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

Abstract

We develop a new nonparametric method to reconstruct the Equation of State (EoS) of Neutron Star with multimessenger data. As an 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 capabilities of fitting the theoretical EoSs and recovering the injected parameters. Then we adopt this nonparametric method to analyze the real data, including mass-tidal deformability measurement from the Binary Neutron Star (BNS) merger Gravitational Wave (GW) event GW170817 and mass-radius measurement of PSR J0030+0451 by {\it NICER}. We take the publicly available samples to construct the likelihood and use the nested sampling to obtain the posteriors of the parameters of FFNN according to the Bayesian theorem, which in turn can be translated to the posteriors of EoS parameters. Combining all these data, for a canonical 1.4 $M_{\odot }$ neutron star, we get the radius $R_{1.4}=11.83_{-1.08}^{+1.25}$ km and the tidal deformability ${\Lambda }_{1.4}=323_{-165}^{+334}$ (90\% confidence interval).Furthermore, we find that in the high density region ($\ge 3{\rho }_{\mathrm{sat}}$), the 90\% lower limits of the $c_{\mathrm{s}}^2/c^2$ ($c_{\mathrm{s}}$ is the sound speed and $c$ is the velocity of light in the vacuum) are above $1/3$, which means that the so-called conformal limit (i.e., $c_{\mathrm{s}}^2/c^2<1/3$) is not always valid in the neutron stars.

11 pages, 3 figures, 2 tables, accepted for publication in ApJ

References in corpus (13)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• PSR J0030+0451 Mass and Radius from NICER Data and Implications for the Properties of Neutron Star Matter
• A NICER View of PSR J0030+0451: Millisecond Pulsar Parameter Estimation
• Refined Mass and Geometric Measurements of the High-Mass PSR J0740+6620
• Constraints on a phenomenologically parameterized neutron-star equation of state
• Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XII: Stiffness and stability of neutron-star matter
• Sound velocity bound and neutron stars
• A NICER view of PSR J0030+0451: Implications for the dense matter equation of state
• New Hyperon Equations of State for Supernovae and Neutron Stars in Density-dependent Hadron Field Theory
• Spectral Representations of Neutron-Star Equations of State
• New equations of state constrained by nuclear physics, observations, and QCD calculations of high-density nuclear matter
• Asymmetric nuclear matter and neutron-skin in extended relativistic mean field model
• Constraint on phase transition with the multimessenger data of neutron stars

Cited by in corpus (34)

• Machine Learning in Nuclear Physics
• Relativistic description of dense matter equation of state and compatibility with neutron star observables: a Bayesian approach
• Exploring QCD matter in extreme conditions with Machine Learning
• Extreme Matter meets Extreme Gravity: Ultra-heavy neutron stars with crossovers and first-order phase transitions
• Maximum gravitational mass $M_{\mathrm{TOV}}=2.25_{-0.07}^{+0.08}{M}_{\odot }$ inferred at about $3\%$ precision with multimessenger data of neutron stars
• Bayesian analysis of neutron-star properties with parameterized equations of state: the role of the likelihood functions
• Merger and post-merger of binary neutron stars with a quark-hadron crossover equation of state
• Equation of state and speed of sound of isospin-asymmetric QCD on the lattice
• Inference of the sound speed and related properties of neutron stars
• Plausible presence of new state in neutron stars with masses above $0.98M_{\mathrm{TOV}}$
• Phase Transition Phenomenology with Nonparametric Representations of the Neutron Star Equation of State
• Neural network reconstruction of the dense matter equation of state from neutron star observables
• Reconstructing the neutron star equation of state from observational data via automatic differentiation
• Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics
• Insights on the peak in the speed of sound of ultradense matter
• Decoding Neutron Star Observations: Revealing Composition through Bayesian Neural Networks
• Applications of machine learning in gravitational wave research with current interferometric detectors
• Constraining neutron star properties with a new equation of state insensitive approach
• Central Speed of Sound, Trace Anomaly and Observables of Neutron Stars from Perturbative Analyses of Scaled TOV Equations
• Nonparametric model for the equations of state of neutron star from deep neural network
• From NS observations to nuclear matter properties: a machine learning approach
• Novel Scalings of Neutron Star Properties from Analyzing Dimensionless Tolman--Oppenheimer--Volkoff Equations
• Neural Simulation-Based Inference of the Neutron Star Equation of State directly from Telescope Spectra
• Nonparametric Representation of Neutron Star Equation of State Using Variational Autoencoder
• Nambu-Jona-Lasinio description of hadronic matter from a Bayesian approach
• Realizing the potential of deep neural network for analyzing neutron star observables and dense matter equation of state
• Mass and radius of the most massive neutron star: The probe of the equation of state and perturbative QCD
• Explainable autoencoder for neutron star dense matter parameter estimation
• Detecting Hyperons in neutron stars -- a machine learning approach
• Conditional variational autoencoder inference of neutron star equation of state from astrophysical observations
• Dependence of postmerger properties on the thermal heating efficiency in neutron star mergers
• Direct Inference of Nuclear Equation-of-State Parameters from Gravitational-Wave Observations
• The maximum mass and rotational kinetic energy of rapidly rotating neutron stars
• Updated estimates of post-merger gravitational wave energy released in GW170817 and the maximum neutron star mass