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Astron. Astrophys. 357, 1056-1062 (2000)

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2. Observations

2.1. Instruments and the reliability

The line-of-sight and transverse magnetograms in the photosphere used for this study were obtained with the Solar Magnetic Field Telescope (SMFT) at the Huairou Solar Observing Station (HSOS) (Ai & Hu 1986). This vector magnetograph has a tunable birefringent filter, which can tune its passband working either at the photospheric line FeI [FORMULA]5324.19 Å, or at the chromospheric line [FORMULA]. For the photospheric observations, the passband is tuned at FeI - 0.075 Å to measure longitudinal components of solar magnetic fields, and at the line center to measure transverse components of the fields for achieving the maximum sensitivity. In the measurement of the magnetic field in solar active regions, the integration of 255 frames and the 4 [FORMULA] 3 average are usually made so as to increase the signal-to-noise ratio. The magnetograms after the average yield the spatial resolution of about 2". The calibration of the observed magnetic field has been well established by Ai, Li & Zhang (1982).

Many factors can affect the quantitative measure of the vector magnetic field. Wang et al. (1996) have discussed in detail the limitation and reliability of the HSOS database. They argued that, for the SMFT, the factors such as Zeeman saturation, Doppler shift, Faraday rotation and the cross talk are insignificant. Except for the sunspot umbra area where the contamination of the stray light is serious, the observed line-of-sight flux density is reliable, and the azimuth of the transverse field is reasonably good when a region is close to the disk center. Therefore, both the morphology and the field evolution can be studied from the HSOS vector magnetograms.

2.2. Data reduction

The active region NOAA 7321 was an emerging flux region (EFR), which was born on October 24, 1992 and disappeared at the western limb on November 2. During this period, its configuration underwent a significant change and flares occurred frequently. For this active region, many studies about the features of magnetic topology and flares have been done (Takakura et al. 1994; Zhang 1995; Wang 1997; Liu et al. 1995, 1998; Wang, Qiu & Zhang 1998; Wang, Wang & Qiu 1999; Wang, Yan & Sakurai 1999; Qiu et al. 1999).

We chose 18 magnetograms within 3 days (listed in Table 1) for our study. The active region was situated at the positions from (E9, S23) to (W20, S23) on the solar disk during this period. As it was very close to the disk center, projection effect on the magnetic data was not significant. So we did not transform the data into the heliospheric plane. On the other hand, this avoids the contamination to the vertical components by the projection correction, because the noise level of transverse field measurements is generally higher than that of longitudinal field measurements by an order of magnitude. Hereafter in this paper we take [FORMULA] as [FORMULA]. The [FORMULA] ambiguity of the transverse field measurements was resolved by a multistep method (Wang et al. 1994).


[TABLE]

Table 1. List of magnetograms in active region NOAA 7321 in 1992.


The total magnetic flux for a region of interest (S) is calculated by

[EQUATION]

where [FORMULA], i.e., the area with [FORMULA] above the 2[FORMULA] level in the region S. We estimated [FORMULA] as the standard deviation of the longitudinal field measurement, while [FORMULA] as the average value of the transverse field measurement, both for a weak-field area. Errors in the sum for [FORMULA] are mainly determined by [FORMULA], thus we estimated the errors using

[EQUATION]

Similarly, the total current is calculated by

[EQUATION]

where

[EQUATION]

and

[EQUATION]

[FORMULA] is deduced with the differencing method for the filtered transverse field measurement with a relative cutoff frequency, 20 (Wang, Qiu & Zhang 1998; Wang, Wang & Qiu 1999). The error of I is given by

[EQUATION]

A convenient way to characterize the twist in magnetic flux is to use the force-free field parameter [FORMULA] which has the physical meaning of current helicity (Pevtsov et al. 1994, 1995). From the measured field the distribution of [FORMULA] can be obtained ([FORMULA]). The global estimate of twist can be estimated by averaging [FORMULA] over the region of interest S where [FORMULA] and [FORMULA] are satisfied.

[EQUATION]

An improved calculation method is to average [FORMULA] weighted by the element flux [FORMULA], which gives a more clear physical implication. If each field line is given a single value of [FORMULA], then the average of [FORMULA] for a bundle of field lines in a region should be,

[EQUATION]

The [FORMULA] describes the twist which is representative of most field lines.

Alternatively, the twist of an entire AR, supposedly a linear force-free field, can be described by a single constant [FORMULA] which is computed from the observed longitudinal field boundary and best fits the transverse components. Two methods can be used to achieve an optimal fit. The first method minimizes the difference between the x and y components of the computed and observed fields (Pevtsov et al. 1995),

[EQUATION]

where Bxo, Byo are the x and y components of the observed field, and Bxc, Byc are those of the computed field. The second method minimizes the angles between the transverse components of the computed and observed fields (Wang, Yan & Sakurai 1999),

[EQUATION]

where [FORMULA], [FORMULA] are the transverse components of the observed and computed fields, respectively. We adopted the optimum technique to determine the value of [FORMULA] which satisfies the condition ([FORMULA]. An advantage in the [FORMULA] method is that the determination of its value does not depend on the [FORMULA]-ambiguity resolution of the observed transverse field.

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© European Southern Observatory (ESO) 2000

Online publication: June 5, 2000
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