  Solar active regions and sunspots are believed to be formed by the emergence
of strong toroidal magnetic flux from the solar interior. Modeling of such
events has focused on the dynamics of compact magnetic entities, colloquially
known as "flux tubes", often considered to be isolated magnetic structures
embedded in an otherwise field-free environment. In this paper, we show that
relaxing such idealized assumptions can lead to surprisingly different
dynamics. We consider the rise of tube-like flux concentrations embedded in a
large-scale volume-filling horizontal field in an initially quiescent
adiabatically-stratified compressible fluid. In a previous letter, we revealed
the unexpected major result that concentrations that have their twist aligned
with the background field at the bottom of the tube are more likely to rise
than the opposite orientation (for certain values of the parameters). This bias
leads to a selection rule which, when applied to solar dynamics, is in
agreement with the observations known as the solar hemispheric helicity rule(s)
(SHHR). Here, we examine this selection mechanism in more detail than was
possible in the earlier letter. We explore the dependence on the parameters via
simulations, delineating the Selective Rise Regime (SRR), where the bias
operates. We provide a theoretical model to predict and explain the simulation
dynamics. Furthermore, we create synthetic helicity maps from Monte Carlo
simulations to mimic the SHHR observations and demonstrate that our mechanism
explains the observed scatter in the rule and its variation over the solar
cycle.
