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On the Availability of Sufficient Twist in Solar Active Regions to Trigger the Kink Instability  

K. D. Leka   Submitted: 2004-12-13 09:45

The question of whether there is sufficient magnetic twist in solar active regions for the onset of the kink instability is examined using a ``blind test'' of analysis methods commonly used to interpret observational data. ``Photospheric magnetograms'' are constructed from a recently-developed numerical simulation of a kink-unstable emerging fluxrope with nearly constant (negative) wind. The calculation of the best-fit linear force-free parameter α m best is applied, with the goal of recovering the model input helicity. It is shown that for this simple magnetic structure, three effects combine to produce an underestimation of the known helicity: (1) the influence of horizontal fields with lower local α values within the fluxrope, (2) an assumed simple relation between α m best and the winding rate q does not apply to non-axis fields in a fluxrope which is not thin, and (3) the difficulty in interpreting the force-free twist parameter measured for a field which is {it forced}. A different method to evaluate the magnetic twist in active region fluxropes is presented which is based on evaluating the peak α value at the fluxrope axis. When applied to data from the numerical simulation, the twist component of the magnetic helicity is essentially recovered. Both the α m best and the new α m peak methods are then applied to observational photospheric vector magnetic field data of NOAA~AR,7201. The α m best approach is then confounded further in AR,7201 by (4) a distribution of α which contains both signs, as is generally observed in active regions. The result from the proposed α m peak approach suggests that a larger magnetic twist is present in this active region's delta-spot than would have been inferred from α m best, by at least a factor of three. It is argued that the magnetic fields in localized active region fluxropes may indeed carry greater than 2pi winds, and thus the kink instability is a possible trigger mechanism for solar flares and Coronal Mass Ejections.

Authors: K.D. Leka, Y. Fan, G. Barnes
Projects:

Publication Status: ApJ, accepted
Last Modified: 2005-03-08 16:07
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Photospheric Magnetic Field Properties of Flaring vs. Flare-QuietActive Regions. II. Discriminant Analysis  

K. D. Leka   Submitted: 2003-06-24 10:59

We apply statistical tests based upon discriminant analysis to the wide range of photospheric magnetic parameters described in Paper~I (Leka & Barnes 2003), with the goal of identifying those properties which are important for the production of energetic events such as solar flares. The photospheric vector magnetic field data from the U.~Hawai`i Imaging Vector Magnetograph are well-sampled both temporally and spatially, and we include here data covering 24 flare-event and flare-quiet epochs taken from seven active regions. The mean value and rate of change of each magnetic parameter are treated as separate variables, thus evaluating both the parameter's state and its evolution, to determine which properties are associated with flaring. Considering single variables first, Hotelling's T^2-tests show small statistical differences between flare-producing and flare-quiet epochs. Even pairs of variables considered simultaneously, which do show statistical difference for a number of properties, have high error rates, implying a large degree of overlap of the samples. To better distinguish between flare-producing and flare-quiet populations, larger numbers of variables are simultaneously considered; lower error rates result, but no unique combination of variables is clearly the best discriminator. The sample size is too small to directly compare the predictive power of large numbers of variables simultaneously. Instead, we rank all possible four-variable permutations based on Hotelling's T^2-test, and look for the most frequently appearing variables in the best permutations, with the interpretation that they are most likely to be associated with flaring. These variables include: an increasing kurtosis of the twist parameter, a larger standard deviation of the twist parameter, but a smaller standard deviation of the distribution of the horizontal shear angle and of the distribution of the horizontal magnetic field, but a larger kurtosis of that horizontal field. To support the ``sorting all permutations'' method of selecting the most frequently occurring variables, we show that the results of a single ten-variable discriminant analysis are consistent with the ranking. We demonstrate that individually, the variables considered here have little ability to differentiate between flaring and flare-quiet populations, but with multi-variable combinations, the populations may be distinguished.

