| In the interior of a neutron star, matter is ultra-dense with its density as high as a few times the nuclear saturation density, and extremely cold compared to its chemical potential. As a result, it is the most likely place where the theoretically-predicted strange quark matter might exist. The aim of this thesis is to reveal how the strange quark matter could influence the static properties and dynamic behaviors of compact stars. This is of great importance because it allows us to draw conclusions about the phase diagram of matter at extreme density, by investigating observable properties of compact stars despite uncertainties in their detailed structures. By studying the microscopic physics of dense matter such as charge-separation phase, hadron-quark conversion and strangeness diffusion process, and applying a generic parametrization of high-density equation of states, we explore implications about mass-radius relationship, r-mode damping and spin evolution etc. of the star.;In the first part of this thesis we calculate the equation of state (EoS) of the mixed phase in strangelet dwarfs, and obtain the mass-radius relation by solving Tolman-Oppenheimer-Volkoff (TOV) equation. In the second and third parts, we first study the mass-radius relation of hybrid stars with a sharp interface between nuclear and quark matter by using the generic "constant speed of sound" (CSS) parameterization, and obtain the phase diagram of possible forms of the mass-radius relation. We then apply the parametrization to the Field Correlator Method (FCM) model of quark matter and express observational constraints as constraints on the CSS parameters. In the fourth part, we propose a novel mechanism for the saturation of unstable oscillation modes in multi-component compact stars based on the periodic conversion between different phases, and study in detail the case of r-modes in a hybrid star with a sharp interface, giving the saturation amplitude and its range of validity to predict observational outcomes. |
