1 Introduction

It is commonly believed that magnetic fields in the solar atmosphere are caused by a dynamo operating at or beneath the bottom of the convection zone and then emerge as $\Omega -$flux tubes on the solar surface to form solar active regions. Joy's Law (Hale et al. 1919) states that in many active regions of bipolar magnetic fields, the magnetic polarity axis has a particular inclination, with the preceding spot closer to the solar equator than the following spot. The angle between the magnetic polarity axis and the solar equator is defined as the "tilt angle''. Observational studies of the tilt angle have been published in many papers (Howard 1989, 1991; Wang & Sheeley 1989; Tian et al. 1999). The physical origin of the tilt angle has been discussed by following authors: Babcock (1961) proposed that, if the interior field has a purely toroidal orientation, Coriolis forces acting on the upwelling fluid associated with an active region would produce a tilt in the sense that is measured. Schmidt (1968) and Wang & Sheeley (1991) suggested that the tilts of active regions are formed by the Coriolis force acting on the expanding plasma contained within a buoyant, rising flux tube, rather than on the surrounding fields. On the other hand, the solar magnetic fields are twisted. The twist has been inferred by a number of methods including studying the morphology of filaments (Martin et al. 1994) and coronal loops (Rust & Kumar 1996), in situ measurements of flux ropes (Burlaga 1988) and interplanetary fields (Bieber et al. 1987), computing the force-free parameter $\alpha_{\rm best}$(Pevtsov et al. 1995) and mean current helicity density $<h_{\vert\vert}>\, =\, <(\bigtriangledown \times \vec{B})_\parallel\cdot \vec{B}_\parallel>$ (Abramenko et al. 1996; Bao & Zhang 1998). Results from these methods reveal the dominance of negative/positive helicity in the northern/southern hemisphere, which is defined as "a rule of helicity sign''.

In studying the origin of the twist, Wang et al. (1994) and Leka et al. (1996) used photospheric observation of magnetic fields to probe sub-photospheric fields. They concluded that some active regions were carrying electric currents prior to their emergence. In other words, the twist of the active region magnetic fields was present in a flux tube below the photosphere. There are many models explaining the origin of the twist of magnetic lines in sub-photospheric magnetic flux tubes. Longcope et al. (1996), Moreno-Insertis & Emonet (1996) and Fan et al. (1998) proposed that twist presented in a flux tube is produced by a solar dynamo before the tube rises. Rust & Kumar (1994) considered that the current helicity is caused by the subphotospheric differential rotation in the convection zone. Longcope & Klapper (1997) suggested that the twist could be given rise to by the tilt of the magnetic polarity axis, which is caused by the Coriolis force acting on the buoyant, rising flux tube as a $\Omega -$loop in the convection zone. In a recent paper, Longcope et al. (1998) proposed that the twist is imparted to the flux tube through the deformation of the axis of the flux tube, which is caused by turbulent motions with a non-zero kinetic helicity $<\vec{u} \times (\bigtriangledown \times \vec{u})>$in the convection zone.

The force-free parameter $\alpha$ and the mean current helicity < h_|| > calculated in the photosphere carry some information on the twist of magnetic lines in a flux tube rising to the photosphere from the view of observations (Seehafer 1990; Pevtsov et al. 1995; Abramenko et al. 1996; Bao & Zhang 1998). Positive/negative values of these parameters correspond to the twist of magnetic lines in the right/left-handedness. We use < h_|| > as a parameter to describe the twist of an active region magnetic fields in this paper.

It is important for some dynamo and flux tube models to study the origin of the twist of magnetic fields in the active regions. Perhaps, the relationship between the twist of the magnetic field and the tilt angle of an active region could shed light on this problem, as Longcope & Klapper (1997) and Longcope et al. (1998) have proposed. After considering helicity conservation in a flux tube with zero helicity, helicity modifies both twist and writhe in the tube. However, the writhe will be opposite in sign to the twist (Moffatt & Ricca 1992) if the Coriolis force produced a twist in originally untwisted flux tubes. Canfield & Pevtsov (1998) first studied the relationship in sign of both the force-free parameter $\alpha$ and tilt per unit length ( $-{\theta\over L}$), where L is the separation between sunspots of opposite polarity. Their data show no reliable anticorrelation in sign between twist and writhe (see Fig. 6 of their paper), as one would expect.

However, the mean current helicity < h_||> was measured by Bao & Zhang (1998) for 422 active regions in the 22nd cycle. They found that almost 80% of active regions adhere to the hemispheric helicity rule, being negative in the northern hemisphere and positive in the southern hemisphere. The tilt angle $\varphi$ was measured by Tian et al. (1999) for 203 bipolar regions among the 422 active regions. They found that almost 70% of bipolar active regions adhere to the Hale-Nickolson Law. What is the relationship in sign between the tilt and the twist using these data? In the present paper, we will use this relationship to investigate where the helicity is produced. Observational techniques and data chosen are described in Sect. 2. Definitions and calculations of tilt angle and current helicity are given in Sect. 3. In Sect. 4, we present the relationship between the sign of the tilt angle of magnetic polarity axis and the sign of the mean current helicity < h_|| > for 286 bipolar active regions. In Sect. 5, we examine the distribution of active regions with "abnormal chirality''. Distribution of 62 X-ray flares larger than M-class is given in Sect. 6. Finally, conclusions and discussions are given in Sect. 7.