Hybrid star within the framework of a lowest-order constraint variational method

Abstract: The hadron-quark phase transition in the core of heavy neutron star (NS) has been studied. For the hadronic sector, we have used the lowest-order constraint variational method by employing $ AV_{18} $, $ AV_{14}$, $ UV_{14}$, and Reid $ 68 $ two-body nucleon-nucleon forces supplemented by the phenomenological Urbana-type three-body force. We have adopted the MIT bag model as well as three-flavor version of the Nambu- Jona-Lasinio (NJL) model to describe the quark phase. The equation of state (EOS) of a hybrid star (HS) is presented by combining two EOS of the hadronic sector and quark sector of a star, which are derived from independent models or theories. The hadron-quark transition is constructed by considering a sharp phase transition, i.e., Maxwell construction. The structure of the HS is calculated and reported by solving Tolman-Oppenheimer-Volkoff equations. Finally the radii and tidal deformability of purely NS and HS for the mass of $ 1.4M_{\odot} $ is computed and new constraints on these quantities are checked. The maximum mass of HS is found more than $ 2 M_{\odot} $ for both the NJL and MIT bag models. However, the maximum mass of $ 1.796 M_{\odot} $ ($ 1.896 M_{\odot} $) was the best result that would be calculated for a stable HS with the pure quark core within the MIT (NJL) model. All the hybrid EOS fulfill the constraints on radii and tidal deformability extracted from the binary GW170817 for HSs. A comprehensive analysis on the structure of purely NS and HS and also compactness, tidal Love number, and tidal deformability for the star with the mass of 1.4 $ M_{\odot} $ has been conducted for various EOS of the hadron sector and several parameter sets of the quark EOS. The results achieved in this study are in good concurrence with the other calculations reported on this subject.