Radial oscillations of color superconducting self-bound quark stars

We investigate the effect of the color-flavor locking pairing pattern on the adiabatic radial oscillations of pure self-bound quark stars using an equation of state in the framework of the MIT Bag model. We integrate the equations of relativistic radial oscillations to determine the fundamental and the first excited oscillation modes for several parameterizations of the equation of state. For low mass stars we find that the period of the fundamental mode is typically $\sim 0.1$ ms and has a small dependence on the parameters of the equation of state. For large mass stars the effect of color-flavor locking is related to the rise of the maximum mass with increasing $Δ$. As for unpaired quark stars, the period of the fundamental mode becomes divergent at the maximum mass but now the divergence is shifted to large masses for large values of the pairing gap $Δ$. As a consequence, the oscillation period is strongly affected by color superconductivity for stars with $M \gtrsim 1.5 \; \textrm{M}_{\odot}$. We fit the period of the fundamental mode with appropriate analytical functions of the gravitational redshift of the star and the pairing gap $Δ$. We further discuss the excitation and damping of the modes and their potential detectability during violent transient phenomena.

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