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Register a new userFrom Neutron Star Observables to the Equation of State. II. Bayesian Inference of Equation of State Pressures
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One of the key goals of observing neutron stars is to infer the equation of state (EoS) of the cold, ultradense matter in their interiors. We present here a Bayesian statistical method of inferring the pressures at five fixed densities, from a sample of mock neutron star masses and radii. We show that while five polytropic segments are needed for maximum flexibility in the absence of any prior knowledge of the EoS, regularizers are also necessary to ensure that simple underlying EoS are not over-parametrized. For ideal data with small measurement uncertainties, we show that the pressure at roughly twice the nuclear saturation density, rho_sat, can be inferred to within 0.3 dex for many realizations of potential sources of uncertainties. The pressures of more complicated EoS with significant phase transitions can also be inferred to within ~30%. We also find that marginalizing the multi-dimensional parameter space of pressure to infer a mass-radius relation can lead to biases of nearly 1 km in radius, towards larger radii. Using the full, five-dimensional posterior likelihoods avoids this bias.
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The increasing number and precision of measurements of neutron star masses, radii, and, in the near future, moments of inertia offer the possibility of precisely determining the neutron star equation of state. One way to facilitate the mapping of observables to the equation of state is through a parametrization of the latter. We present here a generic method for optimizing the parametrization of any physically allowed EoS. We use mock equations of state that incorporate physically diverse and extreme behavior to test how well our parametrization reproduces the global properties of the stars, by minimizing the errors in the observables mass, radius, and the moment of inertia. We find that using piecewise polytropes and sampling the EoS with five fiducial densities between ~1-8 times the nuclear saturation density results in optimal errors for the smallest number of parameters. Specifically, it recreates the radii of the assumed EoS to within less than 0.5 km for the extreme mock equations of state and to within less than 0.12 km for 95% of a sample of 42 proposed, physically-motivated equations of state. Such a parametrization is also able to reproduce the maximum mass to within 0.04 M_sun and the moment of inertia of a 1.338 M_sun neutron star to within less than 10% for 95% of the proposed sample of equations of state.
Finite-size effects on the gravitational wave signal from a neutron star merger typically manifest at high frequencies where detector sensitivity decreases. Proposed sensitivity improvements can give us access both to stronger signals and to a myriad of weak signals from cosmological distances. The latter will outnumber the former and the relevant part of signal will be redshifted towards the detector most sensitive band. We study the redshift dependence of information about neutron star matter and find that single-scale properties, such as the star radius or the post-merger frequency, are better measured from the distant weak sources from $zsim 1$.
The first detection of gravitational waves from a neutron star-neutron star merger, GW170817, has opened up a new avenue for constraining the ultradense-matter equation of state (EOS). The deviation of the observed waveform from a point-particle waveform is a sensitive probe of the EOS controlling the merging neutron stars structure. In this topical review, I discuss the various constraints that have been made on the EOS in the year following the discovery of GW170817. In particular, I review the surprising relationship that has emerged between the effective tidal deformability of the binary system and the neutron star radius. I also report new results that make use of this relationship, finding that the radius inferred from GW170817 lies between 9.8 and 13.2 km at 90% confidence, with distinct likelihood peaks at 10.8 and 12.3 km. I compare these radii, as well as those inferred in the literature, to X-ray measurements of the neutron star radius. I also summarize the various maximum mass constraints, which point towards a maximum mass < 2.3 M_sun, depending on the fate of the remnant, and which can be used to additionally constrain the high-density EOS. I review the constraints on the EOS that have been performed directly, through Bayesian inference schemes. Finally, I comment on the importance of disentangling thermal effects in future EOS constraints from neutron star mergers.
The observations of compact star inspirals from LIGO/Virgo provide a valuable tool to study the highly uncertain equation of state (EOS) of dense matter at the densities in which the compact stars reside. It is not clear whether the merging stars are neutron stars or quark stars containing self-bound quark matter. In this work, we explore the allowed bag-model-like EOSs by assuming the merging stars are strange quark stars (SQSs) from a Bayesian analysis employing the tidal deformability observational data of the GW170817 and GW190425 binary mergers. We consider two extreme states of strange quark matter, either in nonsuperfluid or color-flavor locked (CFL) and find the results in these two cases essentially reconcile. In particular, our results indicate that the sound speed in the SQS matter is approximately a constant close to the conformal limit of $c/sqrt{3}$. The universal relations between the mass, the tidal deformability and the compactness are provided for the SQSs. The most probable values of the maximum mass are found to be $M_{rm TOV}=2.10_{-0.12}^{+0.12}~(2.15_{-0.14}^{+0.16}),M_{odot}$ for normal (CFL) SQSs at a $90%$ confidence level. The corresponding radius and tidal deformability for a $1.4,M_{odot}$ star are $R_{rm 1.4}= 11.50_{-0.55}^{+0.52}~({11.42}_{-0.44}^{+0.52})~rm km$ and $Lambda_{1.4}= {650}_{-190}^{+230}~({630}_{-150}^{+220})$, respectively. We also investigate the possibility of GW190814s secondary component $m_2$ of mass $2.59_{-0.09}^{+0.08},M_{odot}$ being an SQS, and find that it could be a CFL SQS with the pairing gap $Delta$ larger than $244~rm MeV$ and the effective bag parameter $B_{rm eff}^{1/4}$ in the range of $170$ to $192$ MeV, at a $90%$ confidence level.
The joint detection of the gravitational wave GW170817, of the short $gamma$-ray burst GRB170817A and of the kilonova AT2017gfo, generated by the the binary neutron star merger observed on August 17, 2017, is a milestone in multimessenger astronomy and provides new constraints on the neutron star equation of state. We perform Bayesian inference and model selection on AT2017gfo using semi-analytical, multi-components models that also account for non-spherical ejecta. Observational data favor anisotropic geometries to spherically symmetric profiles, with a log-Bayes factor of ${sim}10^{4}$, and favor multi-component models against single-component ones. The best fitting model is an anisotropic three-component composed of dynamical ejecta plus neutrino and viscous winds. Using the dynamical ejecta parameters inferred from the best-fitting model and numerical-relativity relations connecting the ejecta properties to the binary properties, we constrain the binary mass ratio to $q<1.54$ and the reduced tidal parameter to $120<tildeLambda<1110$. Finally, we combine the predictions from AT2017gfo with those from GW170817, constraining the radius of a neutron star of $1.4~{rm M}_odot$ to $12.2pm0.5~{rm km}$ ($1sigma$ level). This prediction could be further strengthened by improving kilonova models with numerical-relativity information.
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