Gravitational radiation from crystalline color-superconducting hybrid stars

Abstract

The interiors of high mass compact (neutron) stars may contain deconfined quark matter in a crystalline color-superconducting (CCS) state. On a basis of microscopic nuclear and quark matter equations of states we explore the internal structure of such stars in general relativity. We find that their stable sequence harbors CCS quark cores with masses ${M}_{\mathrm{core}}\ensuremath{\le}(0.78--0.82){M}_{\ensuremath{\bigodot}}$ and radii ${R}_{\mathrm{core}}\ensuremath{\le}7\text{ }\text{ }\mathrm{km}$. The CCS quark matter can support nonaxisymmetric deformations, because of its finite shear modulus, and can generate gravitational radiation at twice the rotation frequency of the star. Assuming that the CCS core is maximally strained we compute the maximal quadrupole moment it can sustain. The characteristic strain of gravitational wave emission ${h}_{0}$ predicted by our models are compared to the upper limits obtained by the LIGO and GEO 600 detectors. The upper limits are consistent with the breaking strain of CCS matter $\ensuremath{\sigma}\ensuremath{\le}{10}^{\ensuremath{-}4}$ and large pairing gaps $\ensuremath{\Delta}\ensuremath{\sim}50\text{ }\text{ }\mathrm{MeV}$, or, alternatively, with $\ensuremath{\sigma}\ensuremath{\sim}{10}^{\ensuremath{-}3}$ and small pairing gaps $\ensuremath{\Delta}\ensuremath{\sim}15\text{ }\text{ }\mathrm{MeV}$. An observationally determined value of the characteristic strain ${h}_{0}$ can pin down the product $\ensuremath{\sigma}{\ensuremath{\Delta}}^{2}$. On the theoretical side a better understanding of the breaking strain of CCS matter will be needed to predict reliably the level of the deformation of CCS quark core from first principles.