Influence of the definition of dissipative events on their statistics

¹ Institut d'Astrophysique Spatiale, CNRS – Université Paris-Sud, Bât. 121, 91405 Orsay Cedex, France e-mail: eric.buchlin@ias.fr
² Dipartimento di Astronomia e Scienza dello Spazio, Università di Firenze, 50125 Firenze, Italy
³ Istituto Nazionale Fisica della Materia, Sezione A, Università di Pisa, 56100 Pisa, Italy

Received: 12 November 2004
Accepted: 7 February 2005

Abstract

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.