Title: A Two-Fold Approach in Estimating the Relative Magnetic Helicity
in Solar Active Regions

Author_list: Georgoulis, M. K., LaBonte, B. J., Rust, D. M.

Abstract: Using two new techniques, we can calculate both the magnetic
helicity variations in the active region solar photosphere and a total
magnetic helicity budget in solar active regions. The first technique
assumes linear force-free magnetic fields and allows the evaluation of
the relative magnetic helicity integral. The second technique finds a
unique solution of the ideal MHD induction equation and, moreover,
determines a field-aligned velocity field, thus reconstructing fully
the velocity field vector in the active region solar photosphere. The
latter method is completely disentangled from local correlation
tracking (LCT) and, applied to vector magnetograms, allows the
calculation of both the injected helicity and the helicity built-up by
photospheric flows with an accuracy that cannot be matched by LCT. We
apply the two helicity calculation techniques to vector magnetograms of
flaring/CME-prolific active regions and to NOAA AR 8210 and we discuss
the relation between the two types of results. We find that the two
approaches are complementary and provide much needed insight into the
energy release process and the triggering of coronal ejecta.