Neutron Star Equation Of State Research Articles

Neural simulation-based inference of the neutron star equation of state directly from telescope spectra

Neutron stars provide a unique opportunity to study strongly interacting matter under extreme density conditions. The intricacies of matter inside neutron stars and their equation of state are not directly visible, but determine bulk properties, such as mass and radius, which affect the star's thermal X-ray emissions. However, the telescope spectra of these emissions are also affected by the stellar distance, hydrogen column, and effective surface temperature, which are not always well-constrained. Uncertainties on these nuisance parameters must be accounted for when making a robust estimation of the equation of state. In this study, we develop a novel methodology that, for the first time, can infer the full posterior distribution of both the equation of state and nuisance parameters directly from telescope observations. This method relies on the use of neural likelihood estimation, in which normalizing flows use samples of simulated telescope data to learn the likelihood of the neutron star spectra as a function of these parameters, coupled with Hamiltonian Monte Carlo methods to efficiently sample from the corresponding posterior distribution. Our approach surpasses the accuracy of previous methods, improves the interpretability of the results by providing access to the full posterior distribution, and naturally scales to a growing number of neutron star observations expected in the coming years.

Precision constraints on the neutron star equation of state with third-generation gravitational-wave observatories

Precision constraints on the neutron star equation of state with third-generation gravitational-wave observatories

Deriving neutron star equation of state from AdS/QCD

Neutron stars are among the main targets for gravitational wave observatories, however, their equation of state is still not well established. Mainly phenomenological models with many parameters are widely used by far, while theoretical models are not so practical. In arXiv:1902.08477, a theoretical equation of state with only one parameter is derived from Witten–Sakai–Sugimoto model, as an application of AdS/QCD, where pointlike instanton case is taken into consideration. When the tidal deformability constraint from gravitational wave event is satisfied, the maximum mass is about 1.7 solar masses. Now we upgrade this model to instanton gas, with one more variable, the instanton width. This is not naively a free parameter, but a function of the chemical potential. Thus we end up with a more complicated and accurate model, but still with only one adjustable parameter. In this case, we find the maximum mass becomes 1.85 solar masses. This is an encouraging result, as a theoretically derived model.

Inference of neutron-star properties with unified crust-core equations of state for parameter estimation

Context. Relating different global neutron-star (NS) properties, such as tidal deformability and radius, or mass and radius, requires an equation of state (EoS). Determining the NS EoS is therefore not only the science goal of a variety of observational projects, but it also enters in the analysis process; for example, to predict a NS radius from a measured tidal deformability via gravitational waves (GW) during the inspiral of a binary NS merger. To this aim, it is important to estimate the theoretical uncertainties on the EoS, one of which is the possible bias coming from an inconsistent treatment of the low-density region; that is, the use of a so called non-unified NS crust. Aims. We propose a numerical tool allowing the user to consistently match a nuclear-physics informed crust to an arbitrary high-density EoS describing the core of the star. Methods. We introduce an inversion procedure of the EoS close to saturation density that allows users to extract nuclear-matter parameters and extend the EoS to lower densities in a consistent way. For the treatment of inhomogeneous matter in the crust, a standard approach based on the compressible liquid-drop (CLD) model approach was used in our work. A Bayesian analysis using a parametric agnostic EoS representation in the high-density region is also presented in order to quantify the uncertainties induced by an inconsistent treatment of the crust. Results. We show that the use of a fixed, realistic-but-inconsistent model for the crust causes small but avoidable errors in the estimation of global NS properties and leads to an underestimation of the uncertainties in the inference of NS properties. Conclusions. Our results highlight the importance of employing a consistent EoS in inference schemes. The numerical tool that we developed to reconstruct such a thermodynamically consistent EoS, CUTER, has been tested and validated for use by the astrophysical community.

