Recurring region for neutron-star observables

In this letter, we report a novel, somewhat analytical way to produce equations of state (EOSs) that generate particular values of neutron star mass, radius, and tidal deformability. This is possible because our description for the EoS of dense matter can produce recurring regions, small areas where several EoSs cross in the mass-radius and mass-tidal deformability diagrams. We can place recurring regions in desired locations of these diagrams, corresponding e.g., to a given observation. Our prescription is versatile, in the sense that different microscopic models can be used for the low density hadronic phase and high density quark phase, as long as they are connected by a percolation, a description that mimics quark deconfinement and is motivated by QCD. The several EoSs that pass by a recurring region can present different thresholds for the boundaries of the percolation region (different beginning and ending for the quark deconfinement region), as well as different orders for the phase transition at the boundaries. When combining all these features, our prescription allows one not only to produce an EoS that matches an observation, but also one that matches specific chosen criteria for the EoS. The EoSs produced by this new method will be specially suitable for the study of dense-matter properties in future gravitational-wave observations, when both the inspiral and post-merger phase signals will become available. Our numerical code that calculates recurring regions using CompOSE microscopic EoSs is open source and publicly available.