Phase Conversions in Neutron Stars: Implications for Stellar Stability and Gravitational Wave Astrophysics

We review the properties of hybrid stars with a quark matter core and a hadronic mantle, focusing on the role of key micro-physical properties such as the quark/hadron surface and curvature tensions and the conversion speed at the interface between both phases. We summarize the results of works that have determined the surface and curvature tensions from microscopic calculations. If these quantities are large enough, mixed phases are energetically suppressed and the quark core would be separated from the hadronic mantle by a sharp interface. If the conversion speed at the interface is slow, a new class of dynamically stable hybrid objects is possible. Densities tens of times larger than the nuclear saturation density can be attained at the center of these objects. We discuss possible formation mechanisms for the new class of hybrid stars and smoking guns for their observational identification.

Hydrodynamics and Thermodynamics of Newtonian Stars

We investigated spherically symmetric solution for nonrelativistic cosmological fluid equations and thermodynamic equation of state for Newtonian stars. It was shown that the assumption of a polytropic state equation, P 0 = κ ρ 0 γ , at the center of the star only suffices to integrate the equations explicitly. Our exact solution yields many fruitful results such as stellar stability, spherical oscillation and collapses of stars. Pressure, temperature, and density profiles inside stars were obtained. Central densities, pressures and temperatures of the Newtonian stars such as Sun, Jupiter and Saturn were also calculated. Analytical results show that stars with γ ≤ 4/3 are unstable so that they are collapsing or they may expand forever. On the other hand, stars with γ > 4/3 are stables so that they could undergo spherical oscillation. The upper bound value of white dwarf mass obtained turns out to be close to the Chandrasekhar limit. Motion of the Universe was also discussed within the framework of Newtonian mechanics.