Sound Velocity Bound and Neutron Stars

It has been conjectured that the velocity of sound in any medium is smaller than the velocity of light in vacuum divided by $\sqrt{3}$. Simple arguments support this bound in nonrelativistic and/or weakly coupled theories. The bound has been demonstrated in several classes of strongly coupled theories with gravity duals and is saturated only in conformal theories. We point out that the existence of neutron stars with masses around two solar masses combined with the knowledge of the equation of state of hadronic matter at “low” densities is in strong tension with this bound.

Figure 1

Histogram of the number of models as a function of the maximum mass supported.

Figure 2

Radii versus maximum mass for configurations with the largest possible pressure subject to the velocity bound. The 68% and 95% confidence regions are outlines for the radii for three different masses.