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(Abridged) It is well known that the tidal deformability of a compact starcarries important information about the interior equation-of-state (EOS) of thestar. The first gravitational-wave event GW170817 from a binary compact starmerger observed by the LIGO/VIRGO detectors have already put limits on thetidal deformability and provided constraints on the ultra-high nuclear densityEOS. In view of this ground breaking discovery, we revisit and extend ourprevious work [Phys. Rev. D 95, 101302(R) (2017)] which found that taking theeffect of elasticity into account in the calculation of the tidal deformabilityof compact star models composed of crystalline color-superconducting (CCS)quark matter can break the universal I-Love relation discovered for fluidcompact stars. In this paper, we present our formulation in detail and providemore analysis to complement our previous findings. We focus and extend thestudy of the screening effect on the tidal deformability, which we foundpreviously for hybrid star models, to various theoretical two-layer compactstar models. We show that the screening effect of these two-layer models ingeneral depends on the thickness of the envelope and the ratio between thedensity gap and the core density at the core-envelope interface. However, formodels with a fluid envelope and a vanishing small density gap, the screeningeffect remains strong even as the thickness of the envelops tends to zero ifthe quark matter core has a fairly uniform density. The relevance of our studyto GW170817 is also discussed. Our study advocates that the tidal deformabilitynot only provides us information on the EOS, but may also give insights intothe multi-layer structure and elastic properties of compact star modelscomposed of CCS quark matter.

Two-layer compact stars with crystalline quark matter: Screening effect on the tidal deformability