Reconstructing the neutron star equation of state from observational data via automatic differentiation

Abstract

The equation of state (EoS) that describes extremely dense matter under strong interactions is not completely understood. One reason is that the first-principle calculations of the EoS at finite chemical potential are challenging in nuclear physics. However, neutron star observables like masses, radii, moment of inertia and tidal deformability are direct probes to the EoS and hence make the EoS reconstruction task feasible. In this work, we present results from a novel deep learning technique that optimizes a parameterized equation of state in the automatic differentiation framework. We predict stellar structures from a pre-trained Tolman-Oppenheimer-Volkoff solver network, given an EoS represented by neural networks. The latest observational data of neutron stars, specifically their masses and radii, are used to implement the chi-square fitting. We optimize the parameters of the neural network EoS by minimizing the error between observations and predictions. The well-trained neural network EoS gives an estimate of the relationship between the pressure and the mass density. The results presented are consistent with those from conventional approaches and the experimental bound on the tidal deformability inferred from the gravitational wave event, GW170817.

Bayesian Analysis of Neutron-star Properties with Parameterized Equations of State: The Role of the Likelihood Functions

“…Model-agnostic approaches to model the EOS have been employed extensively in recent years and roughly fall into two categories, namely, parameterized and non-parameterized methods. Non-parameterized approaches include, for example, Gaussian processes to infer the EOS (Landry & Essick 2019;Brandes et al 2023;Gorda et al 2022;Legred et al 2022), machine learning (Morawski & Bejger 2020;Fujimoto et al 2021;Han et al 2022b;Soma et al 2022), and nonparametric extensions of spectral expansion method (Han et al 2021(Han et al , 2022a. On the other hand, there exist various parameterized approaches that model the EOS by piecewise polytropes (Read et al 2009;Most et al 2018;Zhao & Lattimer 2018;O'Boyle et al 2020), or via a spectral-method representation of the EOS (Lindblom 2010(Lindblom , 2018, as well as some hybrids of these (Jiang et al 2020;Ferreira & Providência 2021;Huth et al 2022;Tang et al 2021).…”

Gravitational Waves from a Core g-Mode in Supernovae as Probes of the High-Density Equation of State

“…This is due to significant stiffening of the CMF EoS owing to baryon-baryon repulsion [43]. Although not directly related to the formation of quark matter, such a pronounced stiffening at moderately high densities is characteristic of currently viable EoS with a phase transition or crossover to quark matter [56][57][58]. The stiffening is crucial for achieving maximum neutron star masses compatible with observational constraints and already tentatively supported by heavy-ion collisions [59,60].…”

High-energy nuclear physics meets machine learning

“…EoS from astrophysical observables [120,121] and inferring the parton distribution function of pions in lattice QCD studies [122]). The introduced DNN representation can preserve the smoothness of the spectral function automatically, helping to regularize the degeneracy issue in this inverse problem.…”