Bifurcation and stability of coronal magnetic arcades in a linear force-free field

The bifurcation structure as well as the stability property of the solar coronal magnetic arcades in a linear force-free field (LFFF) is carefully investigated. It is clarified that two different modes can cause the bifurcation of the minimum energy arcade profile: the symmetric mode (SM), which has a zero wavevector, and the undulating mode (UM), which has a nonzero wavevector parallel to the magnetic neutral lines. Depending on the geometry and the magnetic helicity contained in the arcades, the minimum energy state is switched among three different solutions of the LFFF: the coupled solution (CS), which consists only of the components coupled with the potential held; the mixed solution (MS), which is composed of the CS and the SM; and the MS of the CS and the UM. It is found that, once the LFFF bifurcates into the CS and the MS, the CS is always unstable against the SM or the UM. Based on the discussion about the relationship between the excess energy and the growth rate, it is proposed that the preflare state is a nonlinearly growing stage of these instabilities rather than a metastable state.