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Toward an Efficient Prediction of Solar Flares: Which Parameters, and How?  

Manolis K. Georgoulis   Submitted: 2013-11-25 07:46

Solar flare prediction has become a forefront topic in contemporary solar physics, with numerous published methods relying on numerous predictive parameters, that can even be divided into parameter classes. Attempting further insight, we focus on two popular classes of flare-predictive parameters, namely multiscale (i.e., fractal and multifractal) and proxy (i.e., morphological) parameters, and we complement our analysis with a study of the predictive capability of fundamental physical parameters (i.e., magnetic free energy and relative magnetic helicity). Rather than applying the studied parameters to a comprehensive statistical sample of flaring and non-flaring active regions, that was the subject of our previous studies, the novelty of this work is their application to an exceptionally long and high-cadence time series of the intensely eruptive National Oceanic and Atmospheric Administration (NOAA) active region (AR) 11158, observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. Aiming for a detailed study of the temporal evolution of each parameter, we seek distinctive patterns that could be associated with the four largest flares in the AR in the course of its five-day observing interval. We find that proxy parameters only tend to show preflare impulses that are practical enough to warrant subsequent investigation with sufficient statistics. Combining these findings with previous results, we conclude that: (i) carefully constructed, physically intuitive proxy parameters may be our best asset toward an efficient future flare-forecasting; and (ii) the time series of promising parameters may be as important as their instantaneous values. Value-based prediction is the only approach followed so far. Our results call for novel signal and/or image processing techniques to efficiently utilize combined amplitude and temporal-profile information to optimize the inferred solar-flare probabilities. Keywords: frequentist data analysis; magnetic field; solar transients

Authors: Georgoulis, M. K.
Projects: SDO-HMI

Publication Status: Entropy, 15(11), 5022-5052, 2013
Last Modified: 2013-11-25 08:32
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Non-neutralized Electric Current Patterns in Solar Active Regions: Origin of the Shear-Generating Lorentz Force  

Manolis K. Georgoulis   Submitted: 2012-10-11 00:53

Using solar vector magnetograms of the highest available spatial resolution and signal-to-noise ratio we perform a detailed study of electric current patterns in two solar active regions: a flaring/eruptive, and a flare-quiet one. We aim to determine whether active regions inject non-neutralized (net) electric currents in the solar atmosphere, responding to a debate initiated nearly two decades ago that remains inconclusive. We find that well-formed, intense magnetic polarity inversion lines (PILs) within active regions are the only photospheric magnetic structures that support significant net current. More intense PILs seem to imply stronger non-neutralized current patterns per polarity. This finding revises previous works that claim frequent injections of intense non-neutralized currents by most active regions appearing in the solar disk but also works that altogether rule out injection of non-neutralized currents. In agreement with previous studies, we also find that magnetically isolated active regions remain globally current-balanced. In addition, we confirm and quantify the preference of a given magnetic polarity to follow a given sense of electric currents, indicating a dominant sense of twist in active regions. This coherence effect is more pronounced in more compact active regions with stronger PILs and must be of sub-photospheric origin. Our results yield a natural explanation of the Lorentz force, invariably generating velocity and magnetic shear along strong PILs, thus setting a physical context for the observed pre-eruption evolution in solar active regions.

Authors: M. K. Georgoulis, V. S. Titov, & Z. Mikic
Projects: Hinode/SOT

Publication Status: ApJ, in press
Last Modified: 2012-10-11 08:04
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Magnetic Energy and Helicity Budgets in the Active-Region Solar Corona. II. Nonlinear Force-Free Approximation  

