Solar flares and avalanches in driven dissipative systems

Lu, Edward T.; Hamilton, Russell J.; McTiernan, J.; Bromund, K. R.

doi:10.1086/172966

Cited by 234 publications

(236 citation statements)

References 0 publications

Supporting

Mentioning

208

Contrasting

Unclassified

Order By: Relevance

“…This model is thus strongly anisotropic, with pseudo-local stability and redistribution, in the sense that these operators now act on nearestneighbors nodes located along each flux strand, rather than in the immediate spatial vicinity of the unstable sites. This is very different from the isotropic Lu et al (1993)-type SOC model used here for validation. Yet, the results compiled in Table 2 of Morales & Charbonneau (2008) for their highest resolution simulations reveal that the theoretical occurrence frequency distributions obtained herein, do hold within the stated uncertainties on the power-law fits.…”

contrasting

confidence: 56%

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

Aschwanden

2012

A&A

118

View full text Add to dashboard Cite

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.

show abstract

contrasting

confidence: 56%

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

Aschwanden

2012

A&A

118

View full text Add to dashboard Cite

show abstract

“…4) that could be characterized by a broken power law (see also Fig. 12 in Aschwanden et al 2000b), by an exponential rollover (Kadanoff et al 1989;Lu et al 1993;Charbonneau et al 2001), or by Pearson distributions (Podladchikova et al 2002). Deviations from pure power laws can also be seen in our synthesized frequency distributions (Figs.…”

Section: Discussion Of Methodical Uncertaintiesmentioning

confidence: 64%

“…While there are a lot of discussions and debates concerning whether the power-law slope of nanoflares energies lies above or below the critical limit of ¼ 2, which decides whether the bulk of energy lies in the smallest events (if > 2) or in the largest events (Hudson 1991), there has been no general theory developed that predicts the slope of nanoflares or flares. Numerical simulations of avalanches in a state of self-organized criticality produce power-law slopes of % 1:4 1:5 (Lu et al 1993;McIntosh et al 2002), but these cellular automata simulations are exclusively based on statistical probabilities of nearest neighbor interactions, and little effort has been made to relate the resulting size distributions to physical energy quantities relevant for nanoflares. A dimensional argument was used to explain an energy distribution of power-law slopes with a value of ¼ 1:5 (Litvinenko 1998a(Litvinenko , 1998b.…”

Section: Introductionmentioning

confidence: 99%

Nanoflare Statistics from First Principles: Fractal Geometry and Temperature Synthesis

Aschwanden

Parnell

2002

ApJ

171

154

View full text Add to dashboard Cite

We derive universal scaling laws for the physical parameters of flarelike processes in a low-plasma, quantified in terms of spatial length scales l, area A, volume V, electron density n e , electron temperature T e , total emission measure M, and thermal energy E. The relations are specified as functions of two independent input parameters, the power index a of the length distribution, NðlÞ / l Àa , and the fractal Haussdorff dimension D between length scales l and flare areas, AðlÞ / l D . For values that are consistent with the data, i.e., a ¼ 2:5 AE 0:2 and D ¼ 1:5 AE 0:2, and assuming the RTV scaling law, we predict an energy distribution NðEÞ / E À with a power-law coefficient of ¼ 1:54 AE 0:11. As an observational test, we perform statistics of nanoflares in a quiet-Sun region covering a comprehensive temperature range of T e % 1 4 MK. We detected nanoflare events in extreme-ultraviolet (EUV) with the 171 and 195 Å filters from the Transition Region and Coronal Explorer (TRACE), as well as in soft X-rays with the AlMg filter from the Yohkoh soft X-ray telescope (SXT), in a cospatial field of view and cotemporal time interval. The obtained frequency distributions of thermal energies of nanoflares detected in each wave band separately were found to have powerlaw slopes of % 1:86 AE 0:07 at 171 Å (T e % 0:7 1:1 MK), % 1:81 AE 0:10 at 195 Å (T e % 1:0 1:5 MK), and % 1:57 AE 0:15 in the AlMg filter (T e % 1:8 4:0 MK), consistent with earlier studies in each wavelength. We synthesize the temperature-biased frequency distributions from each wavelength and find a corrected powerlaw slope of % 1:54 AE 0:03, consistent with our theoretical prediction derived from first principles. This analysis, supported by numerical simulations, clearly demonstrates that previously determined distributions of nanoflares detected in EUV bands produced a too steep power-law distribution of energies with slopes of % 2:0 2:3 mainly because of this temperature bias. The temperature-synthesized distributions of thermal nanoflare energies are also found to be more consistent with distributions of nonthermal flare energies determined in hard X-rays ( % 1:4 1:6) and with theoretical avalanche models ( % 1:4 1:5).

show abstract

“…Cheng et al (1996) noted the similarity of the fluence distribution index for SGR 1806À20 with that determined empirically for earthquakes (Gutenberg & Richter 1956a, 1956b, 1965 and also for the distribution of earthquake energies found in computer simulations (Katz 1986). However, solar flares also show a size distribution, with exponents ranging from 1.53 to 1.73 (Crosby et al 1993;Lu et al 1993). Magnetars are not clearly physically analogous to either system; in magnetars, magnetic stresses are thought to result in stellar crust cracking, which is not the case for earthquakes.…”

Section: Similarities Between Axp and Sgr Burstsmentioning

confidence: 99%

A Comprehensive Study of the X‐Ray Bursts from the Magnetar Candidate 1E 2259+586

Gavriil

Kaspi

Woods

2004

ApJ

117

164

View full text Add to dashboard Cite

We present a statistical analysis of the X-ray bursts observed from the 2002 June 18 outburst of the anomalous X-ray pulsar (AXP) 1E 2259+586, observed with the Proportional Counter Array (PCA) aboard the Rossi X-Ray Timing Explorer. We show that the properties of these bursts are similar to those of soft gamma repeaters (SGRs). We find the following similarities: the burst durations follow a lognormal distribution that peaks at 99 ms, the differential burst fluence distribution is well described by a power law of index À1.7, the burst fluences are positively correlated with the burst durations, the distribution of waiting times is well described by a log normal distribution of mean 47 s, and the bursts are generally asymmetric, with shorter rise than fall times. However, we find several quantitative differences between the AXP and SGR bursts. Specifically, the AXP bursts we observed exhibit a wider range of durations, the correlation between burst fluence and duration is flatter than for SGRs, the observed AXP bursts are on average less energetic than observed SGR bursts, and the more energetic AXP bursts have the hardest spectra-the opposite of what is seen for SGRs. Unlike the case of SGRs, we find a correlation of burst phase with pulsed intensity. We conclude that the bursts are sufficiently similar that AXPs and SGRs can be considered united as a source class, yet there are some interesting differences that may help determine what physically differentiates the two closely related manifestations of neutron stars.

show abstract

Solar flares and avalanches in driven dissipative systems

Cited by 234 publications

References 0 publications

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

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

Nanoflare Statistics from First Principles: Fractal Geometry and Temperature Synthesis

A Comprehensive Study of the X‐Ray Bursts from the Magnetar Candidate 1E 2259+586

Contact Info

Product

Resources

About