Mathematics – Probability
Scientific paper
Dec 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004phdt........41b&link_type=abstract
PhDT.
Mathematics
Probability
1
Sun: Corona, Sun:Flares, Turbulence, Mhd
Scientific paper
In solar physics, the complexity and small scales generated by magnetohydrodynamic (MHD) turbulence suggest to tackle the problem of the heating of the corona using statistics. We use therefore spectra of the fields, distributions of probability of structures or events, and structure functions, to analyze observations and numerical simulations, and to detect common signatures of turbulence, intermittency, and small-scale heating.
Our numerical simulations model a coronal magnetic loop, which is excited by the motions of the photosphere, and in which non-linearly interacting Alfvén waves propagate. As we need statistics, we need to simplify these interactions: we have chosen to model these interactions by cellular automata on one hand, and then by shell-models on the other hand. The results of these loop models are consistent with observations, and allow to understand some observational effects. Furthermore, signatures of intermittency can be found in the shell-model-based model, which includes a better representation of the non-linear terms of MHD than the cellular automata model. The analysis of these models and of their parametric behavior gives some information on the heating mechanisms in the corona and some clues about the interpretation of observations.
We also analyze the intensity and velocity fields observed in 1996 on the quiet Sun with the SoHO/SUMER spectrograph. The statistics of these fields (mainly the intensity field, as the velocity field is regrettably too noisy) acquaint us with the turbulent nature of the corona and with its intermittency.
The discrepancy between the distributions of events observed by different authors in the corona leads us finally to interest ourselves to the different possible definitions of an event. We give a comprehensive set of such definitions and we compare them, using lowly and highly intermittent signals.
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