A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. III. The Free Energy

作者：Aschwanden Markus J^*

来源：Solar Physics, 2013, 287(1-2): 369-389.

DOI：10.1007/s11207-012-0203-6

• Sun: corona
• Sun: magnetic fields

An analytical approximation of a nonlinear force-free magnetic field (NLFFF) solution was developed in Paper I, while a numerical code that performs fast forward-fitting of this NLFFF approximation to a line-of-sight magnetogram and coronal 3D loops has been described and tested in Paper II. Here we calculate the free magnetic energy E (free)=E (N)-E (P), i.e., the difference of the magnetic energies between the non-potential field and the potential field. A second method to estimate the free energy is obtained from the mean misalignment angle change Delta mu=mu (P)-mu (N) between the potential and non-potential field, which scales as E (free)/E (P)a parts per thousand tan(2)(Delta mu). For the four active regions observed with STEREO in 2007 we find free energies in the range of q (free)=(E (free)/E (P))a parts per thousand 1 % -aEuro parts per thousand 10 %, with an uncertainty of less than +/- 2 % between the two methods, while the free energies obtained from 11 other NLFFF codes exhibit a larger scatter of about +/- 10 %. We also find a correlation between the free magnetic energy and the GOES flux of the largest flare that occurred during the observing period, which can be quantified by an exponential relationship, F (GOES)aeexp(q (free)/0.015), implying an exponentiation of the dissipated currents.

• 出版日期2013-10