A Nonlinear ForceFree Magnetic Field Approximation Suitable for Fast ForwardFitting to Coronal Loops III. The Free Energy 

Markus J. Aschwanden Submitted: 20121115 08:03
An analytical approximation of a nonlinear forcefree magnetic field
(NLFFF) solution was developed in Paper I, while a numerical code
that performs fast forwardfitting of this NLFFF approximation to
a lineofsight magnetogram and coronal 3D loops has been described
and tested in Paper II. Here we
calculate the free magnetic energy E_{
m free}=E_{
m N}E_{
m P}, ie the
difference of the magnetic energies between the nonpotential field
and the potential field. A second method to estimate the free energy
is obtained from the mean misalignment angle change
Deltamu=mu_{
m P}mu_{
m N}
between the potential and nonpotential field, which scales as E_{
m free}/E_{
m P}
approx an^2{(Deltamu)}. For four active regions observed with STEREO
in 2007 we find free energies in the range of q_{
m free}=(E_{
m free}/E_{
m P}) approx
1%10%, with an uncertainty of less than pm 2% between the two methods,
while the free energies obtained from 11 other NLFFF codes exhibit a larger
scatter of order approxpm10%. We find also 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_{
m GOES} propto
exp{(q_{
m free}/0.015)}, implying an exponentiation of the dissipated
currents.
Authors: Markus J. Aschwanden
Projects: STEREO

Publication Status: Solar Physics (in press)
Last Modified: 20121120 20:25


