  In this note we investigate bound states, where scalar and vector bosons are
trapped by BPS vortices in the Abelian Higgs model with a critical ratio of the
couplings. A class of internal modes of fluctuation around cylindrically
symmetric BPS vortices is characterized mathematically, analysing the spectrum
of the second-order fluctuation operator when the Higgs and vector boson masses
are equal. A few of these bound states with low values of quantized magnetic
flux are described fully, and their main properties are discussed.