Manolis K. Georgoulis   Submitted: 2012-09-26 02:44

Expanding on an earlier work that relied on linear force-free magnetic fields, we self-consistently derive the instantaneous free magnetic energy and relative magnetic helicity budgets of an unknown three-dimensional nonlinear force-free magnetic structure extending above a single, known lower-boundary magnetic field vector. The proposed method does not rely on the detailed knowledge of the three-dimensional field configuration but is general enough to employ only a magnetic connectivity matrix on the lower boundary. The calculation yields a minimum free magnetic energy and a relative magnetic helicity consistent with this free magnetic energy. The method is directly applicable to photospheric or chromospheric vector magnetograms of solar active regions. Upon validation, it basically reproduces magnetic energies and helicities obtained by well-known, but computationally more intensive and non-unique, methods relying on the extrapolated three-dimensional magnetic field vector. We apply the method to three active regions, calculating the photospheric connectivity matrices by means of simulated annealing, rather than a model-dependent nonlinear force-free extrapolation. For two of these regions we correct for the inherent linear force-free overestimation in free energy and relative helicity that is larger for larger, more eruptive, active regions. In the third studied region, our calculation can lead to a physical interpretation of observed eruptive manifestations. We conclude that the proposed method, including the proposed inference of the magnetic connectivity matrix, is practical enough to contribute to a physical interpretation of the dynamical evolution of solar active regions.

Authors: M. K. Georgoulis, K. Tziotziou, & N.-E. Raouafi
Projects: Hinode/SOT

Publication Status: ApJ, in press
Last Modified: 2012-09-26 09:10
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Comment on ``Resolving the 180-degree Ambiguity in Solar Vector Magnetic Field Data: Evaluating the Effects of Noise, Spatial Resolution, and Method Assumptions''  

Manolis K. Georgoulis   Submitted: 2011-06-24 02:38

In a recent paper, Leka at al. (Solar Phys. 260, 83, 2009)constructed asynthetic vector magnetogram representing a three-dimensional magneticstructure defined only within a fraction of an arcsec in height. They rebinnedthe magnetogram to simulate conditions of limited spatial resolution and thencompared the results of various azimuth disambiguation methods on the resampleddata. Methods relying on the physical calculation of potential and/ornon-potential magnetic fields failed in nearly the same, extended parts of thefield of view and Leka et al. (2009) attributed these failures to the limitedspatial resolution. This study shows that the failure of these methods is notdue to the limited spatial resolution but due to the narrowly defined testdata. Such narrow magnetic structures are not realistic in the real Sun.Physics-based disambiguation methods, adapted for solar magnetic fieldsextending to infinity, are not designed to handle such data; hence, they couldonly fail this test. I demonstrate how an appropriate limited-resolutiondisambiguation test can be performed by constructing a synthetic vectormagnetogram very similar to that of Leka et al. (2009) but representing astructure defined in the semi-infinite space above the solar photosphere. Forthis magnetogram I find that even a simple potential-field disambiguationmethod manages to resolve the ambiguity very successfully, regardless oflimited spatial resolution. Therefore, despite the conclusions of Leka et al.(2009), a proper limited-spatial-resolution test of azimuth disambiguationmethods is yet to be performed in order to identify the best ideas andalgorithms.

Authors: Georgoulis, M. K.
Projects: None

Publication Status: Solar Physics, in press
Last Modified: 2011-06-24 11:54
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Nonlinear Force-Free Reconstruction of the Global Solar Magnetic Field: Methodology  

Manolis K. Georgoulis   Submitted: 2011-01-12 02:58

We present a novel numerical method that allows the calculation of nonlinear force-free magnetostatic solutions above a boundary surface on which only the distribution of the normal magnetic field component is given. The method relies on the theory of force-free electrodynamics and applies directly to the reconstruction of the solar coronal magnetic field for a given distribution of the photospheric radial field component. The method works as follows: we start with any initial magnetostatic global field configuration (e.g. zero, dipole), and along the boundary surface we create an evolving distribution of tangential (horizontal) electric fields that, via Faraday's equation, give rise to a respective normal field distribution approaching asymptotically the target distribution. At the same time, these electric fields are used as boundary condition to numerically evolve the resulting electromagnetic field above the boundary surface, modeled as a thin ideal plasma with non-reflecting, perfectly absorbing outer boundaries. The simulation relaxes to a nonlinear force-free configuration that satisfies the given normal field distribution on the boundary. This is different from existing methods relying on a fixed boundary condition - the boundary evolves toward the a priori given one, at the same time evolving the three-dimensional field solution above it. Moreover, this is the first time a nonlinear force-free solution is reached by using only the normal field component on the boundary. This solution is not unique, but depends on the initial magnetic field configuration and on the evolutionary course along the boundary surface. To our knowledge, this is the first time that the formalism of force-free electrodynamics, used very successfully in other astrophysical contexts, is applied to the global solar magnetic field.

