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Implications of two-flavour colour superconductivity on compact star physics Al-Quaderi, Golam Dastegir

Abstract

In this thesis, we study the thermodynamics of two-flavour colour superconductivity and the effects of its occurrence on the structure and cooling of compact stars. We consider pure two-flavour colour superconductors (2SC), gapless 2SC (g2SC), mixed phase of non-superconducting (normal) quark matter and 2SC or g2SC phase, with possibly free strange quarks present. We employ the BCS pairing interaction through a four-quark operator with the quantum numbers of a single gluon exchange. Low density matter on the crust of the star is modeled by the neutral hadronic phase in the relativistic mean field approximation. The equations of state of the quark and the hadronic phases are found, as well as the phase diagram of the quark matter. The quark matter is seen to undergo second order phase transitions from the mixed phase to pure 2SC or g2SC phase and in between the 2SC and g2SC phases. The quark matter also undergoes a second order phase transition from normal to pure colour superconducting phase with increase of the baryon chemical potential. The mass and structure of the stars are found by solving the Tolman- Oppenheimer-Volkoff equations together with the equation of state of the particular phase. We find a transition from pure quark to hybrid and ultimately pure hadronic stars with increase of bag constant. For certain bag constants, with increase of central pressure, we see an unstable branch in the mass versus radius plot of the hybrid stars which later changes into a stable branch. We find the difference of mass and total baryon number between configurations of the compact stars at zero and finite central temperatures as functions of the central pressure. The cooling stars are considered at fixed total baryon number. We find the thermal capacity or the ratio of the energy lost to the change of central temperature for quark stars with the colour superconducting or normal quark phase. The quark stars without free strange quarks in 2SC phase loose more energy while cooling compared to stars with non-zero strangeness. The cooling quark stars however shrink more if they contain free strange quarks.

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