Constraints on hybrid neutron stars equation of state from neutron stars merging

Using recent gravitational and electromagnetic constraints on the neutron star matter equation of state (EOS) coming from the merge of two neutron stars, we study the physical conditions for which a quark deconfinement phase transition in cold neutron star matter is consistent with these new measurements. To this end, we consider several microscopic EOSs based on various ab initio approaches to describe the confined hadronic phase, and combine them with two phenomenological quark matter EOSs for the deconfined phase. The low and high density phases are then joined up through a mixed phase determined by a Gibbs construction. For each EOS we calculate the dimensionless binary deformability parameter Λ˜ which can be directly related to the constraints derived from the gravitational waves detection. We find that in order to see any difference between the pure hadronic and the hadron-quark EOS for neutron stars with mass in the range (1.4-1.6) M⊙ through the calculation of Λ˜ , the EOSs of both hadronic and quark matter should be quite stiff, otherwise the variation on Λ˜ can be valued just on neutron star masses above 1.8 M⊙ which currently are not constrained by present gravitational waves data. We find in addition that the softening of the hadronic EOS induced by the quark deconfinement phase transition can change the compatibility of a given hadronic EOS with the constraints obtained from neutron stars merging.