Double arc instability in the solar corona

Abstract: The stability of the magnetic field in the solar corona is important for understanding the causes of solar eruptions. Although various scenarios have been suggested to date, the tether-cutting reconnection scenario proposed by Moore et al.(2001) is one of the widely accepted models to explain the onset process of solar eruptions. Although the tether-cutting reconnection scenario proposed that sigmoidal field formed by the internal reconnection is the magnetic field in pre-eruptive state, the stability of the sigmoidal field has not yet been investigated quantitatively. In this paper, in order to elucidate the stability problem of pre-eruptive state, we developed a simple numerical analysis, in which the sigmoidal field is modeled by a double arc electric current loop and its stability is analyzed. As a result, we found that the double arc loop is more easily destabilized than the axisymmetric torus, and it becomes unstable even if the external field does not decay with altitude, which is in contrast to the axisymmetric torus instability. This suggests that the tether-cutting reconnection may well work as the onset mechanism of solar eruptions, and if so the critical condition for eruption under certain geometry may be determined by a new type of instability rather than the torus instability. Based on them, we propose a new type of instability called double arc instability (DAI). We discuss the critical conditions for DAI and derive a new parameter $\kappa$ defined as the product of the magnetic twist and the normalized flux of tether-cutting reconnection.