We have obtained the Love number and corresponding tidal deformabilities $\left(\mathrm{\Lambda }\right)$ associated with the relativistic mean-field parametrizations shown to be consistent (CRMF) with the nuclear matter, pure neutron matter, symmetry energy, and its derivatives [Dutra et al., Phys. Rev. C 90, 055203 (2014)]. Our results show that CRMF models present very good agreement with the recent data from binary neutron star merger event GW170817. They also confirm the strong correlation between ${\mathrm{\Lambda }}_{1.4}$ and the radius of canonical stars $\left(R_{1.4}\right)$. When a recent GW170817 constraint on ${\mathrm{\Lambda }}_{1.4}$ and the corresponding radius $R_{1.4}$ is used, the majority of the models tested are shown to satisfy it.

We perform a detailed analysis of the fundamental mode of nonradial pulsations of color flavor locked strange stars. Solving the general relativistic equations for nonradial pulsations for an equation of state derived within the MIT bag model, we calculate the frequency and the gravitational damping time of the fundamental mode for all the parametrizations of the equation of state that lead to self-bound matter. Our results show that color flavor locked strange stars can emit gravitational radiation in the optimal range for present gravitational wave detectors and that it is possible to constrain the equation of state's parameters if the fundamental oscillation mode is observed and the stellar mass is determined. We also show that the $f$-mode frequency can be fitted as a function of the square root of the average stellar density $\sqrt{M/R^3}$ by a single linear relation that fits quite accurately the results for all parametrizations of the equation of state. All results for the damping time can also be fitted as a function of the compactness $M/R$ by a single empirical relation. Therefore, if a given compact object is identified as a color flavor locked strange star these two relations could be used to determine the mass and the radius from the knowledge of the frequency and the damping time of gravitational waves from the $f$ mode.

Oscillation modes of isolated compact stars can, in principle, be a fingerprint of the equation of state (EoS) of dense matter. We study the non-radial high-frequency $l=2$ spheroidal modes of neutron stars and strange quark stars, adopting a two-component model (core and crust) for these two types of stars. Using perturbed fluid equations in the relativistic Cowling approximation, we explore the effect of a strangelet or hadronic crust on the oscillation modes of strange stars. The results differ from the case of neutron stars with a crust. In comparison to fluid-only configurations, we find that a solid crust on top of a neutron star increases the $p$-mode frequency slightly with little effect on the $f$-mode frequency, whereas for strange stars, a strangelet crust on top of a quark core significantly increases the $f$-mode frequency with little effect on the $p$-mode frequency.

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 $\Delta${}. 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 $\Delta${}. As a consequence, the oscillation period is strongly affected by color superconductivity for stars with M$\gtrsim${}1.5\,\,M$\bigodot${}. We fit the period of the fundamental mode with appropriate analytical functions of the gravitational redshift of the star and the pairing gap $\Delta${}. We further discuss the excitation and damping of the modes and their potential detectability during violent transient phenomena.