Authors: Contopoulos, I., Kalapotharakos, C., and Georgoulis, M. K.
Projects: SoHO-MDI

Publication Status: Solar Physics, in press
Last Modified: 2011-01-12 09:51
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Are Solar Active Regions with Major Flares More Fractal, Multifractal, or Turbulent than Others?  

Manolis K. Georgoulis   Submitted: 2011-01-04 03:01

Multiple recent investigations of solar magnetic field measurements have raised claims that the scale-free (fractal) or multiscale (multifractal) parameters inferred from the studied magnetograms may help assess the eruptive potential of solar active regions, or may even help predict major flaring activity stemming from these regions. We investigate these claims here, by testing three widely used scale-free and multiscale parameters, namely, the fractal dimension, the multifractal structure function and its inertial-range exponent, and the turbulent power spectrum and its power-law index, on a comprehensive data set of 370 timeseries of active-region magnetograms (17,733 magnetograms in total) observed by SOHO's Michelson Doppler Imager (MDI) over the entire Solar Cycle 23. We find that both flaring and non-flaring active regions exhibit significant fractality, multifractality, and non-Kolmogorov turbulence but none of the three tested parameters manages to distinguish active regions with major flares from flare-quiet ones. We also find that the multiscale parameters, but not the scale-free fractal dimension, depend sensitively on the spatial resolution and perhaps the observational characteristics of the studied magnetograms. Extending previous works, we attribute the flare-forecasting inability of fractal and multifractal parameters to i) a widespread multiscale complexity caused by a possible underlying self-organization in turbulent solar magnetic structures, flaring and non-flaring alike, and ii) a lack of correlation between the fractal properties of the photosphere and overlying layers, where solar eruptions occur. However useful for understanding solar magnetism, therefore, scale-free and multiscale measures may not be optimal tools for active-region characterization in terms of eruptive ability or, ultimately,for major solar-flare prediction.

Authors: Georgoulis, M. K.
Projects: SoHO-MDI

Publication Status: Solar Physics, in press
Last Modified: 2011-01-04 13:19
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Subject will be restored when possible  

Manolis K. Georgoulis   Submitted: 2007-12-03 11:48

Using an efficient magnetic complexity index in the active-region solar photosphere, we quantify the preflare strength of the photospheric magnetic polarity inversion lines in 23 eruptive active regions with flare/CME/ICME events tracked all the way from the Sun to the Earth. We find that active regions with more intense polarity inversion lines host statistically stronger flares and faster, more impulsively accelerated, CMEs. No significant correlation is found between the strength of the inversion lines and the flare soft X-ray rise times, the ICME transit times, and the peak Dst indices of the induced geomagnetic storms. Corroborating these and previous results, we speculate on a possible interpretation for the connection between source active regions, flares, and CMEs. Further work is needed to validate this concept and uncover its physical details.

Authors: Georgoulis, M. K.
Projects: SoHO-MDI

Publication Status: Geophys. Res. Lett., in press
Last Modified: 2007-12-03 11:48
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Subject will be restored when possible  

Manolis K. Georgoulis   Submitted: 2007-12-03 11:48

Using an efficient magnetic complexity index in the active-region solar photosphere, we quantify the preflare strength of the photospheric magnetic polarity inversion lines in 23 eruptive active regions with flare/CME/ICME events tracked all the way from the Sun to the Earth. We find that active regions with more intense polarity inversion lines host statistically stronger flares and faster, more impulsively accelerated, CMEs. No significant correlation is found between the strength of the inversion lines and the flare soft X-ray rise times, the ICME transit times, and the peak Dst indices of the induced geomagnetic storms. Corroborating these and previous results, we speculate on a possible interpretation for the connection between source active regions, flares, and CMEs. Further work is needed to validate this concept and uncover its physical details.

