For all 18 magnetograms (see Table 1) we calculated the total flux and the error bars using Eqs. (1) and (2), respectively; and calculated the total positive and negative currents and the error bars using Eqs. (3) and (6), respectively. Along with this we estimated the value of in four ways, i.e. using Eqs. (7), (8), (9) and (10). In the latter two cases we calculated the linear force-free field by the Fourier Transform Method (Alissandrakis 1981). Such algorithms were performed both for the entire active region and for the three main spots separately.
Fig. 1 shows the daily vector magnetograms of the active region. The emergence of the magnetic flux is well pronounced. Three main poles can be revealed: N, S and S1. The corresponding daily maps of density () are presented in Fig. 2. In Figs. 3 and 4 the time variations of the total fluxes and total currents I are shown. The monotonous growth of the total flux both in the entire AR and in the N, S and S1 poles is obvious. The same is valid also for the total currents, except for the total positive currents in S and S1: they are weak and practically constant. The growth rates of the flux and current (estimated from the least-square linear fit in Figs. 3 and 4) are presented in Table 2. One can see that the growth rate of the total positive flux (current) is very close to that of total negative flux (current) for the entire AR. Such a situation can be physically interpreted by the solenoidal nature of and vectors, and this confirms the reliability of our field measurement and current calculations.
The plot of the total current versus the total flux is shown in Fig. 5. It is shown that for the entire AR there are two linear relationships: for the positive branch (with the coefficient ) and for the negative branch (with the coefficient ). Moreover, in both cases, the least-square linear fit does not cross the zero. When , A, and for we have A. In each of the poles studied, there are both positive and negative currents, but the positive (negative) current dominates in the N pole (S, S1 poles). This results in the overall positive (right-handed) twist in the entire AR, which can be estimated from by the least-square linear fit in Fig. 5. The results of this estimation are shown in Columns (2) and (4) in Table 3. Columns (3) and (5) represent the coefficient of the Spearman rank correlation (Press et al. 1994). One can see that the correlations are high enough.
The results of direct calculations of by Eqs. (7), (8), (9) and (10) are given in Fig. 6 and Table 4. The comparison of calculated by different approaches allows us to conclude that the is systematically larger when estimated as (Column (2) in Table 4). Moreover, in the pole N the is negative that disagrees with other forms of estimation in this pole (, and ). This may be caused by the presence of large negative in places of weak field. These places should not weigh a lot in the total twist. So this case (pole N) shows that the method has some intrinsic disadvantage as compared with the method. In addition, shows the better coincidence in values with and as well as the estimate of from (see Tables 3 and 4). This also suggests that the method seems more reasonable than the method to measure the twist of the flux.
So, except , all other estimated are in a good agreement to show that the changes in from day to day were rather small. This result indicates that the twist, or, the magnetic complexity, changes very slowly during the flux emergence.
© European Southern Observatory (ESO) 2000
Online publication: June 5, 2000