Critical Height of the Torus Instability in Two-Ribbon Solar Flares

Abstract

We studied the background field for 60 two-ribbon flares of M-and-above classes during 2011--2015. These flares are categorized into two groups, i.e., \emph{eruptive} and \emph{confined} flares, based on whether a flare is associated with a coronal mass ejection or not. The background field of source active regions is approximated by a potential field extrapolated from the $B_z$ component of vector magnetograms provided by the Helioseismic and Magnetic Imager. We calculated the decay index $n$ of the background field above the flaring polarity inversion line, and defined a critical height $h_{\mathrm{crit}}$ corresponding to the theoretical threshold ($n_{\mathrm{crit}}=1.5$) of the torus instability. We found that $h_{\mathrm{crit}}$ is approximately half of the distance between the centroids of opposite polarities in active regions, and that the distribution of $h_{\mathrm{crit}}$ is bimodal: it is significantly higher for confined flares than for eruptive ones. The decay index increases monotonously with increasing height for 86\% (84\%) of the eruptive (confined) flares but displays a saddle-like profile for the rest 14\% (16\%), which are found exclusively in active regions of multipolar field configuration. Moreover, $n$ at the saddle bottom is significantly smaller in confined flares than that in eruptive ones. These results highlight the critical role of background field in regulating the eruptive behavior of two-ribbon flares.

arXiv commentAccept for publication in Astrophysical Journal Letters

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