Sunspots. The model of “elastic sceletons”. Estimation of sunspot umbra fractal dimension

Chumak, O. V.; Chumak, Z. N.

doi:10.1080/10556799608205449

Cited by 5 publications

(10 citation statements)

References 1 publication

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“…Scale free fractal dimensions of 2.09 ± 0.42 and 1.72 ± 0.4 were found respectively. This value was higher than the value determined by Chumak and Chumak (1996) indicating that the complexity in morphology indicated by the fractal dimension between the umbra and penumbra followed each other in time as well. …”

contrasting

confidence: 47%

“…To determine the fractal dimensions of the sunspot's umbrae and penumbrae, the areaperimeter relation as defined by Chumak and Chumak (1996) was used.…”

Section: Results and Analysismentioning

confidence: 99%

“…spatially or temporally. This study has focused on the structure of sunspots spatially, similar to the analysis from Chumak and Chumak (1996) and unlike the studies by Deng et al (2016c) which focused on the time series variations. Uritsky and Davila (2012) however studied the spatio-temporal evolution of unipolar and bipolar photospheric regions to analyze the fractal dimensions' multiscale behavior.…”

Section: Discussionmentioning

confidence: 99%

“…In this paper we have followed the analysis of Chumak and Chumak (1996) but, applied it to the umbral as well as the penumbral region as well. Fractals can help to determine the nature of the sunspot morphology and in so doing can perhaps help in predicting their evolution from the stage of their formation to their disappearance.…”

Section: Introductionmentioning

confidence: 99%

“…Implication of turbulent structure by use of fractal analysis to sunspots was studied by Chumak and Chumak (1996) where they determined the fractal dimension of the solar sunspot umbra using cross-section area -outline length method which we have used. They found a value for the fractal dimension 1.35 which corresponded to turbulent structure in percolation theory.…”

Section: Introductionmentioning

confidence: 99%

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Fractal Dimensions of Umbral and Penumbral Regions of Sunspots

2017

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Abstract:The images of sunspots in sixteen active regions taken at the UCCI Observatory in Grand Cayman during June -November 2015, were used to determine their fractal dimensions using the perimeter-area method for the umbral and the penumbral region. Scale free fractal dimensions of 2.09 ± 0.42 and 1.72 ± 0.4 were found respectively. This value was higher than the value determined by Chumak and Chumak (1996) indicating that the complexity in morphology indicated by the fractal dimension between the umbra and penumbra followed each other in time as well.

show abstract

contrasting

confidence: 47%

“…To determine the fractal dimensions of the sunspot's umbrae and penumbrae, the areaperimeter relation as defined by Chumak and Chumak (1996) was used.…”

Section: Results and Analysismentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fractal Dimensions of Umbral and Penumbral Regions of Sunspots

2017

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A Fractal Analysis of Magnetograms Within Active Regions

Rajkumar

Haque

2020

Sol Phys

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The magnetograms of sixteen Active Regions, observed during June -November 2015, were obtained from the Joint Science Operations Center and used to determine the fractal dimensions of various magnetic field groups. The fields were divided into strong (positive and negative) and weak (positive and negative) groupings. The area-perimeter method was used to determine the fractal dimensions for the umbral and penumbral regions of the magnetograms. The fractal dimensions were found to be 1.79 ± 0.49 and 1.96 ± 0.29 for strong and weak magnetic fields respectively. When compared to the umbral and penumbral fractal dimensions determined by (Rajkumar, Haque and Hrudey, 2017) using white light images, an inverse relationship was found, with the umbra showing lower fractal dimensions than the penumbra for the magnetic field groups compared to the intensity images. This directly implies that there is greater complexity in the penumbral magnetic field groupings than the umbral region. This has implications for models that constrain how the magnetic field groups are contained in the cooler umbral regions.

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Self-similar and self-affine structures in the observational data on solar activity

Chumak¹

2005

Astronomical & Astrophysical Transactions

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Stochastic self-similarity and self-affinity in the data on the solar activity phenomena is discussed in this paper. The following results are given and discussed. Firstly, the area-perimeter method was applied to obtain the fractal dimension values of solar spot umbras and of equal-intensity field lines in solar active regions (ARs). The fractal dimension value D 0 = 1.35 ± 0.03 has been obtained for sunspot umbras. Field lines of equal intensity have different values of fractal dimensions for north and south polarities. Secondly, it is shown that the fractal dimension extracted from correlation between the magnetic flux and its cross-sectional area (i.e. a photosphere) is temporally invariant for an AR, but the fractal dimensions can be considerably different for various ARs. Thirdly, the multifractal nature of ARs magnetic fields was confirmed by a study of the scaling properties of their Renyi entropy. Fourthly, the R/S analysis was used for the Wolf series with purpose of estimating the long-time 'memory' structure of this series. Time periods with different frequency bands were found in the series. Fifthly, the Renyi entropy and the Higuchi method were used for the study of solar X-ray flux variations. It is shown that the fractal dimensions obtained with this algorithm can be used as a good X-ray index.

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Sunspots. The model of “elastic sceletons”. Estimation of sunspot umbra fractal dimension

Cited by 5 publications

References 1 publication

Fractal Dimensions of Umbral and Penumbral Regions of Sunspots

Fractal Dimensions of Umbral and Penumbral Regions of Sunspots

A Fractal Analysis of Magnetograms Within Active Regions

Self-similar and self-affine structures in the observational data on solar activity

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