Speed of sound constraints from tidal deformability of neutron stars

Abstract: The upper bound of the speed of sound in dense nuclear matter is one of the most interesting but still unsolved problems in Nuclear Physics. Theoretical studies in connection with recent observational data of isolated neutron stars as well as binary neutron stars systems offer an excellent opportunity to shed light on this problem. In the present work, we suggest a method to directly relate the measured tidal deformability (polarizability) of binary neutron stars system (before merger) to the maximum neutron star mass scenario and possible upper bound on the speed of sound. This method is based on the simple but efficient idea that while the upper limit of the effective tidal deformability favors soft equations of state, the recent high measured values of neutron star mass favor stiff ones. In the present work, firstly, using a simple well established model we parametrize the stiffness of the equation of state with the help of the speed of sound. Secondly, in comparison with the recent observations by LIGO/VIRGO collaboration of two events, GW170817 and GW190425, we suggest possible robust constraints. Moreover, we evaluate and postulate, in the framework of the present method, what kind of future measurements could help us to improve the stringent of the constraints on the neutron star equation of state.