Multifractal Measure of the Solar Magnetic Field

Lawrence, J. K.; Ruzmaikin, A.; Cadavid, A. C.

doi:10.1086/173360

Cited by 86 publications

(56 citation statements)

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“…This conclusion is consistent with the previous result by Lawrence, Ruzmaikin, & Cadavid (1993). The degree of intermittency (the interval of allowed h) of the magnetic field in an active region increases as the flaring activity rises.…”

Section: Calculations Of Structure Functions For Eight Active Regionssupporting

confidence: 93%

Scaling Behavior of Structure Functions of the Longitudinal Magnetic Field in Active Regions on the Sun

Abramenko

Yurchyshyn

Wang

et al. 2002

ApJ

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In the framework of a refined Kolmogorov hypothesis, the scaling behavior of the B z -component of the photospheric magnetic field is analyzed and compared with flaring activity in solar active regions. We use Solar and Heliospheric Observatory Michelson Doppler Imager, Huairou (China), and Big Bear measurements of the B z -component in the photosphere for nine active regions. We show that there is no universal behavior in the scaling of the B z -structure functions for different active regions. Our previous study has shown that scaling for a given active region is caused by intermittency in the field, ðBÞ ðxÞ, describing the magnetic energy dissipation. When intermittency is weak, the B z field behaves as a passive scalar in the turbulent flow, and the energy dissipation is largely determined by the dissipation of kinetic energy in the active regions with low flare productivity. However, when the field ðBÞ ðxÞ is highly intermittent, the structure functions behave as transverse structure functions of a fully developed turbulent vector field, and the scaling of the energy dissipation is mostly determined by the dissipation of the magnetic energy (active regions with strong flaring productivity). Based on this recent result, we find that the dissipation spectrum of the B z -component is strongly related to the level of flare productivity in a solar active region. When the flare productivity is high, the corresponding spectrum is less steep. We also find that during the evolution of NOAA Active Region 9393, the B z dissipation spectrum becomes less steep as the active region's flare activity increases. Our results suggest that the reorganization of the magnetic field at small scales is also relevant to flaring: the relative fraction of small-scale fluctuations of magnetic energy dissipation increases as an active region becomes prone to producing strong flares. Since these small-scale changes seem to begin long before the start of a solar flare, we suggest that the relation between scaling exponents, calculated by using only measurements of the B z -component, and flare productivity of an active region can be used to monitor and forecast flare activity.

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Section: Calculations Of Structure Functions For Eight Active Regionssupporting

confidence: 93%

Scaling Behavior of Structure Functions of the Longitudinal Magnetic Field in Active Regions on the Sun

Abramenko

Yurchyshyn

Wang

et al. 2002

ApJ

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“…Earlier attempts to do this have indicated a high degree of scale invariance (Lawrence et al 1993(Lawrence et al , 1996Cadavid et al 1994;Stenflo & Holzreuter 2002, 2003aJanßen et al 2003;Pietarila Graham et al 2009), which is characteristic of a multi-fractal. Our discovery of a magnetic dichotomy, however, suggests a scenario in the spatially unresolved domain that has similarity with the idealized 2-component model, with the flux split into two discrete states, a collapsed and an uncollapsed state, each with well separated distribution functions, one concentrated around high field strengths (of order 1 kG), the other peaked at zero field strength.…”

Section: Discussionmentioning

confidence: 99%

Distribution functions for magnetic fields on the quiet Sun

Stenflo

2010

A&A

144

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The statistical properties of the highly structured magnetic field of the quiet Sun are best described in terms of distribution functions, in particular the probability density functions (PDF) for the flux densities and the angular distribution for the orientations of the field vector. They are needed to test the validity of various MHD simulations, but past determinations have led to contradictory results. A main reason for these difficulties lies in the circumstance that the magnetic structuring continues on scales that are much smaller than the telescope resolution, and that this structuring strongly affects the quantities averaged over each pixel due to the non-linear relation between polarization and magnetic field. Here we use a Hinode SOT/SP data set for the disk center of the quiet Sun to explore the complex behavior of the polarized 6301-6302 Å line system and identify the observables that allow the most robust determinations of inclination angles and flux densities. These observables are then used to derive the empirical distribution functions. Our Stokes V line ratio analysis leads us to an unexpected discovery: a magnetic dichotomy with two distinct populations, representing strong (kG) and weak fields. This can be understood in terms of the convective collapse mechanism, which makes the Sun's magnetic flux end up in two states: collapsed and uncollapsed. With the linear-to-circular polarization ratio as a robust observable for the inclination angles, we find that the angular distribution is extremely peaked around the vertical direction for the largest flux densities, but gradually broadens as we go to smaller flux densities, to become asymptotically isotropic at zero flux density. The PDF for the vertical flux density, after accounting for the smearing effect of measurement noise, is found to have an extremely narrow core peak centered at zero flux density, which can be analytically represented by a stretched exponential. The PDF wings are extended and decline quadratically. The PDFs for the horizontal and total flux densities have a similar behavior. In particular we demonstrate that earlier claims that the PDF for the total flux density increases from small values at zero flux density to have a maximum significantly shifted from zero is an artefact of measurement noise.

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“…The fractal dimension of a multifractal set is the maximum fractal dimension of the fractal subset that comprise the multifractal (Mandelbrot 1983). Numerous studies have revealed the multifractality of solar ARs, but also of the Quiet-Sun magnetic fields (e.g., Lawrence, Ruzmaikin, and Cadavid 1993;Cadavid et al, 1994;Lawrence, Cadavid, and Ruzmaikin 1996;Abramenko et al, 2001;Abramenko et al, 2002).…”

Section: Solar Magnetic Fieldsmentioning

confidence: 99%

Turbulence In The Solar Atmosphere: Manifestations And Diagnostics Via Solar Image Processing

Georgoulis

2005

Sol Phys

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Abstract. 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 nonflaring 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.

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Multifractal Measure of the Solar Magnetic Field

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Cited by 86 publications

References 0 publications

Scaling Behavior of Structure Functions of the Longitudinal Magnetic Field in Active Regions on the Sun

Scaling Behavior of Structure Functions of the Longitudinal Magnetic Field in Active Regions on the Sun

Distribution functions for magnetic fields on the quiet Sun

Turbulence In The Solar Atmosphere: Manifestations And Diagnostics Via Solar Image Processing

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