Eric Buchlin

Influence of the definition of dissipative events on their statistics

A convenient and widely used method to study the turbulent plasma in the solar corona is to examine statistics of properties of events (or structures) associated to flares either in observations or in numerical simulations. Numerous papers have followed such a methodology, using different definitions of an event, but the reasons behind the choice of a particular definition is very rarely discussed. We give here a comprehensive set of possible event definitions starting from a one-dimensional data set such as a time-series of energy dissipation. Each definition is then applied to a time-series of energy dissipation obtained from simulations of a shell-model of magnetohydrodynamic turbulence, or from a new model of coupled shell-models designed to represent a magnetic loop in the solar corona. We obtain distributions of the peak dissipation power, total energy, duration and waiting-time associated with each definition. These distributions are then investigated and compared, and the influence of the definition of an event on the statistics is discussed. In particular, power-law distributions are more likely to appear when using a threshold. The sensitivity of the distributions to the definition of an event seems also to be weaker for events found in a highly intermittent time series. Some implications for statistical results obtained from observations are discussed.

A simplified numerical model of coronal energy dissipation based on reduced MHD

A 3D model intermediate between cellular automata (CA) models and the reduced magnetohydrodynamic (RMHD) equations is presented to simulate solar impulsive events generated along a coronal magnetic loop. The model consists of a set of planes distributed along a magnetic loop between which the information propagates through Alfven waves. Statistical properties in terms of power-laws for energies and durations of dissipative events are obtained, and their agreement with X-ray and UV flares observations is discussed. The existence of observational biases is also discussed.

A statistical study of SUMER spectral images: events, turbulence, and intermittency

We analyze a series of full-Sun observations performed with the SoHO/SUMER instrument between March and October 1996. Some parameters (radiance, shift and width) of the S vi 93.3 nm , S vi 94.4 nm , and Ly e line profiles were computed on board. Radiances and line-of-sight velocities in a large central region of the Sun are studied statistically: distributions of solar structures, field Fourier spectra and structure functions are obtained. The structures have distributions with power-law tails, the Fourier spectra of the radiance fields also display power laws, and the normalized structure functions of the radiance and velocity fields increase at small scales. These results support the idea of the existence of small scales, created by turbulence, and of intermittency of the observed fields. These properties may provide insight into the processes needed for heating the transition region, or, if confirmed in the corona, the corona itself. The difficulties encountered in this analysis, especially for the velocity data, underline the need for sensitive ultraviolet imaging spectrometers.

A solar cellular automata model issued from reduced MHD

A three‐dimensional cellular automata (CA) model inspired by the reduced magnetohydrodynamic equations is presented to describe impulsive events generated along a coronal magnetic loop. It consists of a set of planes, distributed along the loop, between which the information propagates through Alfven waves. Statistical properties in terms of power laws are obtained in agreement with SoHO observations of X‐ray bright points of the quiet Sun. Physical meaning and limits of the model are discussed.