than from noise or error. The bold contours in Fig. 2b and Fig. 2d represent the brightenings of the flare F₁ and the flare F₂, respectively. The H$_{\beta}$ filtergrams of these two flares can be seen in Figs. 1b and 1c. For a convenient description, the active region is partitioned into three parts, panels A, B and C (see Fig. 2a).

From Figs. 2a-2e we see that the distribution of current helicity in panel A hardly varies with time. Panel A is a sunspot region where very strong magnetic fields are observed. Correspondingly, the values of current helicity in panel A are the maximum, but no flare kernel was observed in the panel. This indicates that sites of high current helicity density in active regions do not coincide with flare kernels.

For panel B, the distributions of current helicity in all figures except Fig. 2b are almost the same, as shown in panel A. The only difference among them is that the distribution of positive current helicity (solid contours) in panel B disappears in Fig. 2b. We infer that this phenomenon may be related to the flare (F₁), which occurred near panel B at 01:58 UT. Such a relationship between significant changes of current helicity and flare occurrence is also found in panel C. From Figs. 2a-2d, we can see that the distribution of current helicity in panel C has obvious changes. During the course of the changes there are two flares occurring in panel C. One of them, the flare F₂, is shown in Fig. 2d, and it occurred at 04:34 UT. On the other hand, we find that the distribution of current helicity in panel C has almost no changes between Figs. 2d and 2e, while from 05:04 UT to 06:28 UT no flare was observed in panel C. In other words, this panel is quiet in the interval. Therefore, we conclude that rapid and substantial changes of current helicity distribution in an area or in its vicinity seem to be associated with flare eruptions, but in no-flaring regions, such changes are insignificant.

  

Table 1: Characteristics of selected active regions

4.2 Changes of current helicity in productive and poor flare regions

In order to have sufficient evidence for the above conclusion, we further analyze some active regions whose characteristics are enumerated in Table 1. These active regions are divided into two groups. One group is flare-productive, and the other shows little flare activity. Note that, compared to typical active regions, the selected flare-poor regions are relatively complicated.

  

Figure 3: Maps of the evolution of current helicity imbalance $\rho_{\rm h}$ in four flare-productive active regions (NOAA 6233, NOAA 6891, NOAA 7321 and NOAA 7773). Solid triangles indicate the times of magnetograms recorded. Obvious variations of current helicity for a whole active region are shown

Figure 3 shows the time series changes of current helicity imbalance, $\rho_{\rm h}$, in four flare-productive active regions. The quantity $\rho_{\rm h}$is defined by

$$\begin{eqnarray} \rho_{\rm h}=\frac{\sum h_{\rm c} (i,j)}{\sum \vert h_{\rm c} (i,j) \vert}100\% ,\end{eqnarray}$$ (13)

where $h_{\rm c} (i,j)$ is the value of current helicity at a given pixel (i, j), and the denominator represents the sum of the absolute values of all $h_{\rm c} (i,j)$ in the active region. $\rho_{\rm h}$ is actually a measure of imbalance of current helicity sign over a whole active region (Abramenko et al. 1996; Bao & Zhang 1998), and its significant changes undoubtedly reflect that the distribution of current helicity density in an active region does vary with time. Along with the obvious variations of $\rho_{\rm h}$ in Figs. 3a-3d, some flares occurred in succession (see the arrows in Fig. 5).

  

Figure 4: Maps of the evolution of current helicity imbalance $\rho_{\rm h}$ in four flare-poor active regions (NOAA 5612, NOAA 5738, NOAA 7496 and NOAA 7903). Solid triangles indicate the times of magnetograms recorded. In these regions, variations of $\rho_{\rm h}$ are insignificant

Similarly, Fig. 4 shows the time series changes of $\rho_{\rm h}$in poorly flare-productive active regions. By comparing these two figures, we find that the variations of $\rho_{\rm h}$ are much more significant in Fig. 3 than those in Fig. 4. From this, we may infer that for any active regions, even complicated ones, if the temporal variations of current helicity are insignificant, the frequency of flaring activity is very low; on the contrary, even for ordinary active regions, if their $\rho_{\rm h}$ is changeable, correspondance to the frequency is high.

  

Figure 5: Variations of the average current helicity $<h_{\rm c}\gt$ of the photospheric magnetic fields as a function of time in four flare-productive active regions (NOAA 6233, NOAA 6891, NOAA 7321 and NOAA 7773). Arrows indicate start times of flares

Note that the average current helicity $<h_{\rm c}\gt$ for a whole active region changes as obviously as the current helicity imbalance $\rho_{\rm h}$ in flare-productive active regions, as shown in Fig. 5. From this figure, we can clearly see that the magnitude of current helicity does not always come down after a flare. Flaring activity seems to be globally associated with the rate of variations in $<h_{\rm c}\gt$. However, there is not a one to one relation between flare activity and variation of $<h_{\rm c}\gt$. This result does not agree with that of Pevtsov et al. (1995). We argue that the rate of variation of current helicity in active regions is more closely related to solar flares, and it may better characterize the non-potentiality of active regions rather than the values of current helicity.