Unified neutron star equations of state calibrated to nuclear properties

Recently, a dataset of several equations of state (EOSs) for purely nucleonic stellar matter based on a nonlinear relativistic mean-field model prescription and constrained to properties of nuclear matter, state-of-the-art chiral effective-field theory calculations for low-density neutron matter, and astrophysical data were proposed. In this work, 21 unified neutron star EOSs were chosen from that dataset in such a way that a large range of values of the slope of the symmetry energy at saturation is covered. Several quantities are calculated and discussed, such as the proton fraction and the direct Urca behavior, the density dependence of the speed of sound and the trace anomaly, the crust-core transition properties, the compatibility with astrophysical observations, and the neutron matter properties from chiral effective-field theory calculations and pQCD constraints. We construct unified EOSs where the outer crust is given by the BSk22 functional and the inner crust is calculated from a compressible liquid drop approximation. The core is purely nucleonic; made of protons, neutrons, electrons, and muons; under charge neutrality; and in beta -equilibrium conditions. The correlation of the slope of the symmetry energy at saturation with the crust-core transition density and proton fraction is analyzed, and equations that translate these relations are proposed. Moreover, the spectral representation for all the EOSs is given, which is a convenient representation to study quasi-periodic oscillations with realistic EOSs. We show that several of these EOSs have in the center of the most massive neutron star a speed of sound squared on the order of $ 0.5$. Most of the EOSs predict a maximum central density on the order of about six times the nuclear saturation density. Three of the EOSs satisfy all of the constraints imposed. The 21 unified EOSs are available in the zenodo platform.

Bayesian Survey of the Dense Matter Equation of State Built upon Skyrme Effective Interactions

The nonrelativistic model of nuclear matter (NM) with zero-range Skyrme interactions is employed within a Bayesian approach in order to study the behavior of the neutron star (NS) equation of state (EOS). A minimal number of constraints from nuclear physics and ab initio calculations of pure neutron matter (PNM) are imposed together with causality and a lower limit on the maximum mass of an NS to all our models. Our key result is that accounting for correlations among the values that the energy per neutron in PNM takes at various densities and that are typically disregarded efficiently constrains the behavior of the EOS at high densities. A series of global NS properties, e.g., maximum mass, central density of the maximum mass configuration, minimum NS mass that allows for direct URCA, and radii of intermediate and massive NSs, appear to be correlated with the value of effective neutron mass in PNM at 0.16 fm−3. Together with similar studies in the literature our work contributes to a better understanding of the NS EOS as well as its link with the properties of dense NM.

Insights into Neutron Star Equation of State by Machine Learning

Due to its powerful capability and high efficiency in big data analysis, machine learning has been applied in various fields. We construct a neural network platform to constrain the behaviors of the equation of state of nuclear matter with respect to the properties of nuclear matter at saturation density and the properties of neutron stars. It is found that the neural network is able to give reasonable predictions of parameter space and provide new hints into the constraints of hadron interactions. As a specific example, we take the relativistic mean field approximation in a widely accepted Walecka-type model to illustrate the feasibility and efficiency of the platform. The results show that the neural network can indeed estimate the parameters of the model at a certain precision such that both the properties of nuclear matter around saturation density and global properties of neutron stars can be saturated. The optimization of the present modularly designed neural network and extension to other effective models is straightforward.

Bayesian investigation of the neutron star equation of state vs gravity degeneracy

Bayesian investigation of the neutron star equation of state vs gravity degeneracy

Bayesian analysis of nontrivial features in the speed of sound inside neutron stars in light of astrophysical and pQCD constraints

Functional forms of the neutron star Equation of State (EoS) are required to extract the viable EoS band from neutron star observations. Realistic nuclear EoS, containing deconfined quarks or hyperons, present nontrivial features in the speed of sound such as bumps, kinks, and plateaus. Using modified Gaussian processes to model EoS with nontrivial features, we show in a fully Bayesian analysis incorporating measurements from X-ray sources, gravitational wave observations, and perturbative QCD results that these features are compatible with current constraints. We find that nontrivial behavior in the EoS plays a role in understanding the possible phase structure of neutron stars at densities around 2 nsat.

