Implications from GW170817 and I-Love-Q relations for relativistic hybrid stars

Gravitational wave observations of GW170817 placed bounds on the tidal deformabilities of compact stars, allowing one to probe equations of state for matter at supranuclear densities. Here we design new parametrizations for hybrid hadron-quark equations of state, which give rise to low-mass twin stars, and test them against GW170817. We find that GW170817 is consistent with the coalescence of a binary hybrid star-neutron star. We also test and find that the I-Love-Q relations for hybrid stars in the third family agree with those for purely hadronic and quark stars within $\sim 3\%$ for both slowly and rapidly rotating configurations, implying that these relations can be used to perform equation-of-state independent tests of general relativity and to break degeneracies in gravitational waveforms for hybrid stars in the third family as well.

Figure 1

Pressure vs energy density for the equations of state with first-order phase transitions we consider in this work.

Figure 2

Left: Mass-radius relation for nonrotating HSs. Observe that some EOSs admit a stable third family branch (separate from the stable NS branch). Right: Mass-TD relation for nonrotating stars with the same EOSs. The APR EOS is also shown for comparison.

Figure 3

TDs of compact objects in GW170817 with chirp mass $\mathcal{M}=1.188M_{\odot }$ for the ACS-I (which are indistinguishable from each other for $\mathrm{\Lambda }\ge 70$), ACS-II and ACB EOSs. Solid curves correspond to both stars being in the NS branch while dashed-dotted curves correspond to one of the stars being in the third family (namely, HSs). Note that the gap between the solid and dashed-dotted component of a given color curve arises because the HS member in the binary is unstable. Only the plot above the black dotted line (${\mathrm{\Lambda }}_1={\mathrm{\Lambda }}_2$) is relevant. The dark and light cyan shaded areas correspond to the parameter region within the 50% and 90% credible upper bound set by GW170817 with prior $|\chi |<0.05$ (left panel) and $|\chi |<0.89$ (right panel. The solid black curve corresponds to the APR EOS.

Figure 4

Left: I-Love relations for slowly rotating stars together with the analytic fit of [62]. Right: I-Q relation for slowly and rapidly rotating stars with various dimensionless spin parameters $\chi$ together with the analytic fit in [103]. In both panels $|\overline{\mathrm{I}}-{\overline{\mathrm{I}}}^{(\mathrm{fit})}|/{\mathrm{I}}^{(\mathrm{fit})}$ is the fractional difference between the numerical results and the corresponding analytic fits. The horizontal dashed lines in the $|\overline{\mathrm{I}}-{\overline{\mathrm{I}}}^{(\mathrm{fit})}|/{\mathrm{I}}^{(\mathrm{fit})}$ plots indicate the maximum fractional difference between the numerical results and the fits reported in [62].