Magnetic helicity injection in NOAA 11261 associated with flares

Abstract

Magnetic helicity was found important in understanding solar activities such as flares and coronal mass ejections (CME). Berger and field (1984) derived an expression for helicity flux dHm/dt, that can be applied to an individual solar active region (AR) occupying an area S of the photosphere, (1) \begin{linenomath} dH_{m}/dt=-2\int_{s}[(\mathbf{A_{p}}\cdot \mathbf{V})\mathbf{B}-(\mathbf{A_{p}} \cdot \mathbf{B})\mathbf{V}] dS, \eqno{(1)} \end{linenomath} where Ap is the vector potential of potential field, and V is the plasma velocity at the surface S. The first term describes the effect of magnetic footpoint motions on the surface S. The second term describes the flux of helicity advected through the surface when already twisted and/or writhed flux ropes emerge. Chae (2001) proposed a method of self-consistently determining magnetic helicity injection rate, dH/dt, using a time series of longitudinal magnetograms only: (2) \begin{linenomath} dH/dt=-\int2(\textbf{A}_{p}\cdot \textbf{V}_{LCT})B_{n}dS, \eqno{(2)} \end{linenomath} where n is the normal component of magnetic field. Ap is the vector potential computed from Bn by Fourier transform method. VLCT is the horizontal component of velocity determined by the technique of local correlation tracking (LCT). This technique was applied by some scientists (e.g., Chae et al., 2001; Nindos and Zhang, 2002; Romano et al., 2003). Magnetic helicity injection was found to be strongly correlated with the occurrence of major flares (Moon et al. 2002a, 2002b; Park et al., 2008; Labonte et al., 2007; Maeshiro et al., 2009).