A nanoflare distribution generated by repeated relaxations triggered by kink instability^*

¹ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK e-mail: michael.bareford@postgrad.manchester.ac.uk
² SIDC, Royal Observatory of Belgium, Ringlaan 3, 1180 Brussels, Belgium

Received: January 1900
Accepted: 5 August 2010

Abstract

Context. It is thought likely that vast numbers of nanoflares are responsible for the corona having a temperature of millions of degrees. Current observational technologies lack the resolving power to confirm the nanoflare hypothesis. An alternative approach is to construct a magnetohydrodynamic coronal loop model that has the ability to predict nanoflare energy distributions.

Aims. This paper presents the initial results generated by a coronal loop model that flares whenever it becomes unstable to an ideal MHD kink mode. A feature of the model is that it predicts heating events with a range of sizes, depending on where the instability threshold for linear kink modes is encountered. The aims are to calculate the distribution of event energies and to investigate whether kink instability can be predicted from a single parameter.

Methods. The loop is represented as a straight line-tied cylinder. The twisting caused by random photospheric motions is captured by two parameters, representing the ratio of current density to field strength for specific regions of the loop. Instability onset is mapped as a closed boundary in the 2D parameter space. Dissipation of the loop's magnetic energy begins during the nonlinear stage of the instability, which develops as a consequence of current sheet reconnection. After flaring, the loop evolves to the state of lowest energy where, in accordance with relaxation theory, the ratio of current to field is constant throughout the loop and helicity is conserved.

Results. There exists substantial variation in the radial magnetic twist profiles for the loop states along the instability threshold. These results suggest that instability cannot be predicted by any simple twist-derived property reaching a critical value. The model is applied such that the loop undergoes repeated episodes of instability followed by energy-releasing relaxation. Hence, an energy distribution of the nanoflares produced is collated. This paper also presents the calculated relaxation states and energy releases for all instability threshold points.

Conclusions. The final energy distribution features two nanoflare populations that follow different power laws. The power law index for the higher energy population is more than sufficient for coronal heating.