3.1. Active region NOAA 7321
The active region NOAA 7321 was a new emerging flux region (EFR), passing across the solar disk from October 24 to November 1 in 1992. During this period, it evolved from an explicit main bipole, nearly resembling the potential field, into a complicated configuration with strong shear around the magnetic neutral line when several new satellite spots continuously emerged from between the two main poles (Zhang 1995). On October 27, the active region (then located at S23W18) was fully developed, and a series of flares occurred in the flux-emerging area characterized by strong shear (Wang, Qiu & Zhang 1998). We hence take the observed fields on that day to investigate the 2D topological properties.
The photospheric magnetic field in AR7321 was observed by a vector magnetograph system (Ai & Hu 1986) installed at the Huairou Solar Observing Station (HSOS) of Beijing Astronomical Observatory. To reduce the noise, and to match the practical spatial resolution, the smoothing on the Stokes parameters V, Q and U is made. After the ambiguity is resolved for the transverse field components with a multistep method (Wang et al. 1994), the vector magnetograms are transformed into the heliospheric plane. In addition, we also obtained H filtergrams for a 1N/M1.1 flare on Oct. 27 from HSOS and observations of the SXR emission during 00:48UT-07:58UT from Yohkoh (Tsuneta et al. 1991).
3.2. Data reduction
In order to accurately determine 2D singular points in the observed transverse field, we take a conventional lowpass filter technique to process the raw data, reducing the influence of the measurement noise.
In the Cartesian coordinate system, and represent the observed field components and their Fourier components, respectively. Then the filtered components, , are
where is a filter function. We take as the butterworth form, i.e.
where , and kc is the lowpass cutoff frequency. After the filtering, the spatial resolution of magnetograms is changed as:
where is the relative cutoff frequency, defined as
and are typical sizes of the active region.
The loss of signals in the filtering can be estimated with a parameter, ,
where . and (s=l or t) are the average value and standard deviation of the measurement noise for longitudinal and transverse field components.
Table 1 lists the values of , and in different filtered cases. According to Expr. (3), the cutoff frequencies, =20, 10 and 5, correspond to the effective resolutions of 43, 86 and 1611 pixels. The comparisons show that for the raw data the noise level of Bt is nearly 10 times larger than that of Bl, but their deviations are similar; whereas for the filtered data (=5), the deviations of both Bt and Bl are reduced by about 2/3, but the maximum of the field loss () increases by less than the noise levels (3) for the raw data. The results indicate that such a filtering changes only a bit of fine structures, hence will not distort the 2D magnetic topology on large scale.
Table 1. Comparisons among , and for the data at 01:44UT on October 27 in the raw case and the filtered cases, =20, 10 and 5. All parameters are in units of Gauss.
© European Southern Observatory (ESO) 1999
Online publication: February 23, 1999