We consider quarkyonic matter to naturally explain the observed properties of neutron stars. We argue that such matter might exist at densities close to that of nuclear matter, and at the onset, the pressure and the sound velocity in quarkyonic matter increase rapidly. In the limit of large number of quark colors N_{c}, this transition is characterized by a discontinuous change in pressure as a function of baryon number density. We make a simple model of quarkyonic matter and show that generically the sound velocity is a nonmonotonic function of density-it reaches a maximum at relatively low density, decreases, and then increases again to its asymptotic value of 1/sqrt[3].
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