Rather surprisingly, vortices in spin-0 superfluids generically carry magnetic fields inside their cores, so that even neutral superfluid vortices may be
thought of as magnetic flux tubes. I'll explain how to understand this ‘vortex magnetic effect’ systematically using effective field theory, clarifying earlier literature on the subject.  The vortex magnetic effect may be large enough to be experimentally detectable in superfluid Helium-4.