S. A. Gilchrist, M. S. Wheatland, K. D. Leka
The NOAA active region AR 11029 was a small but highly active sunspot region
which produced 73 GOES soft X-ray flares. The flares appear to show a departure
from the well known power-law frequency-size distribution. Specifically, too
few GOES C-class and no M-class flares were observed by comparison with a
power-law distribution (Wheatland in Astrophys. J. 710, 1324, 2010). This was
conjectured to be due to the region having insufficient magnetic energy to
power large events. We construct nonlinear force-free extrapolations of the
coronal magnetic field of active region AR 11029 using data taken on 24 October
by the SOLIS Vector-SpectroMagnetograph (SOLIS/VSM), and data taken on 27
October by the Hinode Solar Optical Telescope SpectroPolarimeter (Hinode/SP).
Force-free modeling with photospheric magnetogram data encounters problems
because the magnetogram data are inconsistent with a force-free model, and we
employ a recently developed `self-consistency' procedure which addresses this
and accommodates uncertainties in the boundary data (Wheatland and Regnier in
Astrophys. J. 700, L88, 2009). We calculate the total energy and free energy of
the self-consistent solution and find that the free energy was 4x10^29 erg on
24 October, and 7x10^31 erg on 27 October. An order of magnitude scaling
between RHESSI non-thermal energy and GOES peak X-ray flux is established from
a sample of flares from the literature and is used to estimate flare energies
from observed GOES peak X-ray flux. Based on the scaling, we conclude that the
estimated free energy of AR 11029 on 27 October when the flaring rate peaked is
sufficient to power M-class or X-class flares, and hence the modeling does not
appear to support the hypothesis that the absence of large flares is due to the
region having limited energy.
View original:
http://arxiv.org/abs/1110.4418
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