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Modern Solar Facilities – Advanced Solar Science, 185–188 F. Kneer, K. G. Puschmann, A. D. Wittmann (eds.) c  Universitätsverlag Göttingen 2007 Effects of the “false” magnetic-field imbalance in solar active regions I. V. Oreshina* and B. V. Somov Sternberg Astronomical Institute of Moscow State University, Moscow, Russia * Email: ivo@sai.msu.ru Abstract. The imbalance of magnetic fluxes of opposite polarities in solar active regions (ARs) is investigated. On the base of a topological magnetic-field model, we reveal some causes leading to the observations of the imbalance even if real magnetic fluxes are balanced. 1 Introduction The question of whether or not an imbalance of the magnetic field is related to solar flares and coronal mass ejections (CME) is widely debated. Conclusions are often contradictory (Shi & Wang 1994; Gaizauskas et al. 1998; Tian et al. 2002; Wang et al. 2002; Tian & Liu 2003; Green et al. 2003; Chumak et al. 2004). The aims of our study are (1) to demonstrate several effects of “false” magnetic imbalance, i.e. to reveal some causes leading to the observation of imbalance even if real magnetic fluxes are balanced in solar ARs, (2) to propose an explanation of some observational data. 2 Model We assume that the magnetic field is potential and use the magnetic-field topological model (see, for example, Sweet 1958; Gorbachev & Somov 1989; Mandrini et al. 1991; Somov et al. 2005), where the field is created by “effective sources” located below the photosphere. The imbalance value I of an AR is estimated with the formula (Choudhary et al. 2002) I =| Φn | − | Φp || Φn | + | Φp |· 100% , (1) where Φn and Φp are the integrated negative (away from the observer) and positive (toward the observer) magnetic fluxes, respectively. 3 Dependence of the imbalance on the location of active regions on the solar disc Green et al. (2003) have studied magnetic field changes in four ARs during seven days of their disc passage. On the base of MDI/SOHO magnetograms, they have revealed two ef- 186 I. V. Oreshina and B. V. Somov: Magnetic-field imbalance in solar ARs 10 -10 -60 -40 -20 20 40 60 I, % 0 0 Figure 1. The imbalance change during the AR 8086 passage through the solar disc. fects: (1) the imbalance increases when ARs move toward the solar limb and (2) the imbalance sign changes when ARs cross the central meridian. As only line-of-sight magnetograms were used in their work, the above authors could not explain the observations. But they supposed that the observed effects could be due to the presence of horizontal field components (i.e. parallel to the photospheric surface). Let us test this hypothesis using the topological model. Let us consider the AR 8086 which passed the solar disc during September 15-21, 1997 at the latitude of 27◦ N. We model the observed MDI/SOHO magnetogram using 25 magnetic sources and calculate the imbalance change during the AR passage across the solar disc (i.e. imbalance dependence on the longitude ϕ). The results are presented in Fig. 1. The topological model can explain the dominating negative flux in the eastern hemisphere , the imbalance decrease as the AR 8086 moves towards the central meridian, the change of the imbalance sign in the vicinity of the central meridian and its new increase as the AR moves towards the western limb. The maximum imbalance values are 14.4 % near the eastern limb and 18.6% near the western limb. Green et al. (2003) report about 15% for AR 8086. So, both results (observed and theoretical ones) are in good agreement. This allows us to conclude that imbalance effects, reported by Green et al. (2003), can be observed even if the real fluxes are balanced. These effects are due to the 3D structure of the photospheric magnetic field. 4 Imbalance dependence on the size and location of the computational box Investigating the connection of imbalance with flares and CMEs, many authors carried out their calculations in only small regions representing a part of an AR where the magnetic field is the most intense (Wang et al. 2002; Green et al. 2003; Yurchishin et al. 2004). So, it is important to estimate the imbalance dependence on the size and location of the computational box. Choudhary et al. (2002) have studied 137 ARs located near the disc center and found that the average imbalance value is about 9.5%, i.e. in good agreement with our examples. Moreover, 70% of ARs show...

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