Critical Decay Index at the Onset of Solar Eruptions

Abstract

Magnetic flux ropes are topological structures consisting of twisted magnetic field lines that globally wrap around an axis. The torus instability model predicts that a magnetic flux rope of major radius R undergoes an eruption when its axis reaches a location where the decay index −d(ln B ex )/d(ln R) of the ambient magnetic field B ex is larger than a critical value. In the current-wire model, the critical value depends on the thickness and time-evolution of the current channel. We use magneto-hydrodynamic (MHD) simulations to investigate if the critical value of the decay index at the onset of the eruption is affected by the magnetic flux rope's internal current profile and/or by the particular pre-eruptive photospheric dynamics. The evolution of an asymmetric, bipolar active region is driven by applying different classes of photospheric motions. We find that the critical value of the decay index at the onset of the eruption is not significantly affected by either the pre-eruptive photospheric evolution of the active region or by the resulting different magnetic flux ropes. As in the case of the current-wire model, we find that there is a 'critical range' [1.3 − 1.5], rather than a 'critical value' for the onset of the torus instability. This range is in good agreement with the predictions of the current-wire model, despite the inclusion of line-tying effects and the occurrence of tether-cutting magnetic reconnection.

Relative magnetic helicity as a diagnostic of solar eruptivity

“…This is the goal of an ongoing study (Zuccarello et al, in prep. ) that focuses on the analysis of the helicity content of the parametric simulations of Zuccarello et al (2015).…”

“…It is however interesting to note that H j corresponds to a description of the current part of the field while the |H V |, which is dominated by 2H pj , includes the relative properties of the current-carrying field in relation to its surrounding field. In the framework of the torus instability (Kliem & Török 2006;Démoulin & Aulanier 2010;Zuccarello et al 2015), the criterion of instability is also related to the relative properties of the current-carrying structure with regards to its surrounding confining field. Here we speculate that the ratio |H j |/|H V | may somehow be related to the instability criterion of the torus instability.…”

Recurrent CME-like Eruptions in Emerging Flux Regions. I. On the Mechanism of Eruptions

“…The derivation of the torus instability criteria based on previous analytical studies took into account perturbations of a static configuration. Thus, a more accurate estimate of the torus index in our simulations would be to let the envelope field relax at each time step and then calculate n. This can only be done if the driver of the system could be stopped, letting the overall magnetic flux system reach an equilibrium (e.g., Zuccarello et al 2015). However, in our dynamical simulations, there is a certain amount of available magnetic flux, which can emerge into the photosphere and above.…”

“…For thick channels, the critical index for circular and straight channels does not vary much-it takes values ranging from 1.1 to 1.3 (with expansion of the FR) and 1.2-1.5 (without expansion). Zuccarello et al (2015) investigated the role of line-tying effects on the eruption. They performed a series of simulations with a setup similar to that of Aulanier et al (2010), but with different velocity drivers at the photosphere.…”

Solar Eruption and Local Magnetic Parameters

“…Commonly used value for the critical decay index for the torus instability is 1.5 based on the analytical study by Bateman (1978) and Kliem & Török (2006). However, an extensive MHD simulation study found the critical value lying in the range of 1.3-1.5 (Zuccarello, 2015(Zuccarello, , 2016. Another analytical study found a critical range between 1.1 and 1.3, and it depends on the magnetic field and electric current configuration (Demoulin & Aulanier 2010).…”