Quiet Sun coronal heating: A statistical model

¹ LPCE/CNRS UMR 6115, 3A Av. de la Recherche Scientifique, 45071 Orléans, France
² ESST, Kyushu University, 6-1 Kasuga-Koen, Fukuoka 816-0943, Japan
³ DASOP, Paris-Meudon Observatory, 5 Pl. J. Janssen, 92195 Meudon, France

Corresponding author: V. Krasnoselskikh, vkrasnos@cnrs-orleans.fr

Received: 5 March 2001
Accepted: 16 August 2001

Abstract

Recent observations of Krucker & Benz ([CITE]) give strong support to Parker's hypothesis ([CITE]) that small-scale dissipative events make up the main contribution to quiet Sun coronal heating. They also showed that these small-scale events are associated not only with the magnetic network, but also with the cell interiors (Benz & Krucker [CITE]). Taking into account in addition the results of the analysis performed by Priest with co-authors ([CITE]) who demonstrated that the heating is quasi-homogeneous along the arcs, we come to the conclusion that the sources driving these dissipative events are also small-scale sources. Typically they are of the order of or smaller than the linear scale of the events observed, that is <2000 km. To describe statistical properties of quiet Sun corona heating by microflares, nanoflares, and even smaller events, we consider a cellular automata model subject to uniform small-scale driving and dissipation. The model consists of two elements, the magnetic field source supposed to be associated with the small scale hydrodynamic turbulence convected from the photosphere and local dissipation of small scale currents. The dissipation is assumed to be provided by either anomalous resistivity, when the current density exceeds a certain threshold value, or by the magnetic reconnection. The main problem considered is how the statistical characteristics of dissipated energy flow depend upon characteristics of the magnetic field source and on physical mechanism responsible for the magnetic field dissipation. As the threshold value of current is increased, we observe the transition from Gaussian statistics to power-law type. In addition, we find that the dissipation provided by reconnection results in stronger deviations from Gaussian distribution.