TWO-STEP EMERGENCE OF THE MAGNETIC FLUX SHEET FROM THE SOLAR CONVECTION ZONE

We perform two-dimensional magnetodydrodynamic simulations of the flux emergence from the solar convection zone to the corona. The flux sheet is initially located moderately deep in the adiabatically stratified convection zone (-20,000 km) and is perturbed to trigger the Parker instability. The flux rises through the solar interior due to the magnetic buoyancy, but suffers a gradual deceleration and a flattening in the middle of the way to the surface since the plasma piled on the emerging loop cannot pass through the convectively stable photosphere. As the magnetic pressure gradient enhances, the flux becomes locally unstable to the Parker instability so that the further evolution to the corona occurs. The second-step nonlinear emergence is well described by the expansion law by Shibata et al. To investigate the condition for this two-step emergence model, we vary the initial field strength and the total flux. When the initial field is too strong, the flux exhibits the emergence to the corona without a deceleration at the surface and reveals an unrealistically strong flux density at each footpoint of the coronal loop, while the flux either fragments within the convection zone or cannot pass through the surface when the initial field is too weak. The condition for the two-step emergence is found to be 10(21)-10(22) Mx with 10(4) G at z = -20,000 km. We present some discussions in connection with recent observations and the results of the thin-flux-tube model.