Bayesian nonparametric inference of neutron star equation of state via\n neural network

Abstract

We develop a new nonparametric method to reconstruct the Equation of State\n(EoS) of Neutron Star with multimessenger data. As an universal function\napproximator, the Feed-Forward Neural Network (FFNN) with one hidden layer and\na sigmoidal activation function can approximately fit any continuous function.\nThus we are able to implement the nonparametric FFNN representation of the\nEoSs. This new representation is validated by its capabilities of fitting the\ntheoretical EoSs and recovering the injected parameters. Then we adopt this\nnonparametric method to analyze the real data, including mass-tidal\ndeformability measurement from the Binary Neutron Star (BNS) merger\nGravitational Wave (GW) event GW170817 and mass-radius measurement of PSR\nJ0030+0451 by {\\it NICER}. We take the publicly available samples to construct\nthe likelihood and use the nested sampling to obtain the posteriors of the\nparameters of FFNN according to the Bayesian theorem, which in turn can be\ntranslated to the posteriors of EoS parameters. Combining all these data, for a\ncanonical 1.4 $M_\\odot$ neutron star, we get the radius\n$R_{1.4}=11.83^{+1.25}_{-1.08}$ km and the tidal deformability $\\Lambda_{1.4} =\n323^{+334}_{-165}$ (90\\% confidence interval).Furthermore, we find that in the\nhigh density region ($\\geq 3\\rho_{\\rm sat}$), the 90\\% lower limits of the\n$c_{\\rm s}^2/c^2$ ($c_{\\rm s}$ is the sound speed and $c$ is the velocity of\nlight in the vacuum) are above $1/3$, which means that the so-called conformal\nlimit (i.e., $c_{\\rm s}^2/c^2<1/3$) is not always valid in the neutron stars.\n