Dynamics of emerging active region flux loops

The buoyant rise of a magnetic flux loop arising from a single perturbed segment of a toroidal flux ring lying slightly beneath the base of the convection zone is studied by way of numerical simulations. We have considered flux loop evolution assuming both solid-body rotation, and differential rotation consistent with recent results from helioseismology. Our major results are the following: 1. We find that loops with initial toroidal field strengths between 10 and 100 kG all emerge at latitudes that 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 strength B₀ ≥ 40 kG is required to avoid a significant equatorial gap, but if differential rotation is included, B₀ ≥ 20 kG leads to an acceptable butterfly diagram. 2. As was found in the previous work of D'Silva & Choudhuri, the Coriolis force induced by the diverging east-west velocity near the loop apex acts to twist the loop as it rises and produces a tilt angle upon emergence, with the leading leg of the loop closer to the equator than the following. The tilt angles computed from our simulations are consistent with the magnitude and the latitudinal variation of the observed active-region tilt angles, given the range of uncertainties in the observations of Joy's law. 3. From a simple force balance analysis, we derive a scaling law for the tilt angle α in terms of the initial field strength B₀, emerging latitude θ_em, and the total flux Φ of the loop: α ∝ sin θ_em B^-5/4₀Φ^1/4. This scaling relation describes our simulations reasonably well when B₀ ≥ 20 kG. For B₀ < 20 kG, however, the loop tilt angles are found to decrease with decreasing field strength B₀, and in some cases lead to negative tilt values (i.e., opposite to the tilts of active regions). This decrease of tilt for weak-field flux loops is caused by a strong converging parallel flow that sets in when the loop apex reaches the upper layers of the convection zone. 4. We still find, as we did in the multiloop studies in Fan, Fisher, & DeLuca, that the magnetic field in the leading leg of an emerging loop is approximately twice that in the following leg. We argue that this field strength asymmetry is the origin of morphological asymmetries in bipolar active regions. Finally, we offer some speculations on the decay of active regions, based on the results of our studies. We speculate that as plasma in the tube attempts to establish hydrostatic equilibrium along the field lines after the flux emergence has taken place, the tube field strength at some intermediate depths below the surface becomes sufficiently small that the surface portions of the tube (which have cooled and undergone convective collapse) become dynamically disconnected from those portions near the base of the convection zone. The surface portions of the emerged flux tubes are then transported by motions near the photosphere, such as supergranular convection and meridional flow.