Are Coronae of Magnetically Active Stars Heated by Flares? III. Analytical Distribution of Superimposed Flares

(abridged) We study the hypothesis that observed X-ray/extreme ultraviolet emission from coronae of magnetically active stars is entirely (or to a large part) due to the superposition of flares, using an analytic approach to determine the amplitude distribution of flares in light curves. The flare-heating hypothesis is motivated by time series that show continuous variability suggesting the presence of a large number of superimposed flares with similar rise and decay time scales. We rigorously relate the amplitude distribution of stellar flares to the observed histograms of binned counts and photon waiting times, under the assumption that the flares occur at random and have similar shapes. Applying these results to EUVE/DS observations of the flaring star AD Leo, we find that the flare amplitude distribution can be represented by a truncated power law with a power law index of 2.3 +/- 0.1. Our analytical results agree with existing Monte Carlo results of Kashyap et al. (2002) and Guedel et al. (2003). The method is applicable to a wide range of further stochastically bursting astrophysical sources such as cataclysmic variables, Gamma Ray Burst substructures, X-ray binaries, and spatially resolved observations of solar flares.Comment: accepted for publication in Ap

Particle acceleration

Data is compiled from Solar Maximum Mission and Hinothori satellites, particle detectors in several satellites, ground based instruments, and balloon flights in order to answer fundamental questions relating to: (1) the requirements for the coronal magnetic field structure in the vicinity of the energization source; (2) the height (above the photosphere) of the energization source; (3) the time of energization; (4) transistion between coronal heating and flares; (5) evidence for purely thermal, purely nonthermal and hybrid type flares; (6) the time characteristics of the energization source; (7) whether every flare accelerates protons; (8) the location of the interaction site of the ions and relativistic electrons; (9) the energy spectra for ions and relativistic electrons; (10) the relationship between particles at the Sun and interplanetary space; (11) evidence for more than one acceleration mechanism; (12) whether there is single mechanism that will accelerate particles to all energies and also heat the plasma; and (13) how fast the existing mechanisms accelerate electrons up to several MeV and ions to 1 GeV

Gravito-magnetic instabilities in anisotropically expanding fluids

Gravitational instabilities in a magnetized Friedman - Robertson - Walker (FRW) Universe, in which the magnetic field was assumed to be too weak to destroy the isotropy of the model, are known and have been studied in the past. Accordingly, it became evident that the external magnetic field disfavors the perturbations' growth, suppressing the corresponding rate by an amount proportional to its strength. However, the spatial isotropy of the FRW Universe is not compatible with the presence of large-scale magnetic fields. Therefore, in this article we use the general-relativistic (GR) version of the (linearized) perturbed magnetohydrodynamic equations with and without resistivity, to discuss a generalized Jeans criterion and the potential formation of density condensations within a class of homogeneous and anisotropically expanding, self-gravitating, magnetized fluids in curved space-time. We find that, for a wide variety of anisotropic cosmological models, gravito-magnetic instabilities can lead to sub-horizonal, magnetized condensations. In the non-resistive case, the power spectrum of the unstable cosmological perturbations suggests that most of the power is concentrated on large scales (small k), very close to the horizon. On the other hand, in a resistive medium, the critical wave-numbers so obtained, exhibit a delicate dependence on resistivity, resulting in the reduction of the corresponding Jeans lengths to smaller scales (well bellow the horizon) than the non-resistive ones, while increasing the range of cosmological models which admit such an instability.Comment: 10 pages RevTex, 4 figures, accepted for publication in the International Journal of Modern Physics

Local re-acceleration and a modified thick target model of solar flare electrons

The collisional thick target model (CTTM) of solar hard X-ray (HXR) bursts has become an almost 'Standard Model' of flare impulsive phase energy transport and radiation. However, it faces various problems in the light of recent data, particularly the high electron beam density and anisotropy it involves.} {We consider how photon yield per electron can be increased, and hence fast electron beam intensity requirements reduced, by local re-acceleration of fast electrons throughout the HXR source itself, after injection.} {We show parametrically that, if net re-acceleration rates due to e.g. waves or local current sheet electric (${\cal E}$) fields are a significant fraction of collisional loss rates, electron lifetimes, and hence the net radiative HXR output per electron can be substantially increased over the CTTM values. In this local re-acceleration thick target model (LRTTM) fast electron number requirements and anisotropy are thus reduced. One specific possible scenario involving such re-acceleration is discussed, viz, a current sheet cascade (CSC) in a randomly stressed magnetic loop.} {Combined MHD and test particle simulations show that local ${\cal E}$ fields in CSCs can efficiently accelerate electrons in the corona and and re-accelerate them after injection into the chromosphere. In this HXR source scenario, rapid synchronisation and variability of impulsive footpoint emissions can still occur since primary electron acceleration is in the high Alfv\'{e}n speed corona with fast re-acceleration in chromospheric CSCs. It is also consistent with the energy-dependent time-of-flight delays in HXR features.Comment: 8 pages, 2 figure

Stochastic Cellular Automata Model for Stock Market Dynamics

In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid. Active traders are characterised by the decision to buy, (+1), or sell, (-1), a stock at a certain discrete time step. The remaining cells are inactive,(0). The trading dynamics is then determined by the stochastic interaction between traders belonging to the same cluster. Most of the stylized aspects of the financial market time series are reproduced by the model.Comment: 17 pages and 7 figure

Anomalous diffusion in a symbolic model

We address this work to investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following a power law probability density. In this analysis, we consider that the sum of n symbols represents the position of a particle in erratic movement. This approach revealed a rich diffusive scenario characterized by non-Gaussian distributions and, depending on the power law exponent and also on the procedure used to build the walker, we may have superdiffusion, subdiffusion or usual diffusion. Additionally, we use the continuous-time random walk framework to compare with the numerical data, finding a good agreement. Because of its simplicity and flexibility, this model can be a candidate to describe real systems governed by power laws probabilities densities.Comment: Accepted for publication in Physica Script

Magnetohydrodynamics and Plasma Cosmology

We study the linear magnetohydrodynamic (MHD) equations, both in the Newtonian and the general-relativistic limit, as regards a viscous magnetized fluid of finite conductivity and discuss instability criteria. In addition, we explore the excitation of cosmological perturbations in anisotropic spacetimes, in the presence of an ambient magnetic field. Acoustic, electromagnetic (e/m) and fast-magnetosonic modes, propagating normal to the magnetic field, can be excited, resulting in several implications of cosmological significance.Comment: 9 pages, RevTeX, To appear in the Proceedings of the Peyresq X Meeting, IJTP Conference Serie

Turbulence in the Solar Atmosphere: Manifestations and Diagnostics via Solar Image Processing

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 multi-fractal spectrum of generalized correlation dimensions do not have significant predictive ability. The respective multi-fractal structure functions and their inertial-range scaling exponents, however, probably provide some statistical distinguishing features between flaring and non-flaring 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.Comment: 26 pages, 7 figure