Deducing neutron star equation of state from telescope spectra with machine-learning-derived likelihoods

The interiors of neutron stars reach densities and temperatures beyond the limits of terrestrial experiments, providing vital laboratories for probing nuclear physics. While the star's interior is not directly observable, its pressure and density determine the star's macroscopic structure which affects the spectra observed in telescopes. The relationship between the observations and the internal state is complex and partially intractable, presenting difficulties for inference. Previous work has focused on the regression from stellar spectra of parameters describing the internal state. We demonstrate a calculation of the full likelihood of the internal state parameters given observations, accomplished by replacing intractable elements with machine learning models trained on samples of simulated stars. Our machine-learning-derived likelihood allows us to perform maximum a posteriori estimation of the parameters of interest, as well as full scans. We demonstrate the technique by inferring stellar mass and radius from an individual stellar spectrum, as well as equation of state parameters from a set of spectra. Our results are more precise than pure regression models, reducing the width of the parameter residuals by 11.8% in the most realistic scenario. The neural networks will be released as a tool for fast simulation of neutron star properties and observed spectra.

Constraining Nuclear Parameters Using Gravitational Waves from f-mode Oscillations in Neutron Stars

Gravitational waves (GWs) emanating from unstable quasi-normal modes in neutron stars (NSs) could be accessible with the improved sensitivity of the current GW detectors or with the next-generation GW detectors and, therefore, can be employed to study the NS interior. Assuming f-mode excitation in isolated pulsars with typical energy of pulsar glitches and considering potential f-mode GW candidates for A+ (upgraded LIGO detectors operating at fifth observing run design sensitivity) and Einstein Telescope (ET), we demonstrate the inverse problem of NS asteroseismology within a Bayesian formalism to constrain the nuclear parameters and NS equation of state (EOS). We describe the NS interior within relativistic mean-field formalism. Taking the example of glitching pulsars, we find that for a single event in A+ and ET, among the nuclear parameters, the nucleon effective mass (m*) within 90% credible interval can be restricted within 10% and 5%, respectively. At the same time, the incompressibility (K) and the slope of the symmetry energy (L) are only loosely constrained. Considering multiple (10) events in A+ and ET, all the nuclear parameters are well constrained, especially m*, which can be constrained to 3% and 2% in A+ and ET, respectively. Uncertainty in the observables of a 1.4 M ⊙ NS such as radius (), f-mode frequency (), damping time (), and a few EOS properties including squared speed of sound (c s 2) are also estimated.

Phase transition phenomenology with nonparametric representations of the neutron star equation of state

Phase transition phenomenology with nonparametric representations of the neutron star equation of state

Tidal deformability doppelgänger: Implications of a low-density phase transition in the neutron star equation of state

Tidal deformability doppelgänger: Implications of a low-density phase transition in the neutron star equation of state

A Quantum-mechanical Treatment of Electron Broadening in Strong Magnetic Fields

Spectral line-shape fitting is an extremely useful tool in determining the gravity of white dwarf stars. This method is so far limited to nonmagnetic white dwarfs largely because the theory of line broadening in high magnetic fields is not as complete as in the nonmagnetic case. Current Stark+Zeeman models treat plasma particles classically and ignore the motion of the nucleus. We develop the formalism for a quantum-mechanical treatment of the perturbing electrons and include the nuclear motion as part of the broadening and explore their relative importance. The conditions we explore are those found in white dwarf and neutron star atmospheres. We find that, contrary to previous studies, the quantized perturbing electrons create more broadening than perturbers on a straight-path trajectory. Additionally, the quantization of the plasma electrons gives rise to resonances away from the line center. The nuclear motion creates an additional electric field, which also leads to an increase in line broadening; however, this effect in neutron star atmospheres is not as large as previously estimated. This suggests that neutron star spectral lines are sensitive to density and that their mass and radius can be obtained from spectral line fitting, which would help constrain the neutron star equation of state.

I-Love-Q relations for a generic family of neutron star equations of state

ABSTRACT Neutron stars (and quark stars) have recently been found to follow certain universality, the I-Love-Q relations. These relations can provide a greater understanding of the structural and macro properties of compact astrophysical objects with knowledge of any one of the observable. The reason behind this is the lack of sensitivity to the relations with the equation of state (EoS) of matter. In this work, we have investigated the consistency of universal relations for a generic family of equations of state. These equations of state are consistent with the prescribed limits of nuclear theory (low densities) and perturbative QCD (asymptotically high densities) and respecting recent astronomical observations. At intermediate densities, the equations of states are parametrized by the adiabatic speed of sound. Although the spread in the EoS is significant, the universal nature of the I-Love-Q trio holds relatively well up to a specific tolerance limit of 5 per cent fractional percentage error. We have compared the result first with a similar set, but not respecting the recent astrophysical constraints. A deviation from universality is seen and the tolerance exceeds the 5 per cent limit. Next, we have compared our result with a family of EoS having monotonic sound speed inside a neutron star. A slight deviation from universality is seen for this case; however, the tolerance remains within the 5 per cent limit. This shows the existence of a correlation between universal relations and observational constraints.

