Three-Dimensional Magnetohydrodynamic Simulation of Nonlinear Magnetic Buoyancy Instability of Flux Sheets with Magnetic Shear

Abstract

Abstract A series of three-dimensional magnetohydrodynamic simulations is used to study the nonlinear evolution of the magnetic buoyancy instability of a magnetic flux sheet with magnetic shear. A horizontal flux sheet that is initially placed below the solar photosphere is susceptible to both the interchange instability and the Parker instability (the undular mode of the magnetic buoyancy instability). The growth rate in the linear stage of the instability in the numerical simulation is consistent with that predicted by linear theory. In the nonlinear stage, the development depends on the initial perturbation as well as the initial magnetic field configuration (i.e., the presence of magnetic shear). When an initial perturbation is assumed to be periodic, the emerging flux rises to the corona and the magnetic field expands like a potential field, as observed in 2D simulations. When an initial non-periodic perturbation or random perturbations are assumed, the magnetic flux expands horizontally when the magnetic field emerges a little into the photosphere. The distribution of the magnetic field and gas tends to be in a new state of magnetohydrostatic equilibrium. When magnetic shear is present in the initial magnetic flux sheets, the interchange mode is stabilized so that the emerging loop is higher than in the no magnetic shear case. We discuss how the presented results are related to the emerging flux observed on the Sun.