The three-dimensional evolution of buoyant magnetic flux tubes in a model solar convective envelope

We present a set of three-dimensional spherical shell anelastic MHD simulations of the buoyant rise of magnetic flux tubes from the base of the convection zone to a depth of 16 Mm below the photosphere. It is found that when a twisted flux tube arches upward due to buoyancy, it rotates out of the plane and thus produces a tilt at the apex. Our simulations show that for tubes with the twist rate that is necessary for a cohesive rise, the twist-induced tilt dominates that caused by the Coriolis force, and furthermore, the twist-induced tilt is of the wrong direction (opposite to the observational Joy's law) if the twist is left-handed (right-handed) in the northern (southern) hemisphere, following the observed hemispheric preference of the sign of the active region twist. It is found that in order for the emerging tube to show the correct tilt direction (consistent with observations), the initial twist rate of the flux tube needs to be less than half of that needed for a cohesive rise. Under such conditions, severe flux loss is found during the rise. We also found that due to the asymmetric stretching of the rising tube by the Coriolis force, a field strength asymmetry develops, with the field in the leading leg (leading in the direction of rotation) of the Omega-shaped emerging tube being stronger than the field in the following leg, which results in a more compact morphology in the leading polarity of the emerging active region.