Solar coronal heating by relaxation events

Abstract

Abstract.A coronal heating model is proposed which predicts heating by a series of discrete events of various energies, analogous to the observed range of events from large scale flares through various transient brightening phenomena down to the often discussed "nanoflares". We suggest that an energy release event occurs when a field becomes linearly unstable to ideal MHD modes, with dissipation during the nonlinear phase of such an instability due to reconnection in fine-scale structures such as current sheets. The energy release during this complex dynamic period can be evaluated by assuming the field relaxes to a minimum energy state subject to the constraint of helicity conservation. A model problem is studied: a cylindrical coronal loop, with a current profile generated by slow twisting of the photospheric footpoints parameterised by two values of α (the ratio of current density to field strength). Different initial α profiles, corresponding to different footpoint twisting profiles, lead to energy release events of a wide range of magnitudes, but our model predicts an observationally realistic minimum size for these events.

A nanoflare distribution generated by repeated relaxations triggered by kink instability

“…The model discussed here was used by Browning & Van der Linden (2003) and then extended by Browning et al (2008) to include a potential envelope (Fig. 1).…”

“…Essentially, helical current sheets become the site of Ohmic dissipation, resulting in a heating event. Further simulations have revealed the appropriate correlation between magnetic energy and Ohmic heating (Browning & Van der Linden 2003;Browning et al 2008;Hood et al 2009). The energy released by an instability depends on the complex dynamics of the magnetic reconnection events that occur inside the loop.…”

“…In applying relaxation theory to coronal heating, it became clear that the effectiveness of the heating depends on how much free energy is stored before a relaxation event occurs (Heyvaerts & Priest 1984). Browning & Van der Linden (2003) proposed that relaxation is triggered by the onset of ideal MHD instability. Thus, the coronal field evolves quasi-statically in response to slow photospheric driving, building up free magnetic energy -until the field becomes unstable (i.e., the threshold for linear instability is reached).…”

“…Recently, it has been demonstrated using 3D MHD simulations that this process causes the field to relax towards a state which is closely-approximated as a constant-α state, and the energy release is in good agreement with relaxation theory (Browning et al 2008;Hood et al 2009). These papers have investigated field profiles, based on the model of Browning & Van der Linden (2003), in the unstable region of parameter space and have shown that fast reconnection develops in a current sheet, with dissipation of magnetic energy and relaxation to a new, lower-energy state. Efficient "mixing" of the α profile is facilitated in the later phases of the evolution, during which the current sheet fragments (Hood et al 2009).…”

“…Following Browning & Van der Linden (2003), we use a simple cylindrical field model, and represent the nonlinear force-free field using a two-parameter family of current profiles in which α is a piecewise constant. Browning and Van der Linden considered only individual heating events.…”