The State of Self-Organized Criticality of the Sun During the Last 3 Solar Cycles. I. Observations

We analyze the occurrence frequency distributions of peak fluxes $P$, total fluxes $E$, and durations $T$ of solar flares over the last three solar cycles (during 1980--2010) from hard X-ray data of HXRBS/SMM, BATSE/CGRO, and RHESSI. From the synthesized data we find powerlaw slopes with mean values of $\alpha_P=1.72\pm0.08$ for the peak flux, $\alpha_E=1.60\pm0.14$ for the total flux, and $\alpha_T=1.98\pm0.35$ for flare durations. We find a systematic anti-correlation of the powerlaw slope of peak fluxes as a function of the solar cycle, varying with an approximate sinusoidal variation $\alpha_P(t)=\alpha_0+\Delta \alpha \cos{[2\pi (t-t_0)/T_{cycle}]}$, with a mean of $\alpha_0=1.73$, a variation of $\Delta \alpha =0.14$, a solar cycle period $T_{cycle}=12.6$ yrs, and a cycle minimum time $t_0=1984.1$. The powerlaw slope is flattest during the maximum of a solar cycle, which indicates a higher magnetic complexity of the solar corona that leads to an overproportional rate of powerful flares.Comment: subm. to Solar Physic

Recent Advances in Understanding Particle Acceleration Processes in Solar Flares

We review basic theoretical concepts in particle acceleration, with particular emphasis on processes likely to occur in regions of magnetic reconnection. Several new developments are discussed, including detailed studies of reconnection in three-dimensional magnetic field configurations (e.g., current sheets, collapsing traps, separatrix regions) and stochastic acceleration in a turbulent environment. Fluid, test-particle, and particle-in-cell approaches are used and results compared. While these studies show considerable promise in accounting for the various observational manifestations of solar flares, they are limited by a number of factors, mostly relating to available computational power. Not the least of these issues is the need to explicitly incorporate the electrodynamic feedback of the accelerated particles themselves on the environment in which they are accelerated. A brief prognosis for future advancement is offered.Comment: This is a chapter in a monograph on the physics of solar flares, inspired by RHESSI observations. The individual articles are to appear in Space Science Reviews (2011

Microflares and the Statistics of X-ray Flares

This review surveys the statistics of solar X-ray flares, emphasising the new views that RHESSI has given us of the weaker events (the microflares). The new data reveal that these microflares strongly resemble more energetic events in most respects; they occur solely within active regions and exhibit high-temperature/nonthermal emissions in approximately the same proportion as major events. We discuss the distributions of flare parameters (e.g., peak flux) and how these parameters correlate, for instance via the Neupert effect. We also highlight the systematic biases involved in intercomparing data representing many decades of event magnitude. The intermittency of the flare/microflare occurrence, both in space and in time, argues that these discrete events do not explain general coronal heating, either in active regions or in the quiet Sun.Comment: To be published in Space Science Reviews (2011

Energetic particle influence on the Earth's atmosphere

This manuscript gives an up-to-date and comprehensive overview of the effects of energetic particle precipitation (EPP) onto the whole atmosphere, from the lower thermosphere/mesosphere through the stratosphere and troposphere, to the surface. The paper summarizes the different sources and energies of particles, principally galactic cosmic rays (GCRs), solar energetic particles (SEPs) and energetic electron precipitation (EEP). All the proposed mechanisms by which EPP can affect the atmosphere are discussed, including chemical changes in the upper atmosphere and lower thermosphere, chemistry-dynamics feedbacks, the global electric circuit and cloud formation. The role of energetic particles in Earth’s atmosphere is a multi-disciplinary problem that requires expertise from a range of scientific backgrounds. To assist with this synergy, summary tables are provided, which are intended to evaluate the level of current knowledge of the effects of energetic particles on processes in the entire atmosphere

25 Years of Self-organized Criticality: Concepts and Controversies

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak’s own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld’s original papers

Measurements of electron anisotropy in solar flares using albedo with RHESSI X-ray data

The angular distribution of electrons accelerated in solar flares is a key parameter in the understanding of the acceleration and propagation mechanisms that occur there. However, the anisotropy of energetic electrons is still a poorly known quantity, with observational studies producing evidence for an isotropic distribution and theoretical models mainly considering the strongly beamed case. We use the effect of photospheric albedo to infer the pitch-angle distribution of X-ray emitting electrons using Hard X-ray data from RHESSI. A bi-directional approximation is applied and a regularised inversion is performed for eight large flare events to deduce the electron spectra in both downward (towards the photosphere) and upward (away from the photosphere) directions. The electron spectra and the electron anisotropy ratios are calculated for a broad energy range, from about ten up to ∼ 300 keV, near the peak of the flares. The variation of electron anisotropy over short periods of time lasting 4, 8 and 16 seconds near the impulsive peak has been examined. The results show little evidence for strong anisotropy and the mean electron flux spectra are consistent with the isotropic electron distribution. The 3σ level uncertainties, although energy and event dependent, are found to suggest that anisotropic distribution with anisotropy larger than ∼ three are not consistent with the hard X-ray data. At energies above 150 – 200 keV, the uncertainties are larger and thus the possible electron anisotropies could be larger