Torsional oscillations of crystalline color-superconducting hybrid stars: Possible sources for Advanced LIGO?

Abstract

Deconfined quark matter may exist in a crystalline color-superconducting phase in the interiors of compact stars. In this paper, we study the torsional oscillations of compact stars featuring a crystalline color-superconducting quark-matter core in general relativity. Depending on the size of the crystalline core and the value of the gap parameter $\Delta$, we find that the frequencies of the torsional oscillation modes can range from a few hundred hertz to a few kilohertz for our canonical $1.4 M_\odot$ compact star models. We have also studied the prospect for detecting the gravitational-wave signals emitted from these modes in a pulsar glitch event. Assuming that at least $10\%$ of the energy released in a Vela glitch can be channeled to the oscillation modes, we find that the Einstein Telescope should be able to detect these signals in quite general situations. Furthermore, if the size of the crystalline core is comparable to the stellar radius and the gap parameter is relatively small at $\Delta \sim 5$ MeV, the signal-to-noise ratio for Advanced LIGO could reach $\sim$10 for a Vela glitch. Our optimistic results suggest that we might already be able to probe the nature of crystalline color-superconducting quark matter with the second-generation gravitational-wave detectors when they come online in the next few years.