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We study the phase structure and phase transition of cold dense QCD mattervia the Dyson-Schwinger equation approach. We take the rainbow approximationand the Gaussian-type gluon model. In order to guarantee that the quark numberdensity begins to appear at the nuclear liquid-gas phase transition chemicalpotential, we propose a chemical potential dependent modification factor forthe gluon model. We find that for the iso-symmetric quark matter, themodification reduces the chemical potential of the phase coexistence region ofthe first--order phase transition. We also implement the relativistic meanfield theory to describe the hadron matter, and make use of the Maxwell andGibbs construction method to study the phase transition of beta--equilibriumand charge neutral matter in compact stars. The results show that the phasetransition will not happen in case of the Gaussian--type gluon model withoutany modification. The results also indicate that the upper boundary of thecoexistence region should be larger than the current Nambu solution existingregion. We also calculate the mass-radius relation of the compact stars, andfind that the hadron-quark phase transition happens at too high chemicalpotential so that the maximum mass of the compact star is hardly affected bythe hadron-quark phase transition.

QCD phase transition and equation of state of stellar strong interaction matter via Dyson-Schwinger equation approach