Working in the physics of Wilson factor and Aharonov-Bohm effect, we find in the fluxtubequark system the topology of a baryon consisting of three heavy flavor quarks resembles that of the fractional quantum Hall effect （FQHE） in condensed matter. This similarity yields the result that the constituent quarks of baryon have the ＂filling factor＂ 1/3, thus the previous conjecture that quark confinement is a correlation effect is confirmed. Moreover, by deriving a Hamiltonian of the system analogous to that of FQHE, we predict an energy gap for the ground state of a heavy three-quark system.
The properties of hybrid stars are investigated in the framework of the relativistic mean field theory （RMFT） and an MIT bag model with density-dependent bag constant to describe the hadron phase （HP） and quark phase （QP）, respectively. We find that the density-dependent B（p） decreases with baryon density p; this decrement makes the strange quark matter become more energetically favorable than ever, which makes the threshold densities of the hadron-quark phase transition lower than those of the original bag constant case. In this case, the hyperon degrees of freedom can not be considered. As a result, the equations of state of a star in the mixed phase （MP） become softer whereas those in the QP become stiffer, and the radii of the star obviously decrease. This indicates that the extended MIT bag model is more suitable to describe hybrid stars with small radii.
Influences of the bag constant on the properties of hybrid stars are investigated by using relativistic mean field theory and the MIT bag model to describe the hadron phase and quark phase in the interior of neutron stars, respectively. Our results indicate that the onset of hadron-quark phase transition is put off and the appearance of hyperon species is increased with the increase in bag constant. As a result, the hybrid star equation of state for a mixed phase range stiffens whereas that of the quark phase range softens, and the gravitational mass as well as the corresponding radius of hybrid stars are increased obviously. The gravitational mass of a hybrid star is increased from 1.42 M （M is solar mass） to 1.63M and the corresponding radius is changed from 9.1 km to 12.2 km when the bag constant （B1/4） is increased from 170 MeV to 200 MeV. It is interesting to find that hybrid star equations of state become non-smooth when the TM2 parameter sets in the framework of relativistic mean field theory used to describe the hadronic matter, and consequently, the third family of compact stars appear in the mass-radius relations of hybrid stars in the narrow scope of the bag constant from 175 MeV to 180 MeV. These show that the choice of the bag constant in the MIT bag model has significant influence on the properties of hybrid stars.
