Dynamical Phase Transition in Neutron Stars

We have studied the dynamical evolution of the shock in a neutron star (NS). The conversion of nuclear to quark matter (QM) is assumed to take place at the shock discontinuity. The density and pressure discontinuity is studied both spatially and temporally as it starts near the center of the star and moves toward the surface. Polytropic equations of state (EoS), which mimic original nuclear and QM EoS, are used to study such dynamical phase transition (PT). Solving relativistic hydrodynamic equations for a spherically symmetric star, we study the PT, assuming a considerable density discontinuity near the center. We find that as the shock wave propagates outward, its intensity decreases with time; however, the shock velocity peaks up and reaches a value close to that of light. Such fast shock velocity indicates rapid PT in NS taking place on a timescale of some 10s of microseconds. Such a result is quite interesting, and it differs from previous calculations that the PT in NSs takes at least some 10s of milliseconds. Rapid PT can have significant observational significance, because such fast PT would imply rather strong gravitational wave (GW) signals that are rather short lived. Such short-lived GW signals would be accompanied with short-lived gamma-ray bursts and neutrino signals originating from the neutrino and gamma-ray generation from the PT of nuclear matter to QM.