  We compute structures of vortex configurations in a harmonically trapped
Bose-Einstein condensed atom gas within three different gapless self-consistent
mean-field theories. Outside the vortex core region, the density profiles for
the condensate and the thermal gas are found to differ only by a few percent
between the Hartree-Fock-Bogoliubov-Popov theory and two of its recently
proposed gapless extensions. In the core region, however, the differences in
the density profiles are substantial. The structural differences are reflected
in the energies of the quasiparticle states localized near the vortex core.
Especially, the predictions for the energy of the lowest quasiparticle
excitation differ considerably between the theoretical models investigated.
