Using a simple model for the onset of solar eruptions, we investigate how a
n existing magnetic configuration containing a flux rope evolves in respons
e to new emerging flux. Our results show that the emergence of new flux can
cause a loss of ideal MHD equilibrium under certain circumstances, but the
circumstances which lead to eruption are much richer and more complicated
than one might expect given the simplicity of the model. The model results
suggest that the actual circumstances leading to an eruption are sensitive
not only to the polarity of the emerging region, but also to several other
parameters, such as the strength, distance, and area of the emerging region
. It has been suggested by various researchers that the emergence of new fl
ux with an orientation which allows reconnection with the preexisting flux
(a process sometimes referred to as tether cutting) will generally lead to
destabilization of the coronal or prominence magnetic field. Although our r
esults can replicate such behavior for certain restricted classes of bounda
ry conditions, we find that, in general, there is no simple, universal rela
tion between the orientation of the emerging flux and the likelihood of an
eruption.