Constraints on neutron stars equation of state using the tidal deformability derived from BNS mergers

Abstract

The purpose of this work is the study of neutron stars (NS) equation of state (EOS) using constraints on tidal deformability derived from observation of binary neutron star (BNS) mergers, such as GW170817. The mathematical formalism is introduced, and then for a variety of EOS the system is solved numerically, allowing us to determine the mass, the radius, the tidal love number and the tidal deformability of the NS, each one of them unique for each EOS. Moreover, for a fixed value of chirp mass under the assumption that  m2<m1 (where m1 is the heavier component mass of BNS system), the effective (mass-weighted) tidal deformability of the binary system is determined for each EOS. We consider both an upper limit (GW170817) and a lower limit (AT2017gfo) for the effective tidal deformability. Also, we construct the Λ1-Λ2 space and we compare the behavior of EOS with the most recent LIGO’s data. We found out that the most EOS models give values for the effective tidal deformability less than the upper limit and that the most stiff EOS are excluded.