Emerging flux tubes in the solar convection zone. II. The influence of initial conditions

Numerical simulations of rising magnetic flux tubes in the solar convection zone have contributed significantly to our understanding of the basic prop erties of sunspot groups. They have provided an important clue to the opera tion of the solar dynamo by predicting strong (super-equipartition) magneti c fields near the bottom of the convection zone. We have investigated to wh at extent the simulation results (obtained on the basis of the thin flux tu be approximation) depend on the assumptions made about the initial state of a magnetic flux tube at the start of the simulation. Two initial condition s used in the literature have been considered in detail: mechanical equilib rium (MEQ) and temperature balance (TBL). It turns out that the requirement of super-equipartition field strength is a robust feature of the simulatio ns, largely independent of the choice of initial conditions: emergence of a ctive regions at low latitudes and the correct dependence of their tilt ang le (with respect to the east-west direction) as a function of heliographic latitude require an initial magnetic held strength on the order of 10(5) G. Other properties of rising flux tubes, such as the asymmetries of shape an d field strength between the leading and following wings (with respect to t he direction of rotation) of a rising loop, or the anchoring of part of the flux tube in the overshoot region, depend on the initial condition. Observ ed asymmetries in the magnetic flux distribution and of proper motions in e merging active regions favor MEQ over TBL as the proper initial condition. MEQ should also be preferred for other theoretical reasons: it allows for f ewer free parameters, it requires no fine tuning for the tube geometry and background stratification in the overshoot region, and it can be easily mad e compatible with an encompassing model of the generation, storage, and eru ption of the magnetic flux. We have also studied whether an external upflow (convective updraft) can trigger the eruption of an otherwise stably store d flux tube in the overshoot region. We find that a significant deformation and destabilization of a flux tube with equipartition held strength requir es coherent upflow velocities of 20-50 m s(-1) in the overshoot layer, whic h is an order of magnitude larger than current estimates for such velocitie s.