Solar Flares as Cascades of Reconnecting Magnetic Loops

Hughes, David; Paczuski, Maya; Dendy, R. O.; Helander, P.; McClements, K. G.

doi:10.1103/physrevlett.90.131101

Cited by 89 publications

(130 citation statements)

References 24 publications

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“…Solar flares show scale invariance in their energy release statistics over several orders of magnitude (Aschwanden, 2000;Schwanden and Parnell, 2002) which has been discussed in terms of Self-Organized Criticality (SOC, see e.g. Lu and Hamilton, 1991;Hughes et al, 2003;Dendy et al, 2007). There is also recent evidence, that we review here, in noncascade quantities, such as magnetic energy density, of a signature within the inertial range that shows scaling that correlates with the level of magnetic complexity in the corona Kiyani et al, 2007).…”

Section: S C Chapman Et Al: Solar Wind and Solar Cyclementioning

confidence: 97%

Solar cycle dependence of scaling in solar wind fluctuations

Chapman

Hnat

Kiyani

2008

Nonlin. Processes Geophys.

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Abstract. In this review we collate recent results for the statistical scaling properties of fluctuations in the solar wind with a view to synthesizing two descriptions: that of evolving MHD turbulence and that of a scaling signature of coronal origin that passively propagates with the solar wind. The scenario that emerges is that of coexistent signatures which map onto the well known "two component" picture of solar wind magnetic fluctuations. This highlights the need to consider quantities which track Alfvénic fluctuations, and energy and momentum flux densities to obtain a complete description of solar wind fluctuations.

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Section: S C Chapman Et Al: Solar Wind and Solar Cyclementioning

confidence: 97%

Solar cycle dependence of scaling in solar wind fluctuations

Chapman

Hnat

Kiyani

2008

Nonlin. Processes Geophys.

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“…One simulation produced a broken powerlaw distribution with a slope of α P = 3.5 for the smallest events, interpreted as nanoflare regime, while a flatter slope of α P = 1.8 was found for the larger flares (Vlahos et al 1995), a difference that is attributed to the anisotropic next-neighbor interactions applied therein. Another study simulated solar flare events as cascades of reconnecting magnetic loops, with the finding of a powerlaw slope of α E = 3.0 for the released energies (Hughes et al 2003). Interacting loops with a length scale L are bisected during a reconnection step into two shorter scales L/2, and the released energies are defined in terms of the length scale therein, i.e., E ∝ L, for which our model predicts indeed an occurrence frequency distribution of N(E) ∝ N(L) ∝ L −S ∝ L −3 (Eq.…”

Section: Observations Of Solar Flaresmentioning

confidence: 99%

A statistical fractal-diffusive avalanche model of a slowly-driven self-organized criticality system

Aschwanden

2012

A&A

118

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Aims. We develop a statistical analytical model that predicts the occurrence frequency distributions and parameter correlations of avalanches in nonlinear dissipative systems in the state of a slowly-driven self-organized criticality (SOC) system. Methods. This model, called the fractal-diffusive SOC model, is based on the following four assumptions: (i) the avalanche size L grows as a diffusive random walk with time T , following L ∝ T 1/2 ; (ii) the energy dissipation rate f (t) occupies a fractal volume with dimension D S ; (iii) the mean fractal dimension of avalanches in Euclidean space S = 1, 2, 3 is D S ≈ (1 + S )/2; and (iv) the occurrence frequency distributions N(x) ∝ x −αx based on spatially uniform probabilities in a SOC system are given by N(L) ∝ L −S , with S being the Eudlidean dimension. We perform cellular automaton simulations in three dimensions (S = 1, 2, 3) to test the theoretical model. Results. The analytical model predicts the following statistical correlations: F ∝ L D S ∝ T D S/2 for the flux, P ∝ L S ∝ T S /2 for the peak energy dissipation rate, and E ∝ FT ∝ T 1+D S /2 for the total dissipated energy; the model predicts powerlaw distributions for all parameters, with the slopes α T = (1 + S )/2, α F = 1 + (S − 1)/D S , α P = 2 − 1/S , and α E = 1 + (S − 1)/(D S + 2). The cellular automaton simulations reproduce the predicted fractal dimensions, occurrence frequency distributions, and correlations within a satisfactory agreement within ≈10% in all three dimensions. Conclusions. One profound prediction of this universal SOC model is that the energy distribution has a powerlaw slope in the range of α E = 1.40−1.67, and the peak energy distribution has a slope of α P = 1.67 (for any fractal dimension D S = 1, ..., 3 in Euclidean space S = 3), and thus predicts that the bulk energy is always contained in the largest events, which rules out significant nanoflare heating in the case of solar flares.

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“…Subsequently, it has been shown that many networks also have a probability distribution for the number of connections to a node (in network parlance, the degree distribution) that has a power-law tail. Such 'scale-free' networks 25 have been found in an impressively diverse range of fields, including astrophysics, 26 geophysics, 27 information technology, 28 biochemistry, 29,30 ecology 31 and sociology. 32 The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Characterizing the network topology of the energy landscapes of atomic clusters

Doye¹,

Massen²

2005

The Journal of Chemical Physics

103

118

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By dividing potential energy landscapes into basins of attractions surrounding minima and linking those basins that are connected by transition state valleys, a network description of energy landscapes naturally arises. These networks are characterized in detail for a series of small LennardJones clusters and show behaviour characteristic of small-world and scale-free networks. However, unlike many such networks, this topology cannot reflect the rules governing the dynamics of network growth, because they are static spatial networks. Instead, the heterogeneity in the networks stems from differences in the potential energy of the minima, and hence the hyperareas of their associated basins of attraction. The low-energy minima with large basins of attraction act as hubs in the network. Comparisons to randomized networks with the same degree distribution reveals structuring in the networks that reflects their spatial embedding.

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Solar Flares as Cascades of Reconnecting Magnetic Loops

Cited by 89 publications

References 24 publications

Solar cycle dependence of scaling in solar wind fluctuations

Solar cycle dependence of scaling in solar wind fluctuations

A statistical fractal-diffusive avalanche model of a slowly-driven self-organized criticality system

Characterizing the network topology of the energy landscapes of atomic clusters

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