Effect of color superconductivity on the mass of hybrid neutron stars in an effective model with perturbative QCD asymptotics

Abstract

The effective cold quark matter model by Alford, Braby, Paris, and Reddy (ABPR) is used as a tool for discussing the effect of the size of the pairing gap in three-flavor (CFL) quark matter on the maximum mass of hybrid neutron stars (NSs). This equation of state (EOS) has three parameters which we suggest to determine by comparison with a nonlocal Nambu-Jona-Lasinio (nlNJL) model of quark matter in the nonperturbative domain. We show that due to the momentum dependence of the pairing which is induced by the nonlocality of the interaction, the effective gap parameter in the EOS model is well approximated by a constant value depending on the diquark coupling strength in the Nambu-Jona-Lasinio (NJL) model Lagrangian. For the parameter a4=1–2αs/π a constant value below about 0.4 is needed to explain hybrid stars with Mmax≳2.0M⊙, which would translate to an effective constant αs∼1. The matching point with a running coupling at the 1-loop β function level is found to lie outside the range of chemical potentials accessible in NS interiors. A dictionary is provided for translating the free parameters of the nlNJL model to those of the ABPR model. Both models are shown to be equivalent in the nonperturbative domain but the latter one allows to quantify the transition to the asymptotic behavior in accordance with perturbative QCD. We provide constraints on parameter sets that fulfill the 2M⊙ mass constraint for hybrid NSs, as well as the low tidal deformability constraint from GW170817 by a softening of the EOS on the hybrid NS branch with an early onset of deconfinement at Monset<1.4M⊙. We find that the effective constant pairing gap should be around 100 MeV but not exceed values of about 130 MeV because a further increase of the gap would entail a softening of the EOS and contradict the 2M⊙ mass constraint.

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