Are Neutron Stars with Crystalline Color-Superconducting Cores Relevant for the LIGO Experiment?

We estimate the maximal deformation that can be sustained by a rotating neutron star with a crystalline color-superconducting quark core. Our results suggest that current gravitational-wave data from the Laser Interferometer Gravitational-Wave Observatory have already reached the level where a detection would have been possible over a wide range of the poorly constrained QCD parameters. This leads to the nontrivial conclusion that compact objects do not contain maximally strained color crystalline cores drawn from this range of parameter space. We discuss the uncertainties associated with our simple model and how it can be improved in the future.

Figure 1

The left panel shows the density profiles for two different values of the ratio ${\rho }_c/{\rho }_n$. One can see quite clearly that (for a fixed mass and radius of $1.4M_{\odot }$ and 10 km, respectively) the core becomes significantly smaller as the transition density rises. This fact is also illustrated in the right panel, which shows the radius of the core as a function of the transition density.

Figure 2

In the left panel, the ellipticities obtained from our analysis are shown as a function of the core transition density ${\rho }_c/{\rho }_n$, where ${\rho }_n$ is the nuclear saturation density. We consider two breaking strains, a maximum value ${\overline{\sigma }}_{\mathrm{br}}={10}^{-2}$, and a minimum of ${\overline{\sigma }}_{\mathrm{br}}={10}^{-5}$. For each of these values we examine the region between the maximum and the minimum shear modulus $\mu$, obtained for the range of parameters in 9, cf. (2). The shaded region indicates the region permitted by LIGO observations and the horizontal line is the current LIGO upper limit of $ϵ=7.1\times {10}^{-7}$ for PSR J2124-3358 [5]. If the breaking strain is close to the maximum the observations are already confronting the theory, showing that J2124-3358 at least does not contain such a maximally strained core. If the breaking strain is close to the minimum, however, no such conclusion can be drawn. In the right panel we compare the ellipticity obtained by considering the full star, only the core of the full star and just the naked core, with no fluid around it. We take the breaking strain to be ${\overline{\sigma }}_{\mathrm{br}}={10}^{-5}$. As one can see, the results for the two cores do not differ significantly, while the ellipticity of the core plus fluid star is smaller, more so as the core size decreases at higher transition densities.