Phase transition in compact stars due to a violent shock

In this letter we study the dynamics of a first order phase transition from nucleonic to quark matter in neutron stars. Using standard equations of state for these two phases we find the density range where such a transition is possible. Then we study the transformation of the star assuming that the quark core is formed via a spherical shock wave. The thermodynamical conditions in the quark core are found from the conservation laws across the transition region. Their dependence on the density and velocity of the incoming nuclear matter are studied. It is found that the shock is especially violent in the beginning of the conversion process when the velocity of the infalling matter is especially high. As the shock propagates further from the center the front velocity first increases and reaches a maximum value when the incoming velocity is around $0.2$. Finally, the front velocity quickly goes to zero when incoming matter velocity approaches zero. We have shown that the density and pressure jumps are especially large in the begining of the transition process.