Simulating neutron stars with a flexible enthalpy-based equation of state parametrization in spectre

Numerical simulations of neutron star mergers represent an essential step toward interpreting the full complexity of multimessenger observations and constraining the properties of supranuclear matter. Currently, simulations are limited by an array of factors, including computational performance and input physics uncertainties, such as the neutron star equation of state. In this work, we expand the range of nuclear phenomenology efficiently available to simulations by introducing a new analytic parametrization of cold, beta-equilibrated matter that is based on the relativistic enthalpy. We show that the new enthalpy parametrization can capture a range of nuclear behavior, including strong phase transitions. We implement the enthalpy parametrization in the spectre code, simulate isolated neutron stars, and compare performance to the commonly used spectral and polytropic parametrizations. We find comparable computational performance for nuclear models that are well represented by either parametrization, such as simple hadronic equations of state. We show that the enthalpy parametrization further allows us to simulate more complicated hadronic models or models with phase transitions that are inaccessible to current parametrizations.

General-relativistic neutrino-radiation magnetohydrodynamics simulation of seconds-long black hole-neutron star mergers: Dependence on the initial magnetic field strength, configuration, and neutron-star equation of state

As a follow-up study of our previous work [Phys. Rev. D 106, 023008 (2022)], numerical-relativity simulations for seconds-long black hole-neutron star mergers are performed for a variety of setups. Irrespective of the initial and symmetry conditions, we find qualitatively universal evolution processes: The dynamical mass ejection takes place together with a massive accretion disk formation after the neutron star is tidally disrupted; subsequently, the magnetic field in the accretion disk is amplified by the magnetic winding, Kelvin-Helmholtz instability, and magnetorotational instability, which establish a turbulent state inducing the dynamo and angular momentum transport; the postmerger mass ejection by the effective viscous processes stemming from the magnetohydrodynamics turbulence sets in at $\ensuremath{\sim}300--500\text{ }\text{ }\mathrm{ms}$ after the merger and continues for several hundred ms; a magnetosphere near the black-hole spin axis is developed and the collimated strong Poynting flux is generated with its lifetime of $\ensuremath{\sim}0.5--2\text{ }\text{ }\mathrm{s}$. We have newly found that the model of no equatorial-plane symmetry shows the reverse of the magnetic-field polarity in the magnetosphere, which is caused by the dynamo associated with the magnetorotational instability in the accretion disk. The model with initially toroidal fields shows the tilt of the disk and magnetosphere in the late postmerger stage because of the anisotropic postmerger mass ejection. These effects could terminate the strong Poynting-luminosity stage within the timescale of $\ensuremath{\sim}0.5--2\text{ }\text{ }\mathrm{s}$.

Perturbative QCD and the neutron star equation of state

Perturbative QCD and the neutron star equation of state

Degeneracy in the Inference of Phase Transitions in the Neutron Star Equation of State from Gravitational Wave Data.

Gravitational wave (GW) detections of binary neutron star inspirals will be crucial for constraining the dense matter equation of state (EOS). We demonstrate a new degeneracy in the mapping from tidal deformability data to the EOS, which occurs for models with strong phase transitions. We find that there exists a new family of EOS with phase transitions that set in at different densities and that predict neutron star radii that differ by up to ∼500 m but that produce nearly identical tidal deformabilities for all neutron star masses. Next-generation GW detectors and advances in nuclear theory may be needed to resolve this degeneracy.

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

Neutron star observables like masses, radii, and tidal deformability are direct probes to the dense matter equation of state (EoS). A novel deep learning method that optimizes an EoS in the automatic differentiation framework of solving inverse problems is presented. The trained neural network EoS yields narrow bands for the relationship between the pressure and speed of sound as a function of the mass density. The results are consistent with those obtained from conventional approaches and the observational bound on the tidal deformability inferred from the gravitational wave event, GW170817.