Authors: Georgoulis, M. K.
Projects: SoHO-MDI

Publication Status: Geophys. Res. Lett., in press
Last Modified: 2007-12-03 14:51
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Survey of Magnetic Helicity Injection in Regions Producing X-Class Flares  

Manolis K. Georgoulis   Submitted: 2007-08-09 13:04

Virtually all X-class flares produce a coronal mass ejection (CME), and each CME carries magnetic helicity into the heliosphere. Using magnetograms from the Michelson Doppler Imager on the Solar and Heliospheric Observatory, we surveyed magnetic helicity injection into 48 X-flare producing active regions recorded by the MDI between 1996 July and 2005 July. Magnetic helicity flux was calculated according to the method of Chae for the 48 X-flaring regions and for 345 non-X-flaring regions. Our survey revealed that a necessary condition for the occurrence of an X flare is that the peak helicity flux has a magnitude > 6 x 1036 Mx^2/s. X-flaring regions also consistently had a higher net helicity change during the ~ 6-day measurement intervals than non-flaring regions. We find that the weak hemispherical preference of helicity injection, positive in the south and negative in the north, is caused by the solar differential rotation, but it tends to be obscured by the intrinsic helicity injection which is more disorganized and tends to be of opposite sign. An empirical fit to the data shows that the injected helicity over the range 1039 - 1043 Mx^2/s is proportional to magnetic flux squared. Similarly, over a range of 0.3 to 3000 days, the time required to generate the helicity in a CME is inversely proportional to the magnetic flux squared. Most of the X-flare regions generated the helicity needed for a CME in a few days to a few hours.

Authors: LaBonte, B. J., Georgoulis, M. K., & Rust, D. M.
Projects: SoHO-MDI

Publication Status: ApJ, in press
Last Modified: 2007-08-10 11:00
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Automatic Active-Region Identification and Azimuth Disambiguation of the SOLIS/VSM Full-Disk Vector Magnetograms  

Manolis K. Georgoulis   Submitted: 2007-06-29 09:49

The Vector Spectromagnetograph (VSM) of the NSO's Synoptic Optical Long-Term Investigations of the Sun (SOLIS) facility is now operational and obtains the first-ever vector magnetic field measurements of the entire visible solar hemisphere. To fully exploit the unprecedented SOLIS/VSM data, however, one must first address two critical problems: first, the study of solar active regions requires an automatic, physically intuitive, technique for active-region identification in the solar disk. Second, use of active-region vector magnetograms requires removal of the azimuthal 180°-ambiguity in the orientation of the transverse magnetic field component. Here we report on an effort to address both problems simultaneously and efficiently. To identify solar active regions we apply an algorithm designed to locate complex, flux-balanced, magnetic structures with a dominant E-W orientation on the disk. Each of the disk portions corresponding to active regions is thereafter extracted and subjected to the Nonpotential Magnetic Field Calculation (NPFC) method that provides a physically-intuitive solution of the 180°-ambiguity. Both algorithms have been integrated into the VSM data pipeline and operate in real time, without human intervention. We conclude that this combined approach can contribute meaningfully to our emerging capability for full-disk vector magnetography as pioneered by SOLIS today and will be carried out by ground-based and space-borne magnetographs in the future.

