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The relativistic inverse stellar structure problem determines the equation of state of the stellar matter given a knowledge of suitable macroscopic observable properties (e.g. their masses and radii) of the stars composed of that material. This study determines how accurately this equation of state can be determined using noisy mass and radius observations. The relationship between the size of the observational errors and the accuracy of the inferred equation of state is evaluated, and the optimal number of adjustable equation of state parameters needed to achieve the highest accuracy is determined. 

Causal parametric representations of neutron-star equations of state are constructed here using Chebyshev polynomial based spectral expansions. The accuracies of these representations are evaluated for a collection of model equations of state from a variety of nuclear-theory models and also a collection of equations of state with first- or second-order phase transitions of various sizes. These tests show that the Chebyshev based representations are convergent (even for equations of state with phase transitions) as the number of spectral basis functions is increased. This study finds that the Chebyshev based representations are generally more accurate than a previously studied power-law based spectral representation, and that pressure-based representations are generally more accurate than those based on enthalpy. 

This paper explores the use of low-dimensional parametric representations of neutron-star equations of state that include discontinuities caused by phase transitions. The accuracies of optimal piecewise-analytic and spectral representations are evaluated for equations of state having first- or second-order phase transitions with a wide range of discontinuity sizes. These results suggest that the piecewise-analytic representations of these nonsmooth equations of state are convergent, while the spectral representations are not. Nevertheless, the lower-order (2 ≤ N parms ≤ 7) spectral representations are found to be more accurate than the piecewise-analytic representations with the same number of parameters. 

The effectiveness of the hyperbolic relaxation method for solving the Einstein constraint equations numerically is studied here on a variety of compact orientable three-manifolds. Convergent numerical solutions are found using this method on manifolds admitting negative Ricci scalar curvature metrics, i.e., those from the 𝐻3 and the 𝐻2×𝑆1 geometrization classes. The method fails to produce solutions, however, on all the manifolds examined here admitting non-negative Ricci scalar curvatures, i.e., those from the 𝑆3, 𝑆2×𝑆1, and the 𝐸3 classes. This study also finds that the accuracy of the convergent solutions produced by hyperbolic relaxation can be increased significantly by performing fairly low-cost standard elliptic solves using the hyperbolic relaxation solutions as initial guesses. 

Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by expanding the class of suitable triangulations, significantly increasing the number of manifolds to which these methods apply. These new results show that this expanded class of triangulations is still a small subset of all possible triangulations. This demonstrates that fundamental changes to these methods are needed to further expand the collection of manifolds on which differentiable structures can be constructed numerically. 

Abstract 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. 

Abstract We report on a new search for continuous gravitational waves from NS 1987A, the neutron star born in SN 1987A, using open data from Advanced LIGO and Virgo’s third observing run (O3). The search covered frequencies from 35–1050 Hz, more than 5 times the band of the only previous gravitational-wave search to constrain NS 1987A. Our search used an improved code and coherently integrated from 5.10 to 14.85 days depending on frequency. No astrophysical signals were detected. By expanding the frequency range and using O3 data, this search improved on strain upper limits from the previous search and was sensitive at the highest frequencies to ellipticities of 1.6 × 10⁻⁵andr-mode amplitudes of 4.4 × 10⁻⁴, both an order of magnitude improvement over the previous search and both well within the range of theoretical predictions. 

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 performmaximum a posterioriestimation 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. 

Abstract Numerical solutions to the Einstein constraint equations are constructed on a selection of compact orientable three-dimensional manifolds with non-trivial topologies. A simple constant mean curvature solution and a somewhat more complicated non-constant mean curvature solution are computed on example manifolds from three of the eight Thursten geometrization classes. The constant mean curvature solutions found here are also solutions to the Yamabe problem that transforms a geometry into one with constant scalar curvature.