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 nonrelativistic 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 $\approx 2M_{\odot }$. 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 and infrared counterpart sets the radius of a canonical $1.4M_{\odot }$ neutron star to be $11.82\le R_{1.4}\le 13.72\mathrm{km}$.

We carry out the study of finite nuclei, infinite nuclear matter, and neutron star properties with the newly developed relativistic force, the Institute of Physics Bhubaneswar-I (IOPB-I). Using this force, we calculate the binding energies, charge radii, and neutron-skin thickness for some selected nuclei. From the ground-state properties of superheavy nuclei ($Z=120$), it is noticed that considerable shell gaps appear at neutron numbers $N=172$, 184, and 198, manifesting the magicity at these numbers. The low-density behavior of the equation of state for pure neutron matter is compatible with other microscopic models. Along with the nuclear symmetry energy, its slope and curvature parameters at the saturation density are consistent with those extracted from various experimental data. We calculate the neutron star properties with the equation of state composed of nucleons and leptons in $\beta$-equilibrium, which are in good agreement with the x-ray observations by Steiner [ Astrophys. J. 722, 33 (2010)] and Nättilä [ Astron. Astrophys. 591, A25 (2016)]. Based on the recent observation of GW170817 with a quasi-universal relation, Rezzolla et al. [ Astrophys. J. Lett. 852, L25 (2018)] have set a limit for the maximum mass that can be supported against gravity by a nonrotating neutron star in the range $2.01\pm 0.04\lesssim M\left(M_{\odot }\right)\lesssim 2.16\pm 0.03$. We find that the maximum mass of the neutron star for the IOPB-I parametrization is $2.15M_{\odot }$. The radius and tidal deformability of a canonical neutron star of mass $1.4M_{\odot }$ are 13.2 km and $3.9\times {10}^{36}\mathrm{g}{\mathrm{cm}}^2{\mathrm{s}}^2$, respectively.

Because all neutron stars share a common equation of state, tidal deformability constraints from the compact binary coalescence GW170817 have implications for the properties of neutron stars in other systems. Using equation-of-state insensitive relations between macroscopic observables like moment of inertia ($I$), tidal deformability ($\mathrm{\Lambda }$) and stellar compactness, we derive constraints on these properties as a function of neutron star mass based on the LIGO-Virgo Collaboration’s canonical deformability measurement, ${\mathrm{\Lambda }}_{1.4}=190_{-120}^{+390}$. Specific estimates of $\mathrm{\Lambda }$, $I$, dimensionless spin $\chi$, and stellar radius $R$ for a few systems targeted by radio or x-ray studies are extracted from the general constraints. We also infer the canonical neutron star radius as $R_{1.4}={10.9}_{-1.5}^{+1.9}\mathrm{km}$ at 90% confidence. We further demonstrate how a gravitational-wave measurement of ${\mathrm{\Lambda }}_{1.4}$ can be combined with independent measurements of neutron star radii to tighten constraints on the tidal deformability as a proxy for the equation of state. We find that GW170817 and existing observations of six thermonuclear bursters in low-mass x-ray binaries jointly imply ${\mathrm{\Lambda }}_{1.4}=196_{-63}^{+92}$ at the 90% confidence level.

Continued observation of PSR J0737-3039, the double pulsar, is expected to yield a precise determination of its primary component’s moment of inertia in the next few years. Since the moment of inertia depends sensitively on the neutron star’s internal structure, such a measurement will constrain the equation of state of ultra-dense matter, which is believed to be universal. Independent equation-of-state constraints have already been established by the gravitational-wave measurement of neutron star tidal deformability in GW170817. Here, using well-known universal relations among neutron star observables, we translate the reported 90% credible bounds on tidal deformability into a direct constraint, , on the moment of inertia of PSR J0737-3039A. Should a future astrophysical measurement of I _⋆ disagree with this prediction, it could indicate a breakdown in the universality of the neutron star equation of state.

We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various Love numbers $k_l\left(l=2,3,4\right)$, that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through an advanced LIGO detector from the final stages of an inspiraling binary neutron star merger.