Tidal deformations of compact stars with crystalline quark matter

We study the tidal deformability of bare quark stars and hybrid compact stars composed of a quark matter core in general relativity, assuming that the deconfined quark matter exists in a crystalline color superconducting phase. We find that taking the elastic property of crystalline quark matter into account in the calculation of the tidal deformability can break the universal I-Love relation discovered for fluid compact stars, which connects the moment of inertia and tidal deformability. Our result suggests that measurements of the moment of inertia and tidal deformability can in principle be used to test the existence of solid quark stars, despite our ignorance of the high density equation of state (EOS). Assuming that the moment of inertia can be measured to 10% level, one can then distinguish a 1.4 (1) $M_\odot$ solid quark star described by our quark matter EOS model with a gap parameter $\Delta=25$ MeV from a fluid compact star if the tidal deformability can be measured to about 10% (45%) level. On the other hand, we find that the nuclear matter fluid envelope of a hybrid star can screen out the effect of the solid core significantly so that the resulting I-Love relation for hybrid stars still agrees with the universal relation for fluid stars to about 1% level.