  In this ISSI-supported series of studies on magnetic helicity in the Sun, we
systematically implement different magnetic helicity calculation methods on
high-quality solar magnetogram observations. We apply finite-volume, discrete
flux tube (in particular, connectivity-based) and flux-integration methods to
data from Hinode's Solar Optical Telescope. The target is NOAA active region
10930 during a ~1.5 day interval in December 2006 that included a major
eruptive flare (SOL2006-12-13T02:14X3.4). Finite-volume and connectivity-based
methods yield instantaneous budgets of the coronal magnetic helicity, while the
flux-integration methods allow an estimate of the accumulated helicity injected
through the photosphere. The objectives of our work are twofold: A
cross-validation of methods, as well as an interpretation of the complex events
leading to the eruption. To the first objective, we find (i) strong agreement
among the finite-volume methods, (ii) a moderate agreement between the
connectivity-based and finite-volume methods, (iii) an excellent agreement
between the flux-integration methods, and (iv) an overall agreement between
finite-volume and flux-integration based estimates regarding the predominant
sign and magnitude of the helicity. To the second objective, we are confident
that the photospheric helicity flux significantly contributed to the coronal
helicity budget, and that a right-handed structure erupted from a predominantly
left-handed corona during the X-class flare. Overall, we find that the use of
different methods to estimate the (accumulated) coronal helicity may be
necessary in order to draw a complete picture of an active-region corona, given
the careful handling of identified data (preparation) issues, which otherwise
would mislead the event analysis and interpretation.
