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Register a new userTidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817
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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.
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We explore in a parameterized manner a very large range of physically plausible equations of state (EOSs) for compact stars for matter that is either purely hadronic or that exhibits a phase transition. In particular, we produce two classes of EOSs with and without phase transitions, each containing one million EOSs. We then impose constraints on the maximum mass, ($M < 2.16 M_{odot}$), and on the dimensionless tidal deformability ($tilde{Lambda} <800$) deduced from GW170817, together with recent suggestions of lower limits on $tilde{Lambda}$. Exploiting more than $10^9$ equilibrium models for each class of EOSs, we produce distribution functions of all the stellar properties and determine, among other quantities, the radius that is statistically most probable for any value of the stellar mass. In this way, we deduce that the radius of a purely hadronic neutron star with a representative mass of $1.4,M_{odot}$ is constrained to be $12.00!<!R_{1.4}/{rm km}!<!13.45$ at a $2$-$sigma$ confidence level, with a most likely value of $bar{R}_{1.4}=12.39,{rm km}$; similarly, the smallest dimensionless tidal deformability is $tilde{Lambda}_{1.4}!>!375$, again at a $2$-$sigma$ level. On the other hand, because EOSs with a phase transition allow for very compact stars on the so-called `twin-star branch, small radii are possible with such EOSs although not probable, i.e. $8.53!<!R_{1.4}/{rm km}!<!13.74$ and $bar{R}_{1.4}=13.06,{rm km}$ at a $2$-$sigma$ level, with $tilde{Lambda}_{1.4}!>!35.5$ at a $3$-$sigma$ level. Finally, since these EOSs exhibit upper limits on $tilde{Lambda}$, the detection of a binary with total mass of $3.4,M_{odot}$ and $tilde{Lambda}_{1.7}!>!461$ can rule out twin-star solutions.
Using a Bayesian approach, we combine measurements of neutron star macroscopic observables obtained by astrophysical and gravitational observations, to derive joint constraints on the equation of state (EoS) of matter at supranuclear density. In our analysis we use two sets of data: (i) the masses and tidal deformabilities measured in the binary neutron star event GW170817, detected by LIGO and Virgo; (ii) the masses and stellar radii measured from observations of nuclear bursts in accreting low-mass X-ray binaries. Using two different parametrizations of the equation of state, we compute the posteriorprobability distributions of the EoS parameters, using which we infer the posterior distribution for the radius and the mass of the two neutron stars of GW170817. The constraints we set on the radii are tighter than previous bounds.
Finite size effects in a neutron star merger are manifested, at leading order, through the tidal deformabilities (Lambdas) of the stars. If strong first-order phase transitions do not exist within neutron stars, both neutron stars are described by the same equation of state, and their Lambdas are highly correlated through their masses even if the equation of state is unknown. If, however, a strong phase transition exists between the central densities of the two stars, so that the more massive star has a phase transition and the least massive star does not, this correlation will be weakened. In all cases, a minimum Lambda for each neutron star mass is imposed by causality, and a less conservative limit is imposed by the unitary gas constraint, both of which we compute. In order to make the best use of gravitational wave data from mergers, it is important to include the correlations relating the Lambdas and the masses as well as lower limits to the Lambdas as a function of mass. Focusing on the case without strong phase transitions, and for mergers where the chirp mass M_chirp<1.4M_sun, which is the case for all observed double neutron star systems where a total mass has been accurately measured, we show that the dimensionless Lambdas satisfy Lambda_1/Lambda_2= q^6, where q=M_2/M_1 is the binary mass ratio; $M$ is mass of each star, respectively. Moreover, they are bounded by q^{n_-}>Lambda_1/Lambda_2> q^{n_{0+}+qn_{1+}}, where n_-<n_{0+}+qn_{1+}; the parameters depend only on M_chirp, which is accurately determined from the gravitational-wave signal. We also provide analytic expressions for the wider bounds that exist in the case of a strong phase transition. We argue that bounded ranges for Lambda_1/Lambda_2, tuned to M_chirp, together with lower bounds to Lambda(M), will be more useful in gravitational waveform modeling than other suggested approaches.
We present predictions for neutron star tidal deformabilities obtained from a Bayesian analysis of the nuclear equation of state, assuming a minimal model at high-density that neglects the possibility of phase transitions. The Bayesian posterior probability distribution is constructed from priors obtained from microscopic many-body theory based on realistic two- and three-body nuclear forces, while the likelihood functions incorporate empirical information about the equation of state from nuclear experiments. The neutron star crust equation of state is constructed from the liquid drop model, and the core-crust transition density is found by comparing the energy per baryon in inhomogeneous matter and uniform nuclear matter. From the cold $beta$-equilibrated neutron star equation of state, we then compute neutron star tidal deformabilities as well as the mass-radius relationship. Finally, we investigate correlations between the neutron star tidal deformability and properties of finite nuclei.
With the first observation of a binary neutron star merger through gravitational waves and light GW170817, compact binary mergers have now taken the center stage in nuclear astrophysics. They are thought to be one of the main astrophysical sites of production of r-process elements, and merger observations have become a fundamental tool to constrain the properties of matter. Here, we review our current understanding of the dynamics of neutron star mergers, in general, and of GW170817 in particular. We discuss the physical processes governing the inspiral, merger, and postmerger evolution, and we highlight the connections between these processes, the dynamics, and the multimessenger observables. Finally, we discuss open questions and issues in the field and the need to address them through a combination of better theoretical models and new observations.
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