2 Observational techniques and data

2.1 Observational technique

We use the data of vector magnetic fields obtained by the Solar Magnetic Field Telescope, an imaging vector magnetograph installed at Huairou Solar Observing Station of the Beijing Astronomical Observatory, with a field of view of about 5 $.\mkern-4mu^\prime$$23\times3$ $.\mkern-4mu^\prime$63 ( $512\times512$ pixels of the CCD). The temporal and spatial resolution of the vector magnetograms depend on the number of video frames that are integrated to make one magnetogram. Each magnetogram used in this paper is the sum of 256 individual frames for both line-of-sight and transverse fields. Temporal resolution is about 5 min for each vector magnetogram. Each pixel is about 0 $.\!\!^{\prime\prime}$$6\times 0$ $.\!\!^{\prime\prime}$4. After performing a $3\times4$ pixels smoothing average, the spatial resolution is 2 $^{\prime\prime}\times$2 $^{\prime\prime}$.

The vector magnetic field in the photosphere was obtained on the basis of narrow-band images (filtergrams) of four Stokes parameters I, V, Q, U in FeI 5324.191 Å. The longitudinal magnetic field strength (B_||) and transverse magnetic field strength ($B_\perp$) are given, respectively, by

$$B_{\vert\vert}=C_{\vert\vert}{\frac{V}{I}}$$ (1)

$$B_{\perp}=C_{\perp}\left(\frac{Q^2}{I^2}+\frac{U^2}{I^2}\right)^{\frac{1}{4}},$$ (2)

where C_|| and $C_{\perp}$ are the calibration coefficients for line-of-sight and transverse components of the magnetic fields. However, a precise calibration of a vector magnetograph is very complicated and difficult. Both theoretical and empirical methods are used to calibrate the vector magnetograms (Ai et al. 1982; Wang et al. 1996).

The 180-degree azimuthal ambiguity in determining the transverse field direction is an intrinsic defect of the Zeeman effect (Harvey 1969). It may be resolved according to the potential field approximation method (Wang & Lin 1993; Wang et al. 1994) taking into account the evolution of active regions and the orientation of chromospheric fibrils. After the 3$\times$4 pixel smoothing average of V, Q and U was made, the noise level was less than 10 G for the line-of-sight field and 100 G for the transverse field over the same integration time.

It should be mentioned that magneto-optical effects (Faraday rotation) is insignificant (Wang et al. 1996) in FeI 5324.191 Å. Several tests were made particularly to compare the measured field azimuth for a few sunspots when switching the bandpass from line center to line wing, and differences in the observed azimuth were less than 10$^\circ$. On the other hand, after Bao et al. (2000) compared the vector magnetograms of an active region, NOAA 5747, from Huairou and Mees Solar Observation, they found a qualitative agreement between them. Then, they estimated that Faraday rotation in the Huairou magnetogram contributes about 12$^\circ$ in the azimuth difference when possible sources of error are taken into account. After considering the role of Faraday rotation in computation of < h_|| >, Bao et al. (2000) conclude that it does not affect the strength of the hemispheric helicity rule.

2.2 Data

In our study, we have chosen 286 active regions which belong to $\beta$ sunspots in the magnetic classification. Most of the active regions are formed by two main bigger spots. Among them, 203 active regions have simpler magnetic configuration (i.e. the magnetic fields in these regions can be simply divided into areas with N and S polarities) and 83 are more complicated (i.e. there is some small scale inverse regions in the dominated polarities).

We analyze the vector magnetograms of these active regions obtained from 1988 to 1996 at Huairou Solar Observing Station of the Beijing Astronomy Observatory, and compare them with their images of sunspots in the photosphere and fulldisk magnetograms published in the SGD. It is found that these active region are much better bipolar regions and are isolated from others. The magnetograms always cover the entire active region. All the vector magnetic field data included in this study were carefully chosen and acquired with favorable weather and seeing conditions during the observations. Thus, the noise level could be lowered to 6 G for the line-of-sight field and 60 G for the transverse field in the photosphere. When an active region developed maturely and was located near the central meridian, it is included in the sample. Therefore, most of the active regions are not new emerging and young active regions. We then calculate tilts and current helicity of those active regions using the best magnetograms. The projection effect for high latitude active regions were removed according to the formulae given by Gary & Hagyard (1990).