DYNAMICS OF EMERGING ACTIVE-REGION FLUX LOOPS

The buoyant rise of a magnetic flux loop arising from a single perturb ed segment of a toroidal flux ring lying slightly beneath the base of the convection zone is studied by way of numerical simulations. We hav e considered flux loop evolution assuming both solid-body rotation, an d differential rotation consistent with recent results from helioseism ology. 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, ass uming a dynamo wave propagating from 30 degrees latitude to the equato r at the base of the convection zone. In the case of solid-body rotati on, a toroidal field strength B-0 greater than or equal to 40 kG is re quired to avoid a significant equatorial gap, but if differential rota tion is included, B-0 greater than or equal to 20 kG leads to an accep table butterfly diagram. 2. As was found in the previous work of D'Sil va & Choudhuri, the Coriolis force induced by the diverging east-west velocity near the loop apex acts to twist the loop as it rises and pro duces a tilt angle upon emergence, with the leading leg of the loop cl oser 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 o f uncertainties in the observations of Joy's law. 3. From a simple for ce balance analysis, we derive a scaling law for the tilt angle alpha in terms of the initial field strength B-0, emerging latitude theta(em ), and the total flux Phi of the loop: alpha proportional to sin theta (em) B-0(-5/4 Phi 1/4). This scaling relation describes our simulation s reasonably well when B-0 greater than or equal to 20 kG. For B-0 < 2 0 kG, however, the loop tilt angles are found to decrease with decreas ing field strength B-0, and in some cases lead to negative tilt values (i.e., opposite to the tilts of active regions). This decrease of til t for weak-field Aux loops is caused by a strong converging parallel f low that sets in when the loop apex reaches the upper layers of the co nvection zone. 4. We still find, as we did in the multiloop studies in Fan, Fisher, & DeLuca, that the magnetic held in the leading leg of a n emerging loop is approximately twice that in the following leg. We a rgue that this field strength asymmetry is the origin of morphological asymmetries in bipolar active regions. Finally, we offer some specula tions on the decay of active regions, based on the results of our stud ies. We speculate that as plasma in the tube attempts to establish hyd rostatic equilibrium along the held lines after the flux emergence has taken place, the tube field strength at some intermediate depths belo w 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 conv ection zone. The surface portions of the emerged flux tubes are then t ransported by motions near the photosphere, such as supergranular conv ection and meridional flow.