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Register a new userConstraining the neutron star equation of state using multi-band independent measurements of radii and tidal deformabilities
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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.
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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.
A precise moment of inertia measurement for PSR J0737-3039A in the double pulsar system is expected within the next five years. We present here a new method of mapping the anticipated measurement of the moment of inertia directly into the neutron star structure. We determine the maximum and minimum values possible for the moment of inertia of a neutron star of a given radius based on physical stability arguments, assuming knowledge of the equation of state only at densities below the nuclear saturation density. If the equation of state is trusted up to the nuclear saturation density, we find that a measurement of the moment of inertia will place absolute bounds on the radius of PSR J0737-3039A to within $pm$1 km. The resulting combination of moment of inertia, mass, and radius measurements for a single source will allow for new, stringent constraints on the dense-matter equation of state.
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.
The increasing richness of data related to cold dense matter, from laboratory experiments to neutron-star observations, requires a framework for constraining the properties of such matter that makes use of all relevant information. Here, we present a rigorous but practical Bayesian approach that can include diverse evidence, such as nuclear data and the inferred masses, radii, tidal deformabilities, moments of inertia, and gravitational binding energies of neutron stars. We emphasize that the full posterior probability distributions of measurements should be used rather than, as is common, imposing a cut on the maximum mass or other quantities. Our method can be used with any parameterization of the equation of state (EOS). We use both a spectral parameterization and a piecewise polytropic parameterization with variable transition densities to illustrate the implications of current measurements and show how future measurements in many domains could improve our understanding of cold catalyzed matter. We find that different types of measurements will play distinct roles in constraining the EOS in different density ranges. For example, better symmetry energy measurements will have a major influence on our understanding of matter somewhat below nuclear saturation density but little influence above that density. In contrast, precise radius measurements or multiple tidal deformability measurements of the quality of those from GW170817 or better will improve our knowledge of the EOS over a broader density range.
We show how observations of gravitational waves from binary neutron star (BNS) mergers over the next few years can be combined with insights from nuclear physics to obtain useful constraints on the equation of state (EoS) of dense matter, in particular, constraining the neutron-matter EoS to within 20% between one and two times the nuclear saturation density $n_0approx 0.16 {text{fm}^{-3}}$. Using Fisher information methods, we combine observational constraints from simulated BNS merger events drawn from various population models with independent measurements of the neutron star radii expected from x-ray astronomy (the Neutron Star Interior Composition Explorer (NICER) observations in particular) to directly constrain nuclear physics parameters. To parameterize the nuclear EoS, we use a different approach, expanding from pure nuclear matter rather than from symmetric nuclear matter to make use of recent quantum Monte Carlo (QMC) calculations. This method eschews the need to invoke the so-called parabolic approximation to extrapolate from symmetric nuclear matter, allowing us to directly constrain the neutron-matter EoS. Using a principal component analysis, we identify the combination of parameters most tightly constrained by observational data. We discuss sensitivity to various effects such as different component masses through population-model sensitivity, phase transitions in the core EoS, and large deviations from the central parameter values.
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