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We report here on the present state-of-the-art in algorithms used for resolving the 180 • ambiguity in solar vector magnetic field measurements. With present observations and techniques, 268 T.R. METCALF ET AL. some assumption must be made about the solar magnetic field in order to resolve this ambiguity. Our focus is the application of numerous existing algorithms to test data for which the correct answer is known. In this context, we compare the algorithms quantitatively and seek to understand where each succeeds, where it fails, and why. We have considered five basic approaches: comparing the observed field to a reference field or direction, minimizing the vertical gradient of the magnetic pressure, minimizing the vertical current density, minimizing some approximation to the total current density, and minimizing some approximation to the field's divergence. Of the automated methods requiring no human intervention, those which minimize the square of the vertical current density in conjunction with an approximation for the vanishing divergence of the magnetic field show the most promise.

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Chae (2001) first proposed a method of self-consistently determining the rate of change of magnetic helicity using a time series of longitudinal magnetograms only, such as taken by SOHO/MDI. Assuming that magnetic fields in the photosphere are predominantly vertical, he determined the horizontal component of velocity by tracking the displacements of magnetic flux fragments using the technique of local correlation tracking (LCT). In the present paper, after briefly reviewing the recent advance in helicity rate measurement, we argue that the LCT method can be more generally applied even to regions of inclined magnetic fields. We also present some results obtained by applying the LCT method to the active region NOAA 10365 under emergence during the observable period, which are summarized as follows.(1) Strong shearing flows were found near the polarity inversion line that were very effective in helicity injection. (2) Both the magnetic flux and helicity of the active region steadily increased during the observing period, and reached 1.2×10 22 Mx and 8 × 10 42 Mx 2 , respectively, 4.5 days after the birth of the active region. (3) The corresponding ratio of the helicity to the square of the magnetic flux, 0.05, is roughly compatible with the values determined by other studies using linear-force-free modeling. (4) A series of flares took place while the rate of helicity injection was high. (5) The choice of a smaller window size or a shorter time interval in the LCT method resulted in a bigger value of the LCT velocity and a bigger value of the temporal fluctuation of the helicity rate. (6) Nevertheless when averaged over a time period of about one hour or longer, the average rate of helicity became about the same within about 10%, almost irrespective of the chosen window size and time interval, indicating that short-lived, fluctuating flows may be insignificant in transferring magnetic helicity. Our results suggest that the LCT method may be applied to 96-minute cadence full-disk MDI magnetograms or other data of similar kind, to provide a practically useful, if not perfect, way of monitoring the magnetic helicity content of active regions as a function of time.

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To measure the magnetic field strength in the solar corona, we examined 10 fast (≥ 1000 km s −1 ) limb CMEs which show clear shock structures in SOHO/LASCO images. By applying piston-shock relationship to the observed CME's standoff distance and electron density compression ratio, we estimated the Mach number, Alfven speed, and magnetic field strength in the height range 3 to 15 solar radii (R s ). Main results from this study are: (1) the standoff distance observed in solar corona is consistent with those from a magnetohydrodynamic (MHD) model and near-Earth observations; (2) the Mach number as a shock strength is in the range 1.49 to 3.43 from the standoff distance ratio, but when we use the density compression ratio, the Mach number is in the range 1.47 to 1.90, implying that the measured density compression ratio is likely to be underestimated due to observational limits; (3) the Alfven speed ranges from 259 to 982 km s −1 and the magnetic field strength is in the range 6 to 105mG when the standoff distance is used; (4) if we multiply the density compression ratio by a factor of 2, the Alfven speeds and the magnetic field strengths are consistent in both methods; (5) the magnetic field strengths derived from the shock parameters are similar to those of empirical models and previous estimates.

In this paper, we present observations and analysis of an interesting sigmoid formation, eruption, and the associated flare that occurred on 2014 April 18 using multi-wavelength data sets. We discuss the possible role of the sigmoid eruption in triggering the flare, which consists of two different sets of ribbons: parallel ribbons and a large-scale quasi-circular ribbon. Several observational evidence and nonlinear force-free field extrapolation results show the existence of a large-scale fan-spine type magnetic configuration with a sigmoid lying under a section of the fan dome. The event can be explained with the following two phases. During the preflare phase, we observed the formation and appearance of the sigmoid via tether-cutting reconnection between the two sets of sheared fields under the fan dome. The second, main flare phase features the eruption of the sigmoid, the subsequent flare with parallel ribbons, and a quasi-circular ribbon. We propose the following multi-stage successive reconnection scenario for the main flare. First, tether-cutting reconnection is responsible for the formation and the eruption of the sigmoid structure. Second, the reconnection occurring in the wake of the erupting sigmoid produces the parallel flare ribbons on the both sides of the circular polarity inversion line. Third, the null-type reconnection higher in the corona, possibly triggered by the erupting sigmoid, leads to the formation of a large quasi-circular ribbon. For the first time, we suggest a mechanism for this type of flare consisting of a double set of ribbons triggered by an erupting sigmoid in a large-scale fan-spine-type magnetic configuration.

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