Authors: Georgoulis, M. K., Raouafi, N.-E., and Henney, C. J.
Projects: None

Publication Status: Proc. NSO Workshop 24, ASP Conf. Series, submitted
Last Modified: 2007-06-29 10:08
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Magnetic Energy and Helicity Budgets in the Active-Region Solar Corona. I. Linear Force-Free Approximation  

Manolis K. Georgoulis   Submitted: 2007-06-29 09:47

We self-consistently derive the magnetic energy and relative magnetic helicity budgets of a three-dimensional linear force-free magnetic structure rooted in a lower boundary plane. For the potential magnetic energy we derive a general expression that gives results practically equivalent to those of the magnetic Virial theorem. All magnetic energy and helicity budgets are formulated in terms of surface integrals applied to the lower boundary, thus avoiding computationally intensive three-dimensional magnetic field extrapolations. We analytically and numerically connect our derivations with classical expressions for the magnetic energy and helicity, thus presenting a so-far lacking unified treatment of the energy/helicity budgets in the constant α approximation. Applying our derivations to photospheric vector magnetograms of an eruptive and a noneruptive solar active regions, we find that the most profound quantitative difference between these regions lies in the estimated free magnetic energy and relative magnetic helicity budgets. If this result is verified with a large number of active regions, it will advance our understanding of solar eruptive phenomena. We also find that the constant α approximation gives rise to large uncertainties in the calculation of the free magnetic energy and the relative magnetic helicity. Therefore, care must be exercised when this approximation is applied to photospheric magnetic field observations. Despite its shortcomings, the constant α approximation is adopted here because this study will form the basis of a comprehensive nonlinear force-free description of the energetics and helicity in the active-region solar corona, which is our ultimate objective.

Authors: Georgoulis, M. K., and LaBonte, B. J.
Projects: None

Publication Status: ApJ, in press
Last Modified: 2007-06-29 10:08
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Quantitative Forecasting of Major Solar Flares  

Manolis K. Georgoulis   Submitted: 2007-04-06 12:24

We define the effective connected magnetic field, Beff, a single metric of the flaring potential in solar active regions. We calculated Beff for 298 active regions (93 X- and M-flaring, 205 nonflaring) as recorded by SoHO/MDI during a 10-year period covering much of solar cycle 23. We find that Beff is a robust criterion for distinguishing flaring from nonflaring regions. A well-defined twelve-hour conditional probability for major flares depends solely on Beff. This probability exceeds 0.95 for M-class and X-class flares if Beff > 1600 G and Beff > 2100 G, respectively, while the maximum calculated Beff-values are near 4000 G. Active regions do not give M-class and X-class flares if Beff < 200 G and Beff < 750 G, respectively. We conclude that Beff is an efficient flare-forecasting criterion that can be computed on a timely basis from readily available data.

Authors: Georgoulis, M. K., and Rust, D. M.
Projects: SoHO-MDI

Publication Status: ApJ Letters, in press
Last Modified: 2007-04-06 19:46
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Reconstruction of an Inductive Velocity Field Vector from Doppler Motions and a Pair of Solar Vector Magnetograms  

Manolis K. Georgoulis   Submitted: 2005-09-12 10:00

We outline a general methodology to infer the inductive velocity field vector in solar active regions. For the first time, both the field-aligned and the cross-field velocity components are reconstructed. The cross-field velocity solution accounts for the changes of the vertical magnetic field seen between a pair of successive active-region vector magnetograms via the ideal induction equation. The field-aligned velocity is obtained using the Doppler velocity and the calculated cross-field velocity. Solving the ideal induction equation in vector magnetograms measured at a given altitude in the solar atmosphere is an under-determined problem. In response, our general formalism allows the use of any additional constraint for the inductive cross-field velocity to enforce a unique solution in the induction equation. As a result, our methodology can give rise to new velocity solutions besides the one presented here. To constrain the induction equation, we use a special case of the minimum structure approximation that was introduced in previous studies and is already employed here to resolve the 180°-ambiguity in the input vector magnetograms. We reconstruct the inductive velocity for three active regions, including NOAA AR 8210 for which previous results exist. Our solution believably reproduces the horizontal flow patterns in the studied active regions but breaks down in cases of localized rapid magnetic flux emergence or submergence. Alternative approximations and constraints are possible and can be accommodated into our general formalism

Authors: Manolis K. Georgoulis & Barry J. LaBonte
Projects: None

Publication Status: ApJ, in press
Last Modified: 2005-09-12 10:00
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A New Technique for a Routine Azimuth Disambiguation of Solar Vector Magnetograms  

