Studying VLOCV twin compact stars with binary mergers

GW170817 has provided valuable constraints on the equations of state of merging binary neutron stars, which can be considered as the most probable candidate for the source of gravitational waves. On the other hand, these natural laboratories of extreme temperature and density may lead to the estimation of some exotic matter like deconfined quark matter in their cores. In this paper, we investigate the neutron star matter equation of state (EoS) with the lowest order constrained variational (LOCV) method considering the excluded volume effect (VLOCV) for nucleons to compute the tidal deformability of binary neutron star mergers (BNSMs). Within this approach, the size of nucleons makes the EoS so stiff that requires a phase transition in order to avoid causality violation. Therefore, this phase transition may lead to the appearance of the third family of compact stars including “twin star” configurations. Our EoS models are confronted with observations from GW170817, GW190814, GW190425, and also NICER. We find out that regarding all these constraints, the EoS models having the transition $\text{pressure}\approx 30–100\mathrm{MeV}/{\mathrm{fm}}^3$ and the energy density discontinuity $\mathrm{\Delta }ϵ\lesssim 300\mathrm{MeV}/{\mathrm{fm}}^3$ are preferable.

Figure 1

Radius of nucleon as a function of density for ${\mathrm{r}}_0=0.4\mathrm{fm}$.

Figure 2

Candidate equations of state with ${\mathrm{AV}}_{18}$ potential considering the impact of nucleon size and TNI.

Figure 3

The schematic trend of mass-radius relation for the classes of twin stars, I-IV, defined in the text.

Figure 4

The mass-radius relation of VLOCV (${\mathrm{AV}}_{18}$) EoS with categories II, III, and IV. It should be noted that the values of $p_{\text{trans}}$ and $\mathrm{\Delta }ϵ$ are given in units of $\mathrm{MeV}/{\mathrm{fm}}^3$.

Figure 5

The mass-radius relation of LOCV (${\mathrm{AV}}_{18}+\mathrm{TNI}$) EoS with categories III and IV. The values of $p_{\text{trans}}$ and $\mathrm{\Delta }ϵ$ are given in units of $\mathrm{MeV}/{\mathrm{fm}}^3$.

Figure 6

The relation between tidal deformabilities of the components of binary system considering strong first order phase transition for the VLOCV (${\mathrm{AV}}_{18}$) model. The values of $p_{\text{trans}}$ and $\mathrm{\Delta }ϵ$ are given in units of $\mathrm{MeV}/{\mathrm{fm}}^3$. Dashed (solid) lines correspond to the 50% (90%) credible region for the TaylorF2, PhenomPNRT and PhenomDNRT waveform models [58].

Figure 7

Comparative relation between tidal deformabilities of the components of binary system for category III of both VLOCV (${\mathrm{AV}}_{18}$) and the LOCV (${\mathrm{AV}}_{18}+\mathrm{TNI}$) models. The short-dotted style refers to the results of VLOCV method, while the solid one depicts those of LOCV (${\mathrm{AV}}_{18}+\mathrm{TNI}$). Dashed (solid) lines correspond to the 50% (90%) credible region for the TaylorF2, PhenomPNRT and PhenomDNRT waveform models [58].