Dynamic evolution of emerging magnetic flux tubes in the solar convective envelope

Abstract

Given the present consensus that the solar cycle dynamo is operating in a thin "overshoot layer" between the convection zone and the radiative interior, this dissertation studies the dynamics of transporting toroidal magnetic flux from the dynamo layer to the Sun's photosphere. I have carried out numerical simulations of the buoyant rise of toroidal magnetic flux tubes through the convection zone in the form of emerging loops, whose footpoints remain anchored in the overshoot layer. My major conclusions are: 1) As each loop rises due to buoyancy, the Coriolis force transports mass out of the leading leg (leading in the direction of rotation) into the following leg of the loop, and causes the field strength in the loop's leading leg to be twice that in the following. This field strength asymmetry naturally explains the observed more compact and less fragmented morphology of the leading polarity of an active region compared to its following polarity. 2) The Coriolis force induced by the diverging east-west velocity near the apex of a rising loop acts to twist the loop, and produces a tilt angle upon emergence. For reasonable choices of toroidal field strength 3x10^4 G ≤B0 ≤9x10^4 G, the computed tilt angles are consistent with the sign, magnitude and latitudinal variation of the observed active region tilt angles. The variation of the computed tilt angle α with the characteristic field strength B, latitude θ, and the total flux Φ of the loop can be described by the scaling law: α ∝sin θB^-5/4 Φ^1/4. However, for toroidal fields B0≤ 2x10^4 G, loops emerge with tilts that are opposite from those of most active regions. 3) The latitudes of loop emergence are consistent with the observed butterfly diagram assuming a dynamo wave propagating from 30° latitude to the equator at the base of the convection zone. In the case of solid-body rotation, a toroidal field B0 ≥6x10^4 G is required to avoid a significant equatorial gap, but if differential rotation is included, B0 ≥3x10^4 G leads to an acceptable butterfly diagram.