Manolis K. Georgoulis   Submitted: 2005-06-29 14:34

We introduce a non-potential magnetic field calculation (NPFC) technique to perform azimuth disambiguation in solar vector magnetograms. It is shown that resolving the 180-degree ambiguity would be a numerically fully determined problem if the vertical electric current density was known a priori. Since this is not the case, we explicitly impose a minimum-magnitude current density solution. The NPFC disambiguation is otherwise assumption-free, with the quality of the results depending on the quality of the measurements. The NPFC method first infers the non-potential magnetic field component responsible for the assumed vertical currents and then determines the vertical magnetic field whose potential extrapolation added to the non-potential field best reproduces the observationally inferred horizontal magnetic field. The technique is fast, effective, and physically sound, so it may be instrumental to a routine, real-time, disambiguation of future space-borne solar vector magnetograms.

Authors: Georgoulis, M. K.
Projects: None

Publication Status: ApJ Letters, in press
Last Modified: 2005-06-29 14:34
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Turbulence in the Solar Atmosphere: Manifestations and Diagnostics via Solar Image Processing  

Manolis K. Georgoulis   Submitted: 2005-02-10 09:25

Intermittent magnetohydrodynamical turbulence is most likely at work in the magnetized solar atmosphere. As a result, an array of scaling and multi-scaling image processing techniques can be used to measure the expected self-organization of solar magnetic fields. While these techniques advance our understanding of the physical system at work, it is unclear whether they can be used to predict solar eruptions, thus obtaining a practical significance for space weather. We address part of this problem by focusing on solar active regions and by investigating the usefulness of scaling and multi-scaling image processing techniques in solar flare prediction. Since solar flares exhibit spatial and temporal intermittency, we suggest that they are the products of instabilities subject to a critical threshold in a turbulent magnetic configuration. The identification of this threshold in scaling and multi-scaling spectra would then contribute meaningfully to the prediction of solar flares. We find that the fractal dimension of solar magnetic fields and their multifractal spectrum of generalized correlation dimensions do not have significant predictive ability. The respective multifractal structure functions and their inertial-range scaling exponents, however, probably provide some statistical distinguishing features between flaring and non-flaring active regions. More importantly, the temporal evolution of the above scaling exponents in flaring active regions probably shows a distinct behavior starting a few hours prior to a flare and therefore this temporal behavior may be practically useful in flare prediction. The results of this study need to be validated by more comprehensive works over a large number of solar active regions. Sufficient statistics may also establish critical thresholds in the values of the multifractal structure functions and/or their scaling exponents above which a flare may be predicted with a high level of confidence.

Authors: Manolis K. Georgoulis
Projects: None

Publication Status: Solar Physics, in press
Last Modified: 2005-02-10 09:25
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Reconstruction of a Magnetohydrodynamic Velocity Field Vector from Doppler Motions and a Pair of Solar Vector Magnetograms  

Manolis K. Georgoulis   Submitted: 2004-09-28 15:30

We introduce a minimum structure reconstruction technique to infer the velocity field vector in solar active regions. The velocity solution accounts for the changes of the vertical magnetic field seen in a pair of active region vector magnetograms via the ideal induction equation. The minimum structure approximation, already introduced to resolve the 180-degree ambiguity in the input magnetograms,assumes space-filling magnetic fields without resorting to any force-free or minimum energy assumption and is herein extended to support the velocity field calculation. The minimum structure analysis simultaneously determines the field-aligned flows and enforces a unique cross-field velocity solution of the induction equation. Moreover, it is completely independent from the local correlation tracking velocity. We reconstruct the minimum structure velocity field using photospheric vector magnetograms of three active regions, including NOAA AR 8210 for which previous results exist. All different techniques reasonably agree for the flow patterns that are contributed by the solution of the induction equation, but the minimum structure solution provides the field-aligned flows besides the cross-field flows. The minimum structure solution does not reproduce the apparent flows caused by inclined emerging magnetic structures, which are picked up by the local correlation tracking techniques. This is because tracking techniques attribute a fictitious horizontal velocity to motions caused by purely vertical flows.

