Hadron-quark phase transition in dense matter and neutron stars

Abstract

We study the hadron-quark phase transition in the interior of neutron stars (NS's). We calculate the equation of state (EOS) of hadronic matter using the Brueckner-Bethe-Goldstone formalism with realistic two-body and three-body forces, as well as a relativistic mean field model. For quark matter we employ the MIT bag model constraining the bag constant by using the indications coming from the recent experimental results obtained at the CERN SPS on the formation of a quark-gluon plasma. We find necessary to introduce a density dependent bag parameter, and the corresponding consistent thermodynamical formalism. We calculate the structure of NS interiors with the EOS comprising both phases, and we find that the NS maximum masses fall in a relatively narrow interval, 1.4 M ⊙ ≤ M max ≤ 1.7 M ⊙ . The precise value of the maximum mass turns out to be only weakly correlated with the value of the energy density at the assumed transition point in nearly symmetric nuclear matter.

Properties of Neutron Stars with Hyperons and Quarks Using Relativistic Hartree–Fock Approximation and MIT Bag Model

“…The EoS for uniform hadronic matter has been constructed using the CQMC model within relativistic Hatree-Fock approximation, while the EoS for quark matter was calculated using the MIT bag model with one-gluon-exchange interaction. In addition, we have introduced the density-dependent bag constant to study the effect of the phase transition [13,14], assuming the first-order phase transition from hadrons to quarks under Gibbs criteria for chemical equilibrium [15].…”

“…In order to study the effect of quark matter on neutron stars, we introduce a density-dependent bag constant as follows [13,14]:…”

Neutron Star Structure with Hyperons and Quarks

“…This surprising result is due to the strong softening of the baryonic EOS when including hyperons as additional degrees of freedom, and one does not expect substantial changes when introducing refinements of the theoretical framework, such as hyperon-hyperon potentials, hyperonic TBF [14], relativistic corrections, etc.. The only remaining possibility to reach larger maximum masses appears the transition to another phase of dense (quark) matter inside the star [15][16][17][18].…”

“…It has been found [15,21] that within the MIT bag model (without color superconductivity) with a density-independent bag constant B, the maximum mass of a NS cannot exceed a value of about 1.6 solar masses. Indeed, the maximum mass increases as the value of B decreases, but too small values of B are incompatible with a hadron-quark transition density ρ (2 − 3)ρ 0 in nearly symmetric nuclear matter, as demanded by heavy-ion collision phenomenology.…”

“…In order to overcome these restrictions of the model, one can introduce an empirical density-dependent bag parameter B(ρ), and this approach was followed in Refs. [15][16][17]. This allows one to lower the value of B at large density, providing a stiffer QM EOS and increasing the value of the maximum mass, while at the same time still fulfilling the condition of no phase transition below ρ ≈ 3ρ 0 in symmetric nuclear matter.…”