FIRST THREE-DIMENSIONAL RECONSTRUCTIONS OF CORONAL LOOPS WITH THE STEREO A plus B SPACECRAFT. IV. MAGNETIC MODELING WITH TWISTED FORCE-FREE FIELDS

The three-dimensional coordinates of stereoscopically triangulated loops provide strong constraints for magnetic field models of active regions in the solar corona. Here, we use STEREO/A and B data from some 500 stereoscopically triangulated loops observed in four active regions (2007 April 30, May 9, May 19, and December 11), together with SOHO/MDI line-of-sight magnetograms. We measure the average misalignment angle between the stereoscopic loops and theoretical magnetic field models, finding a mismatch of mu = 19 degrees-46 degrees for a potential field model, which is reduced to mu = 14 degrees-19 degrees for a non-potential field model parameterized by twist parameters. The residual error is commensurable with stereoscopic measurement errors (mu(SE) approximate to 8 degrees-12 degrees). We developed a potential field code that deconvolves a line-of-sight magnetogram into three magnetic field components (B-x, B-y, B-z), as well as a non-potential field forward-fitting code that determines the full length of twisted loops (L approximate to 50-300 Mm), the number of twist turns (median N-twist = 0.06), the nonlinear force-free a-parameter (median alpha approximate to 4 x 10(-11) cm(-1)), and the current density (median j(z) approximate to 1500 Mx cm(-2) s(-1)). All twisted loops are found to be far below the critical value for kink instability, and Joule dissipation of their currents is found to be far below the coronal heating requirement. The algorithm developed here, based on an analytical solution of nonlinear force-free fields that is accurate to second order (in the force-free parameter alpha), represents the first code that enables fast forward fitting to photospheric magnetograms and stereoscopically triangulated loops in the solar corona.