  Superfluid vortices in the color-flavor-locked (CFL) phase of dense quark
matter are known to be energetically disfavored relative to well-separated
triplets of "semi-superfluid" color flux tubes. However, the short-range
interaction (metastable versus unstable) has not been established. In this
paper we perform numerical calculations using the effective theory of the
condensate field, mapping the regions in the parameter space of coupling
constants where the vortices are metastable versus unstable. For the case of
zero gauge coupling we analytically identify a candidate for the unstable mode,
and show that it agrees well with the results of the numerical calculations. We
find that in the region of the parameter space that seems likely to correspond
to real-world CFL quark matter the vortices are unstable, indicating that if
such matter exists in neutron star cores it is very likely to contain
semi-superfluid color flux tubes rather than superfluid vortices.
