5 Current helicity evolution

NOAA 9077 is at the central meridian on 14 July. HSOS observed this active region and obtained vector magnetic field data during good seeing conditions. We choose 18 magnetograms (13-15 July, listed in Table 1) for the study of the $\delta$-configuration P6-F4. Because the active region is very close to the disk center, we assume that the longitudinal field B_|| can be approximated by B_z. In the data reduction, we avoid the negative effects listed in Sect. 2 for the reasons stated there. The vertical current density is calculated by

$$% J_z=\frac{1}{\mu_0}\left(\frac{\partial B_y}{\partial x}- \frac{\partial{B_x}}{\partial{y}}\right),$$ (1)

with the differencing method for the filtered transverse field measurement.

We define the density of vertical current helicity as

$$% h_{\rm c}=B_z\cdot J_z.$$ (2)

It is a measurable component of the photospheric field and has been widely used in helicity research (e.g., Bao & Zhang 1998).

Figure 6 shows the evolution of the current density for P6-F4 over three days. The positive polarity of the magnetic field is given in white, while the negative is given in black. Solid contours represent upward components of current density, while dashed represent downward components. The levels of current density are $\pm$2, 8, and 20 Am^-2. Positions of P6 and F4 are also precisely marked in this figure.

Figure 4: Proper motions of F4 and P6 on 14 July 2000. Arrowheads and black points represent positions with time, the coordinates are in the Carrington system. "0'' - 23:59, "1'' - 01:39, "2'' - 03:15, "3'' - 04:51, "4'' - 06:24, "5'' - 08:00, "6'' - 09:36, "7'' - 11:12, and "8'' - 12:48.

Figure 5: Velocity of spots F4 and P6 as a function of time. F4 is denoted by squares and P6 by diamonds. The left panel shows the velocity of F4 on 14 July and the right panel corresponds to P6. The dashed lines indicate the time of the major flare at its maximum (10:24 UT). The errors are smaller than the sizes of the squares and the diamonds.

We find an obvious current reversing process for F4. On 13 July, F4 is dominated by a large, positive current patch (its helicity is negative and the same as the predominant, left-handed twist of the northern hemisphere). On 14 July, the current density of F4 is decreased and the patch separates from its environment. Finally, its current density becomes negative on 15 July. During the three days, the current of P6 retains the same negative polarity. From Eq. (2) we can see that if the sign of the average vertical current is reversed then the sign of the chirality (current helicity) will also be reversed. We also demonstrate the process of helicity evolution in Table 1 and Fig. 7. In Fig. 7, F4 and P6 are shown in the top two panels, the total active region and the $\delta$-configuration of F4-P6 are shown in the bottom two panels. The helicity density of NOAA 9077 varies over a small range from -2 to $-7 \times10^{-3}$ G² m^-1, while the other three objects (F4, P6, and F4-P6) fluctuate over wider ranges from near zero to more than $-100\times10^{-3}$ G² m^-1. At 05:53 UT on 14 July, F4 reverses the helicity sign once (see Table 1), but returns to its original state in the next magnetogram. This may be due to the onset of strong disturbance. Between 08:12 UT and 08:43 UT, about two hours before the major flare, F4 alters irreversibly its chirality.

Figure 6: Evolution of vertical current density over three days. The positive polarity magnetic field is in white, while the negative is in black. The solid contours represent upward components of current density, while the dashed represent downward components, their levels are $\pm$2, 8, and 20 Am-2. P6 and F4 are marked on their locations precisely in the figure. The FOV is $0.9'\times 0.9'$ and the differences in the gray level of the magnetic field are due to seeing. Note the current evolution in the neighborhood of F4.

Figure 7: Measurement of $h_{\rm c}$ based on 18 magnetograms for three successive days for AR 9077. One asterisk represents one magnetogram. Error bars reflect the variation in $h_{\rm c}$ from independent measurements. The top two panels are the results of spots F4 and P6, respectively. The bottom two panels are the total active region and total $\delta$-spot F4-P6, respectively. The vertical dashed lines represent the time of the flare maximum and the horizontal lines represent to zero helicity.