Authors: Manolis K. Georgoulis & Barry J. LaBonte
Projects: None

Publication Status: ApJ, submitted
Last Modified: 2004-09-28 15:30
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Vertical Lorentz Force and Cross-Field Currents in the Photospheric Magnetic Fields of Solar Active Regions  

Manolis K. Georgoulis   Submitted: 2004-06-16 13:40

We demonstrate that the vertical Lorentz force and a corresponding lower limit of the cross-field electric current density can be calculated from vector magnetograms of solar active regions obtained at a single height in the solar atmosphere, provided that the vertical gradient of the magnetic field strength is known at this height. We use a predicted vertical magnetic field gradient, derived from a previous analysis. By testing various force-free solutions, we find that the numerical accuracy of our method is satisfactory. Applying the method to active-region photospheric vector magnetograms we find vertical Lorentz forces ranging from several hundredths to a few tenths of the typical photospheric gravitational force, and typical cross-field current densities up to several tens of mA;m-2. The typical vertical current density is found to be 2-3 times smaller, of the order (10-15);mA;m-2. These differences are above the associated uncertainties. The values of the cross-field currents decrease in an averaged vector magnetogram, but the ratio of the cross-field to the vertical current density increases, also above the uncertainties. We conclude that the photospheric active-region magnetic fields are not force-free, contrary to the conjectures of some recent studies.

Authors: Manolis K. Georgoulis & Barry J. LaBonte
Projects:

Publication Status: ApJ (in press)
Last Modified: 2004-07-19 08:41
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On the Self-Similarity of Unstable Magnetic Discontinuities inSolar Active Regions  

Manolis K. Georgoulis   Submitted: 2004-01-20 17:12

We investigate the statistical properties of possible magnetic discontinuities in two solar active regions over the course of several hours. We use linear force-free extrapolations to calculate the three-dimensional magnetic structure in the active regions. Magnetic discontinuities are identified using various selection criteria. Independently of the selection criterion, we identify large numbers of magnetic discontinuities whose free magnetic energies and volumes obey well-formed power-law distribution functions. The power-law indices for the free energies are in the range [-1.6,-1.35], in remarkable agreement with the power-law indices found in the occurrence frequencies of solar flare energies. This agreement and the strong self-similarity of the volumes that are likely to host flares suggests that the observed statistics of flares may be the natural outcome of a pre-existing spatial self-organization accompanying the energy fragmentation in solar active regions. We propose a dynamical picture of flare triggering consistent with recent observations by reconciling our results with the concepts of percolation theory and self-organized criticality. These concepts rely on self-organization, which is expected from the fully turbulent state of the magnetic fields in the solar atmosphere.

Authors: Vlahos, L. and Georgoulis, M. K.
Projects: None

Publication Status: ApJ Letters, in press
Last Modified: 2004-01-20 17:12
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On the Resolution of the Azimuthal Ambiguity in Vector Magnetograms of Solar Active Regions  

