Recurring region for neutron-star observables

In this letter, we report a new phenomena of recurring regions when relating observables for hybrid neutron stars and hybrid neutron-star mergers. To describe dense matter within hybrid stars, we introduce a percolation to vary the size and characteristics of the deconfinement phase transition to quark matter. Before and after the percolation, we keep the hadronic and quark phases the same, described by different realistic models for the equation of state of beta-equilibrated, charge-neutral, zero-temperature matter. When solving spherical and deformed equations for neutron stars in general relativity, we find that: no matter the size or characteristics of the percolation region, or the order of the phase transition on either side (hadronic and quark), as long as we minimize the average sound speed from the beginning of the percolation region to the central density for a given star, we can produce equations of state that cross through the same, small recurring region within mass-radius and mass-tidal deformability diagrams. Our findings provide a new way to produce hybrid equations of state for dense matter that match a given observation of neutron stars or neutron star mergers.