Piecewise polytropic meshing and refinement method for the reconstruction of the neutron star equation of state using tidal deformabilities and constraints in the piecewise polytropic parameters given by the GW170817 event

Abstract

In this paper we present a new approach to the inverse problem for relativistic stars using the piecewise polytropic parametrization of the equation of state. The algorithm is a piecewise polytropic meshing and refinement method that reconstructs the neutron star equation of state from experimental data of the mass and the tidal Love parameter. We use an initial mesh of 65536 equations of state in a 4-volume of piecewise polytropic parameters that contains most of the candidate equations of state used today. The refinement process drives us to the reconstruction of the equation of state with a certain precision. Using the reconstructed equation of state, we calculate predictions for quasinormal modes and slow rotation parameters. In order to check the meshing and refinement method, we use as input data a few (6) configurations of a given equation of state. We reconstruct the equation of state in a quite good approximation, and then we compare the curves of physical parameters from the original equation of state and the reconstructed one. We obtain a relative difference for all the parameters smaller than 7.5%. We also study the constraints that impose the GW170817 event on the piecewise polytropic parameters $\{{\log }_{10}{p}_1,{\Gamma }_1,{\Gamma }_2,{\Gamma }_3\}$. We use the waveform model TaylorF2 for the low-spin scenario, and see that the EOSs that lie outside the 90% credible region when ${\bar{\lambda }}_1^{tid}={\bar{\lambda }}_2^{tid}$ define a zone of polytropic parameters that does not depend on ${\Gamma }_3$.

arXiv comment12 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1901.10851

References in corpus (17)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• GW170817: Measurements of Neutron Star Radii and Equation of State
• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• Tidal Love numbers of neutron stars
• A unified equation of state of dense matter and neutron star structure
• Properties of the binary neutron star merger GW170817
• Constraints on a phenomenologically parameterized neutron-star equation of state
• Formation of Double Neutron Star Systems
• Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817
• Composition and stability of hybrid stars with hyperons and quark color-superconductivity
• Reconstructing the neutron-star equation of state with gravitational-wave detectors from a realistic population of inspiralling binary neutron stars
• The inverse problem for pulsating neutron stars: A ``fingerprint analysis'' for the supranuclear equation of state
• Measuring the neutron star tidal deformability with equation-of-state-independent relations and gravitational waves
• A Spectral Approach to the Relativistic Inverse Stellar Structure Problem
• Comparing two models for measuring the neutron star equation of state from gravitational-wave signals
• Solving the relativistic inverse stellar problem through gravitational waves observation of binary neutron stars