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 _ { core } \leq ( 0.78 - 0.82 ) M _ { \odot } and radii R _ { core } \leq 7 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 \sigma \leq 10 ^ { -4 } and large pairing gaps \Delta \sim 50 MeV , or , alternatively , with \sigma \sim 10 ^ { -3 } and small pairing gaps \Delta \sim 15 MeV .
An observationally determined value of the characteristic strain h _ { 0 } can pin down the product \sigma \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 .