Constraining the nuclear symmetry energy and properties of the neutron star from GW170817 by Bayesian analysis

Based on the distribution of tidal deformabilities and component masses of binary neutron star merger GW170817, the parametric equation of state (EOS) is employed to probe the nuclear symmetry energy and the properties of the neutron star. To obtain a proper distribution of the parameters of the EOS that is consistent with the observation, Bayesian analysis is used and the constraints of causality and maximum mass are considered. From this analysis, it is found that the symmetry energy and pressure at twice the saturation density of nuclear matter can be constrained within Esym(2ρ0)=34.5-2.3+20.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_{sym}(2{\rho _{0}}) = 34.5^{+20.5}_{-2.3}$$\end{document} MeV and P(2ρ0)=3.81-2.32+1.18×1034\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P (2{\rho _{0}}) = 3.81^{+1.18}_{-2.32}\times 10^{34}$$\end{document} dyn cm-2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-2}$$\end{document} at 90% credible level, respectively. Moreover, the constraints on the radii and dimensionless tidal deformabilities of canonical neutron stars are also demonstrated through this analysis, and the corresponding constraints are 10.80 km ≤R1.4≤\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\le R_{1.4} \le $$\end{document} 13.20 km and 133≤Λ1.4≤686\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$133 \le \Lambda _{1.4} \le 686$$\end{document} at 90% credible level, with the most probable value of R¯1.4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{R}_{1.4}$$\end{document} = 12.60 km and Λ¯1.4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{\Lambda }_{1.4}$$\end{document} = 500, respectively. With respect to the prior, our result (posterior result) prefers a softer EOS, corresponding to a lower expected value of symmetry energy, a smaller stellar radius, and a smaller tidal deformability.