Manolis K. Georgoulis   Submitted: 2003-08-22 16:37

We introduce a novel, semi-analytical ``structure minimization'' technique to resolve the azimuthal ambiguity of 180 degrees, intrinsic in solar vector magnetic field measurements. Structure minimization attempts to minimize the complexity in solar active regions {it (i)} by approximating the sunspot magnetic fields with an axisymmetric force-free solution, and {it (ii)} by minimizing the magnitude of ``sheath'' currents wrapped around the emerged flux tubes in the solar atmosphere. The structure minimization method consists of two steps: {it First}, we construct a structure minimization function, relying on physical and geometrical arguments. This function includes only derivatives of the unambiguous magnetic field strength and hence it has only two values at any given location, independent from its corresponding values elsewhere on the plane of the observations. The structure minimization function yields a preliminary, local ambiguity solution when minimized. {it Second}, we subject the initial solution to a numerical analysis that yields a global ambiguity solution and ensures maximum continuity of the resulting magnetic field vector. The structure minimization algorithm reduces the required computation to a small fraction of that required by existing techniques. Moreover, structure minimization is disentangled from any explicit use of potential or linear force-free extrapolations for the first time. All other ambiguity resolution techniques rely explicitly on such extrapolations to a larger or a lesser degree. We apply structure minimization to four active regions, located at various distances from disk center, and we compare the results with those of the ``energy minimization'' method of Metcalf (1994). We find correlation coefficients between the two azimuth solutions in excess of 90% for strong field regions. The excellent agreement between the two methods is not a function of the distance of an active region from disk center, but only of the complexity of the photospheric magnetic field vector. Structure minimization breaks down only when an active region is so close to the solar limb that the coordinate transformation yields extremely large sizes for the heliographic plane. A by-product of the structure minimization method is the calculation of an ambiguity-free vertical field gradient which allows study of the variation of the magnetic field with height and an estimate of the magnetic scale height. We find qualitative agreement with recent studies that the scale height distribution broadens tremendously in the sunspot penumbrae, as opposed to the distribution in the umbrae which is much narrower and centered around much smaller scale heights. This suggests that our analytical estimation of the vertical gradient is consistent with physical measurements. The structure minimization method is fast and fully automated. Therefore, it may be used for a near real-time processing of acquired solar vector magnetograms; a task not possible in the past. This feature might be of specific interest to both existing and future ground-based and space-borne solar missions.

Authors: Georgoulis, M. K., LaBonte, B. J., and Metcalf, Th. R.
Projects: None

Publication Status: Submitted to ApJ
Last Modified: 2003-08-22 16:37
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Emerging Flux and the Heating of Coronal Loops  

Manolis K. Georgoulis   Submitted: 2003-08-22 16:31

We use data collected by a multi-wavelength campaign of observations to describe how the fragmented, asymmetric emergence of magnetic flux in NOAA active region 8844 triggers the dynamics in the active-region atmosphere and leads to the formation and heating of coronal loops. Observations of various instruments on board {it Yohkoh}, SOHO, and TRACE complement high-resolution observations of the balloon-borne Flare Genesis Experiment, obtained on January 25, 2000. We find that coronal loops appeared 6 pm 2;hr after the first detection of emerging magnetic flux. The loops evolved rapidly when the active region entered its impulsive flux emergence phase. In the low chromosphere, flux emergence was reflected in intense Ellerman bomb activity. Besides chromosphere, we find that Ellerman bombs may also heat the transition region, by contributing to the moss emission. Areas prolific in Ellerman bombs show moss sim 100% brighter than areas without Ellerman bombs. Only the strongest Ellerman bombs can heat their surroundings to coronal temperatures. In the corona, we find a spatio-temporal anti-correlation between the soft X-ray (SXT) and the extreme ultraviolet (TRACE) loops: {it First}, the SXT loops preceded the appearance of the TRACE loops by 30-40;min. {it Second}, the TRACE loops had different shapes and different footpoints compared to the SXT loops. The SXT loops were rooted in relatively strong field areas (several 102;G to about 103;G) characterized by bright moss, whereas the TRACE loops were rooted in relatively weaker field areas and a fainter moss. {it Third}, the SXT loops were longer and higher than the TRACE loops although a particular group of high TRACE loops did not have a SXT counterpart. We conclude that the TRACE and the SXT loops were formed independently. The TRACE loops matched well with the low-lying magnetic canopy of the emerging flux region, and thus heating was probably concentrated close to their footpoints. The SXT loops brightened in response to coronal interaction of emerging magnetic dipoles, so heating of these loops was due to magnetic reconnection in the corona. In summary, magnetic flux emergence triggered a variety of coupled activity, from the photosphere to the active-region corona. We uncover links between the various aspects of this activity which lead to a unified picture of the evolution in the active region.

Authors: Schmieder, B., Rust, D. M., Georgoulis, M. K., Demoulin, P., and Bernasconi, P. N.
Projects: Soho-MDI,Yohkoh-SXT

Publication Status: Submitted to ApJ
Last Modified: 2003-08-22 16:31
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