Cycle 23 Variation in Solar Flare Productivity

The NOAA listings of solar flares in cycles 21-24, including the GOES soft X-ray magnitudes, enable a simple determination of the number of flares each flaring active region produces over its lifetime. We have studied this measure of flare productivity over the interval 1975-2012. The annual averages of flare productivity remained approximately constant during cycles 21 and 22, at about two reported M or X flares per region, but then increased significantly in the declining phase of cycle 23 (the years 2004-2005). We have confirmed this by using the independent RHESSI flare catalog to check the NOAA events listings where possible. We note that this measure of solar activity does not correlate with the solar cycle. The anomalous peak in flare productivity immediately preceded the long solar minimum between cycles 23 and 24

Nonlinear force-free modeling of coronal magnetic fields Part I: A quantitative comparison of methods

We compare six algorithms for the computation of nonlinear force-free (NLFF) magnetic fields (including optimization, magnetofrictional, Grad–Rubin based, and Green's function-based methods) by evaluating their performance in blind tests on analytical force-free-field models for which boundary conditions are specified either for the entire surface area of a cubic volume or for an extended lower boundary only. Figures of merit are used to compare the input vector field to the resulting model fields. Based on these merit functions, we argue that all algorithms yield NLFF fields that agree best with the input field in the lower central region of the volume, where the field and electrical currents are strongest and the effects of boundary conditions weakest. The NLFF vector fields in the outer domains of the volume depend sensitively on the details of the specified boundary conditions; best agreement is found if the field outside of the model volume is incorporated as part of the model boundary, either as potential field boundaries on the side and top surfaces, or as a potential field in a skirt around the main volume of interest. For input field (B) and modeled field (b), the best method included in our study yields an average relative vector error E n = 〈 |B−b|〉/〈 |B|〉 of only 0.02 when all sides are specified and 0.14 for the case where only the lower boundary is specified, while the total energy in the magnetic field is approximated to within 2%. The models converge towards the central, strong input field at speeds that differ by a factor of one million per iteration step. The fastest-converging, best-performing model for these analytical test cases is the Wheatland, Sturrock, and Roumeliotis (2000) optimization algorithm as implemented by Wiegelmann (2004)