On the sound velocity bound in neutron stars

It has been suggested in the literature that the sound velocity of the nuclear matter $v_s$ violates the so-called sound velocity bound $v_s \le c/\sqrt{3}$ at high density, where $c$ is the speed of light. In this paper, we revisit this issue and confront the current measurements of mass, radius, and tidal deformability of neutron stars with $10^5$ different equations of state which are parametrized at low density and saturates the sound velocity bound beyond twice the saturation density where the equation of state has not been constrained yet, by which we can conservatively obtain the maximum mass of the neutron stars compatible both with the observed properties of neutron stars and the sound velocity bound. We find that majority of the models are eliminated by the incompatibility with the observations and, especially, the recently detected massive pulsar ($2.35\pm 0.17 M_\odot$) is hardly realized by our simulations. Our study strongly supports the violation of the sound velocity bound.