Unstable Coronal Loops: Numerical Simulations with Predicted Observational Signatures

Arber, T. D.; Longbottom, A. W.; Linden, R. A. M. Van der

doi:10.1086/307222

Cited by 33 publications

(52 citation statements)

References 16 publications

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“…LARE3D uses shock viscosity [33] capture the heating effect of shocks, which is implemented by adding an extra term to the energy equation. This term is expressed as the product of the rate of strain tensor, 8) and the shock tensor,…”

Section: (A) Shock Resolutionmentioning

confidence: 99%

Shock heating in numerical simulations of kink-unstable coronal loops

Bareford

Hood

2015

Phil. Trans. R. Soc. A.

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An analysis of the importance of shock heating within coronal magnetic fields has hitherto been a neglected area of study. We present new results obtained from nonlinear magnetohydrodynamic simulations of straight coronal loops. This work shows how the energy released from the magnetic field, following an ideal instability, can be converted into thermal energy, thereby heating the solar corona. Fast dissipation of magnetic energy is necessary for coronal heating and this requirement is compatible with the time scales associated with ideal instabilities. Therefore, we choose an initial loop configuration that is susceptible to the fast-growing kink, an instability that is likely to be created by convectively driven vortices, occurring where the loop field intersects the photosphere (i.e. the loop footpoints). The largescale deformation of the field caused by the kinking creates the conditions for the formation of strong current sheets and magnetic reconnection, which have previously been considered as sites of heating, under the assumption of an enhanced resistivity. However, our simulations indicate that slow mode shocks are the primary heating mechanism, since, as well as creating current sheets, magnetic reconnection also generates plasma flows that are faster than the slow magnetoacoustic wave speed.

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Section: (A) Shock Resolutionmentioning

confidence: 99%

Shock heating in numerical simulations of kink-unstable coronal loops

Bareford

Hood

2015

Phil. Trans. R. Soc. A.

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“…As the deformation continues, areas of high current are produced, allowing magnetic reconnection to take place. Hence, energy is released from the magnetic field during the nonlinear phase of an ideal kink instability, as shown by many three-dimensional (3D) magnetohydrodynamic (MHD) models (Baty & Heyvaerts 1996;Velli et al 1997;Arber et al 1999;Baty 2000;Browning et al 2008;Hood et al 2009). …”

Section: Introductionmentioning

confidence: 99%

Coronal heating by the partial relaxation of twisted loops

Bareford

Hood

Browning

2013

A&A

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Context. Relaxation theory offers a straightforward method for estimating the energy that is released when continual convective driving causes a magnetic field to become unstable. Thus, an upper limit to the heating caused by ensembles of nanoflaring coronal loops can be calculated and checked against the level of heating required to maintain observed coronal temperatures (T 10 6 K). Aims. We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. All of the initial loop configurations discussed are known to be linearly kink unstable. The purpose of this work is to determine whether or not the simulation results agree with Taylor relaxation, which will require a modified version of relaxation theory applicable to unbounded field configurations. In addition, we show for two cases how the relaxation process unfolds. Methods. A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate the evolution of a line-tied cylindrical coronal loop model. This model comprises three concentric layers surrounded by a potential envelope; hence, being twisted locally, each loop configuration is distinguished by a piecewise-constant current profile, featuring three parameters. Initially, all configurations carry zero-net-current fields and are in ideally unstable equilibrium. The simulation results are compared with the predictions of helicityconserving relaxation theory. Results. For all simulations, the change in helicity is no more than 2% of the initial value; also, the numerical helicities match the analytically-determined values. Magnetic energy dissipation predominantly occurs via shock heating associated with magnetic reconnection in distributed current sheets. The energy release and final field profiles produced by the numerical simulations are in agreement with the predictions given by a new model of partial relaxation theory: the relaxed field is close to a linear force free state; however, the extent of the relaxation region is limited, while the loop undergoes some radial expansion. Conclusions. The results presented here support the use of partial relaxation theory, specifically, when calculating the heating-event distributions produced by ensembles of kink-unstable loops. The energy release increases with relaxation radius; but, once the loop has expanded by more than 50%, further expansion yields little more energy. We conclude that the relaxation methodology may be used for coronal heating studies.

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“…We suppose that it is ideal MHD instabilities that trigger heating events. This is inspired by 3D numerical simulations which show that fine-scale current structures naturally arise in the nonlinear phase of kink instability (Baty & Heyvaerts 1996;Velli et al 1997;Lionello et al 1998;Arber et al 1999;Baty 2000;Gerrard et al 2001). Relaxation theory is used to determine the energy release, which could otherwise only be calculated with three-dimensional resistive MHD simulations.…”

Section: Introductionmentioning

confidence: 99%

Solar coronal heating by relaxation events

Browning¹,

Linden²

2003

A&A

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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.

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Unstable Coronal Loops: Numerical Simulations with Predicted Observational Signatures

Cited by 33 publications

References 16 publications

Shock heating in numerical simulations of kink-unstable coronal loops

Shock heating in numerical simulations of kink-unstable coronal loops

Coronal heating by the partial relaxation of twisted loops

Solar coronal heating by relaxation events

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