BRUNT-VAISALA GROWTH-RATE AND THE RADIAL EMERGENCE OF EQUIPARTITION FIELDS

It is believed that the dynamo operates in the overshoot region at the base of the solar convection zone (CZ), and the magnetic features we see at the surface are formed when flux tubes rise through the CZ and appear at the photosphere. Studies of dynamics of flux tubes have poin ted out that 10 kG tubes, which are nearly in energy equipartition wit h the velocity field at the base of the CZ, are weakly buoyant and hen ce overwhelmed by the Coriolis force. They move parallel to the rotati on axis and emerge at very high latitudes, well above the sunspot zone , which makes it difficult to explain the formation of sunspots. Influ ence of the Coriolis force was found to be overcome only if flux tubes were stronger than roughly a 100 kG. The Brunt-Vaisala growth rate (w e define as root\N-2\; where N is the Brunt-Vaisala frequency) of the CZ plays an important role in the dynamics of rising flux tubes. In an isothermal rise, when the flux tube is in thermal equilibrium with it s surroundings, \N-2\ is shown to play a negligible role. However, in an adiabatic rise the role of \N-2\ is dominant; if \N-2\ is larger th an roughly 10(-12) s(-2) in the lower CZ, magnetic buoyancy is shown t o rise exponentially as the flux tube emerges. Further if \N-2\ > 4 X 10(-11) s(-2), the exponential rise is sufficiently rapid to enable eq uipartition fields to overcome the influence of the Coriolis force and emerge radially. In the CZ of the solar model of Christensen-Dalsgaar d, Proffitt, and Thompson (1993; model-CPT) equipartition fields are f ound to emerge at high latitudes. However, an increase of \N-2\ in the lower CZ, on average, roughly by a factor of 8 would make them emerge radially to sunspot latitudes. If this is possible, there would be no need for the dynamo to produce extraordinarily strong fields to expla in the formation of sunspots. Conversely, if such a large \N-2\ is not possible for the lower layers of the CZ, then our results actually re inforce the conclusion in previous work that field strengths at the CZ base of order 100 kG are necessary for sunspot strength magnetic fiel ds to emerge at sunspot latitudes.