The Three-dimensional Evolution of Rising, Twisted Magnetic Flux Tubes in a Gravitationally Stratified Model Convection Zone

We present three-dimensional numerical simulations of the rise and fragmentation of twisted, initially horizontal magnetic flux tubes that evolve into emerging Ω-loops. The flux tubes rise buoyantly through an adiabatically stratified plasma that represents the solar convection zone. The MHD equations are solved in the anelastic approximation, and the results are compared with studies of flux-tube fragmentation in two dimensions. We find that if the initial amount of field line twist is below a critical value, the degree of fragmentation at the apex of a rising Ω-loop depends on its three-dimensional geometry: the greater the apex curvature of a given Ω-loop, the lesser the degree of fragmentation of the loop as it approaches the photosphere. Thus, the amount of initial twist necessary for the loop to retain its cohesion can be reduced substantially from the two-dimensional limit. The simulations also suggest that, as a fragmented flux tube emerges through a relatively quiet portion of the solar disk, extended crescent-shaped magnetic features of opposite polarity should form and steadily recede from one another. These features eventually coalesce after the fragmented portion of the Ω-loop emerges through the photosphere.