Very recently the NICER collaboration published the first-ever accurate measurement of mass and radius together for PSR J0030+0451, a nearby isolated quickly rotating neutron star (NS). In this work we set the joint constraints on the equation of state (EoS) and some bulk properties of NSs with the data of PSR J0030+0451, GW170817, and some nuclear experiments. The piecewise polytropic expansion method and the spectral decomposition method have been adopted to parameterize the EoS. The resulting constraints are consistent with each other. Assuming the maximal gravitational mass of nonrotating NS M TOV lies between 2.04M ⊙ and 2.4M ⊙, with the piecewise method the pressure at twice nuclear saturation density is measured to be at the 90% level. For an NS with canonical mass of 1.4M ⊙, we have the moment of inertia , tidal deformability , radius , and binding energy at the 90% level, which are improved in comparison to the constraints with the sole data of GW170817. These conclusions are drawn for the mass/radius measurements of PSR J0030+0451 by Riley et al. For the measurements of Miller et al., the results are rather similar.
We develop a new nonparametric method to reconstruct the equation of state (EoS) of a neutron star with multimessenger data. As a universal function approximator, the feed-forward neural network (FFNN) with one hidden layer and a sigmoidal activation function can approximately fit any continuous function. Thus, we are able to implement the nonparametric FFNN representation of the EoSs. This new representation is validated by its capability of fitting the theoretical EoSs and recovering the injected parameters. Then, we adopt this nonparametric method to analyze the real data, including the mass–tidal deformability measurement from the binary neutron star merger gravitational-wave event GW170817 and mass–radius measurement of PSR J0030+0451 by NICER. We take the publicly available samples to construct the likelihood and use the nested sampling to obtain the posteriors of the parameters of the FFNN according to the Bayesian theorem, which in turn can be translated to the posteriors of the EoS parameters. Combining all of these data for a canonical 1.4 M ⊙ neutron star, we get a radius R 1.4 = 11.83 − 1.08 + 1.25 km and tidal deformability Λ 1.4 = 323 − 165 + 334 (90% confidence interval). Furthermore, we find that in the high-density region (≥3ρ sat), the 90% lower limits of c s 2 / c 2 (where c s is the sound speed and c is the velocity of light in vacuum) are above 1/3, which means that the so-called conformal limit (i.e., c s 2 / c 2 < 1 / 3 ) is not always valid in the neutron stars.
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