Tidal deformability of strange stars and the GW170817 event

In this work we consider strange stars formed by quark matter in the color-flavor-locked (CFL) phase of color superconductivity. The CFL phase is described by a Nambu-Jona-Lasinio model with four-fermion vector and diquark interaction channels. The effect of the color superconducting medium on the gluons are incorporated into the model by including the gluon self-energy in the thermodynamic potential. We construct parametrizations of the model by varying the vector coupling $G_V$ and comparing the results to the data on tidal deformability from the GW170817 event, the observational data on maximum masses from massive pulsars such as the MSP $\mathrm{J}0740+6620$, and the mass/radius fits to NICER data for PSR $\mathrm{J}003+0451$. Our results point out to windows for the $G_V$ parameter space of the model, with and without gluon effects included, that are compatible with all these astrophysical constraints, namely, $0.21<G_V/G_S<0.4$, and $0.02<G_V/G_S<0.1$, respectively. We also observe a strong correlation between the tidal deformabilites of the GW170817 event and $G_V$. Our results indicate that strange stars cannot be ruled out in collisions of compact binaries from the structural point of view.

Figure 1

Quark star mass, in units of $M_{\odot }$, as a function of its radius generated from the CFL phase (a) without and (b) with gluons contribution. Bands extracted from Refs. [28, 29, 30]. Circles with error bars are related to the NICER data [45, 50, 51].

Figure 2

Energy density as a function of pressure for the CFL phase (a) without and (b) with gluons contribution.

Figure 3

Dimensionless tidal deformability as a function of quark star mass, in units of $M_{\odot }$, for the CFL phase (a) without and (b) with gluons contribution. Full circle: result of ${\mathrm{\Lambda }}_{1.4}=190_{-120}^{+390}$ obtained by LVC [25].

Figure 4

${\mathrm{\Lambda }}_{1.4}$ as a function of the vector channel strength, in units of $G_S$, for the CFL phase with and without gluons contribution. Dashed blue lines: ${\mathrm{\Lambda }}_{1.4}=190_{-120}^{+390}$ obtained by LVC [25].

Figure 5

$\lambda$ as a function of $R$ for the CFL phase (a) without and (b) with gluons contribution.

Figure 6

Dimensionless tidal deformabilities for the case of high-mass (${\mathrm{\Lambda }}_1$) and low-mass (${\mathrm{\Lambda }}_2$) components of the GW170817 event for stars in the CFL phase (a) without and (b) with gluons contribution. The confidence lines (50% and 90%) are taken from Ref. [25]. The dots on the curves denote the values that corresponds to $M_1=1.4M_{\odot }$ and ${\mathrm{\Lambda }}_1={\mathrm{\Lambda }}_{1.4}$.

Figure 7

$\tilde{\mathrm{\Lambda }}$ for different parametrizations (different $G_V$ values) for strange stars in the CFL phase (a) without and (b) with gluons contribution. Dashed lines: range of $\tilde{\mathrm{\Lambda }}=300_{-230}^{+420}$ determined by LVC [26].

Figure 8

Compilation of $G_V$ ranges predicted by this work from comparison with astrophysical data. The intersection of the ranges is (a) $0.02<G_V/G_S<0.1$, and (b) $0.21<G_V/G_S<0.4$ for the model without and with gluons contribution included, respectively.