Constraining crystalline color superconducting quark matter with gravitational-wave data

Abstract

We estimate the maximum equatorial ellipticity sustainable by compact stars composed of crystalline color-superconducting quark matter. For the theoretically allowed range of the gap parameter $\Delta$, the maximum ellipticity could be as large as $10^{-2}$, which is about 4 orders of magnitude larger than the tightest upper limit obtained by the recent science runs of the LIGO and GEO600 gravitational wave detectors based on the data from 78 radio pulsars. We point out that the current gravitational-wave strain upper limit already has some implications for the gap parameter. In particular, the upper limit for the Crab pulsar implies that $\Delta$ is less than O(20) MeV for a range of quark chemical potential accessible in compact stars, assuming that the pulsar has a mass $1.4 M_{\odot}$, radius 10 km, breaking strain $10^{-3}$, and that it has the maximum quadrupole deformation it can sustain without fracturing.