3-DIMENSIONAL Evolution of a Magnetic Flux Tube Emerging Into the Solar Atmosphere

We present results on the emergence of a magnetic flux tube into the solar atmosphere, obtained by 3-dimensional MHD numerical simulation. The simulation shows that emerging field lines can be classified as either expanding field lines or undulating field lines according to their evolution. Field lines that emerge with a large aspect ratio (the ratio of height to footpoint distance) simply continue to expand into the outer atmosphere, while field lines emerging with a small aspect ratio show an undulating behavior in the lower atmosphere. Those undulating field lines subsequently either expand into the outer atmosphere or sink toward the photosphere; in the latter case a dipped structure develops in the middle of field lines. For the field lines composing a twisted magnetic flux tube, the outer field lines are expanding field lines and the inner field lines are undulating field lines. We analyze the injection of magnetic energy and magnetic helicity into the atmosphere during the simulated flux emergence. Each of the injection rates can be divided into contributions from horizontal shearing flows and vertical emergence flows at the base of the atmosphere. We find that the emergence contributions are the dominant ones at the early phase of flux emergence and that later that role is played by the shearing contributions. The emergence starts with a simple dipole structure formed in the photosphere, which is subsequently deformed and fragmented, leading to a quadrapole structure.