Nonlinear fast magnetoacoustic wave propagation in the neighbourhood of a 2D magnetic X-point: oscillatory reconnection

Abstract

Context. This paper extends the models of Craig & McClymont (1991, ApJ, 371, L41) and McLaughlin & Hood (2004, A&A, 420, 1129 to include finite β and nonlinear effects. Aims. We investigate the nature of nonlinear fast magnetoacoustic waves about a 2D magnetic X-point. Methods. We solve the compressible and resistive MHD equations using a Lagrangian remap, shock capturing code (Arber et al. 2001, J. Comp. Phys., 171, 151) and consider an initial condition in u × B ·ẑ (a natural variable of the system). Results. We observe the formation of both fast and slow oblique magnetic shocks. The nonlinear wave deforms the X-point into a "cusp-like" point which in turn collapses to a current sheet. The system then evolves through a series of horizontal and vertical current sheets, with associated changes in connectivity, i.e. the system exhibits oscillatory reconnection. Our final state is non-potential (but in force balance) due to asymmetric heating from the shocks. Larger amplitudes in our initial condition correspond to larger values of the final current density left in the system. Conclusions. The inclusion of nonlinear terms introduces several new features to the system that were absent from the linear regime.

Spine-fan reconnection

“…What we do see in our transiently driven simulations in common with those of McLaughlin et al (2009) is a move toward a non-potential final state in force balance through plasma pressure. This final state indicates that even small perturbations of the spine or fan will lead to a non-potential fan plane magnetic field and preferential heating there.…”

“…An interesting finding from these transiently driven cases is that unlike in the 2D wave driven case (Craig & McClymont 1991;McLaughlin et al 2009) we see no evidence of oscillatory reconnection as the system relaxes once the driving ceases (i.e. no change in sign of E dl, Fig.…”

Stellar flare oscillations: evidence for oscillatory reconnection and evolution of MHD modes

“…This further generates the quasi-periodic modulation in the observed emissions (Nakariakov et al 2006). The external wave driver in the vicinity may be playing a role in triggering oscillations in the flaring region in its rising phase (McLaughlin et al 2009). The triggering mechanism describes that an oscillatory disturbance reaching the X-point of the flare current sheet may periodically trigger the reconnection rate causing the modulation in the emission during the rise phase of the flare (Nakariakov et al 2006).…”

Steady state reconnection at a single 3D magnetic null point

“…This type of behaviour was seen in Galsgaard et al (2003), where the null point was perturbed by two rotational twist waves centred on the spine axis. Here the fast mode wave wraps around the null and concentrates part of the energy of the perturbation there (see also McLaughlin et al 2009, who studied the 2D case).…”