Authors: K. D. Leka and G. Barnes
Projects:

Publication Status: ApJ (accepted)
Last Modified: 2003-06-24 11:00
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Photospheric Magnetic Field Properties of Flaring vs. Flare-Quiet Active Regions I: Data, General Approach, and Sample Results  

K. D. Leka   Submitted: 2003-06-24 10:56

Photospheric vector magnetic field data from the U. Hawai`i Imaging Vector Magnetograph with good spatial and temporal sampling, are used to study the question of identifying a pre-flare signature unique to flare events in parameters derived from BB. In this first of a series of papers, we present the data analysis procedure and sample results focusing only on three active regions (NOAA Active Regions #8636, #8771, and #0030), three flares (two M-class and one X-class), and (most importantly) a flare-quiet epoch in a comparable flare-producing region. Quantities such as the distribution of the field morphology, horizontal spatial gradients of the field, vertical current, current helicity, ``twist'' parameter α and magnetic shear angles are parameterized using their moments and appropriate summations. The time series of the resulting parameterizations are examined one at a time for systematic differences in overall magnitude and evolution between the flare and flare-quiet examples. The variations expected due to atmospheric seeing changes are explicitly included. In this qualitative approach we find (1) no obvious flare-imminent signatures from the plain magnetic field vector and higher moments of its horizontal gradient, or from most parameterizations of the vertical current density; (2) counter-intuitive but distinct flare-quiet implications from the inclination angle, and higher moments of the photospheric excess magnetic energy; (3) flare-specific or flare-productivity signatures, sometimes weak, from the lower moments of the field gradients, kurtosis of the vertical current density, magnetic twist, current helicity density and magnetic shear angle. The strongest results are, however, that (4) in ensuring a flare-unique signature, numerous candidate parameters (considering both their variation and overall magnitude) are nullified on account of similar behavior in a flare-quiet region, and hence (5) considering single parameters at a time in this qualitative manner is inadequate. To address these limitations, a quantitative statistical approach is presented in Paper II (Leka and Barnes 2003).

Authors: K. D. Leka and G. Barnes
Projects: None

Publication Status: ApJ (accepted)
Last Modified: 2003-06-24 10:56
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Active Region Magnetic Structure Observed in the Photosphere and Chromosphere  

K. D. Leka   Submitted: 2002-10-28 10:35

The full magnetic vector has been measured in both the photosphere and chromosphere across sunspots and plage in NOAA Active Region 8299. We investigate the vertical magnetic structure above the umbral, penumbral and plage regions using quantitative statistical comparisons of the photospheric and chromospheric magnetic data. The results include: (1) a general decrease in average magnetic flux density with height, (2) the direct detection of the superpenumbral canopy in the chromosphere; (3) values for dB/dz which are consistent with earlier investigations when derived from a straight difference between the two measurements, but which are somewhat small when derived from the ablacdotBB=0 condition, (4) a monolithic structure in the umbrae which extends well into the upper chromosphere, with a very complex and varied structure in penumbrae and plage, as evidenced by (5) a uniform magnetic scale height in the umbrae with an abrupt jump to widely varying scale heights in penumbral and plage regions. Further, we find (6) evidence that field extrapolations using the photospheric flux as the boundary may not agree with expectations or with observed coronal structures as well as those which use the emph{chromospheric} magnetic flux as the extrapolation starting point.

Authors: Leka, K. D. and Metcalf, Thomas R.
Projects: None

Publication Status: Solar Physics v 212
Last Modified: 2004-12-13 09:48
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Abstracts by Author
On the Availability of Sufficient Twist in Solar Active Regions to Trigger the Kink Instability
Photospheric Magnetic Field Properties of Flaring vs. Flare-QuietActive Regions. II. Discriminant Analysis
Photospheric Magnetic Field Properties of Flaring vs. Flare-Quiet Active Regions I: Data, General Approach, and Sample Results
Active Region Magnetic Structure Observed in the Photosphere and Chromosphere

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