We compute the tidal deformabilities for neutron star merger for equations of state with a strong first order phase transition producing a new separate branch in the mass-radius diagram. A case is found where all three possible pairs of combinations between these two neutron star branches are present for the total mass of $M=2.7M_odot$ of the observed merger event GW170817. It is demonstrated that the plot of the two tidal deformabilities $Lambda_1$ and $Lambda_2$ of the binary neutron star can show up to three separate branches. We propose that the future detections of neutron star merger events with the same value for $Lambda_1$ but different values of $Lambda_2$ serve as a signal for the existence of a strong first order phase transition in neutron star matter.
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 J0740+6620, and the mass/radius fits to NICER data for PSR J003+0451. Our results points 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.
The sound velocity $v_s$ and dimensionless tidal deformability $Lambda$ are analyzed using the pseudo-conformal model we developed before. In contrast to the conclusion obtained in the previous works in the literature, our model with the upper bound of the sound velocity $v_s = 1/sqrt{3}$, the so-called conformal sound velocity, set in at a { density relevant to compact stars} $gsim 2 n_0$ where $n_0$ is the normal nuclear matter density, can accommodate {it all} presently established nuclear matter and compact-star properties including the maximum star-mass constraint $ simeq 2.3 M_odot$. This observation is associated with a possible emergence of pseudoconformal structure in compact star matter---in which the trace of energy-momentum tensor is a nearly density-independent nonzero constant---brought in by a topology change at $2.0 lesssim n_{1/2}/n_0 lesssim 4.0$ commensurate with a possible change of degrees of freedom from hadrons.
Compact stars may contain quark matter in their interiors at densities exceeding several times the nuclear saturation density. We explore models of such compact stars where there are two first-order phase transitions: the first from nuclear matter to a quark-matter phase, followed at higher density by another first-order transition to a different quark matter phase [e.g., from the two-flavor color superconducting (2SC) to the color-flavor-locked (CFL) phase). We show that this can give rise to two separate branches of hybrid stars, separated from each other and from the nuclear branch by instability regions and, therefore, to a new family of compact stars, denser than the ordinary hybrid stars. In a range of parameters, one may obtain twin hybrid stars (hybrid stars with the same masses but different radii) and even triplets where three stars, with inner cores of nuclear matter, 2SC matter, and CFL matter, respectively, all have the same mass but different radii.
We use gravitational-wave observations of the binary neutron star merger GW170817 to explore the tidal deformabilities and radii of neutron stars. We perform Bayesian parameter estimation with the source location and distance informed by electromagnetic observations. We also assume that the two stars have the same equation of state; we demonstrate that for stars with masses comparable to the component masses of GW170817, this is effectively implemented by assuming that the stars dimensionless tidal deformabilities are determined by the binarys mass ratio $q$ by $Lambda_1/Lambda_2 = q^6$. We investigate different choices of prior on the component masses of the neutron stars. We find that the tidal deformability and 90$%$ credible interval is $tilde{Lambda}=222^{+420}_{-138}$ for a uniform component mass prior, $tilde{Lambda}=245^{+453}_{-151}$ for a component mass prior informed by radio observations of Galactic double neutron stars, and $tilde{Lambda}=233^{+448}_{-144}$ for a component mass prior informed by radio pulsars. We find a robust measurement of the common areal radius of the neutron stars across all mass priors of $8.9 le hat{R} le 13.2$ km, with a mean value of $langle hat{R} rangle = 10.8$ km. Our results are the first measurement of tidal deformability with a physical constraint on the stars equation of state and place the first lower bounds on the deformability and areal radii of neutron stars using gravitational waves.
Constraints set on key parameters of the nuclear matter equation of state (EoS) by the values of the tidal deformability, inferred from GW170817, are examined by using a diverse set of relativistic and non-relativistic mean field models. These models are consistent with bulk properties of finite nuclei as well as with the observed lower bound on the maximum mass of neutron star $sim 2 ~ {rm M}_odot$. The tidal deformability shows a strong correlation with specific linear combinations of the isoscalar and isovector nuclear matter parameters associated with the EoS. Such correlations suggest that a precise value of the tidal deformability can put tight bounds on several EoS parameters, in particular, on the slope of the incompressibility and the curvature of the symmetry energy. The tidal deformability obtained from the GW170817 and its UV/optical/infrared counterpart sets the radius of a canonical $1.4~ {rm M}_{odot}$ neutron star to be $11.82leqslant R_{1.4}leqslant13.72$ km.
Jan-Erik Christian
,Andreas Zacchi
,Jurgen Schaffner-Bielich
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(2018)
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"Signals in the tidal deformability for phase transitions in compact stars with constraints from GW170817"
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Jan-Erik Christian
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