Validity of NLFFF Optimization Reconstruction

Abstract: We evaluate validity of NLFFF extrapolation performed with Optimization class (OPTI) codes. While explaining inevitable for OPTI partial non-solenoidality caused by the gas pressure notable role in pressure balance at photospheric heights and by mathematical aspects related to optimization and BVP (boundary value problem), we justify elimination of the non-solenoidal component (postprocessing) from the OPTI result obtained. In essence, postprocessing converts the entire non-solenoidal part into a solenoidal force part, which possibly reflects factual deviation of magnetic field from its force-free pproximation on the photosphere and in the solar corona. Two forms of postprocessing have been analyzed in this paper.Postprocessing I eliminates the non-solenoidal component without changing transverse field at the measurement level, and Postprocessing II leaves the field normal component unchanged. Extrapolation, postprocessing, and then comparison of metric and energy characteristics are performed over AR 11158 active region for a small fragment of its evolution containing the February X-class flare.Our version of OPTI code showed that free energy decreased by $\sim 10^{32}$ erg within 1 hour, which corresponds to theoretical estimations of the flare-caused magnetic energy loss. This result differs significantly from the one in Sun et al. (2012).Therefore, we also comment on some features of our OPTI code implementation, which may cause significant differences between our results and those obtained using the Wiegelmann (2004) version of OPTI code in study by Sun et al. (2012).