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

Abstract

We have investigated the systematic differences introduced when performing a Bayesian-inference analysis of the equation of state (EOS) of neutron stars employing either variable- or constant-likelihood functions. The former has the advantage of retaining the full information on the distributions of the measurements, making exhaustive usage of the data. The latter, on the other hand, has the advantage of a much simpler implementation and reduced computational costs. In both approaches, the EOSs have identical priors and have been built using the sound speed parameterization method so as to satisfy the constraints from X-ray and gravitational waves observations, as well as those from chiral effective theory and perturbative quantum chromodynamics. In all cases, the two approaches lead to very similar results and the 90% confidence levels essentially overlap. Some differences do appear, but in regions where the probability density is extremely small and are mostly due to the sharp cutoff on the binary tidal deformability Λ ˜ ≤ 720 set in the constant-likelihood approach. Our analysis has also produced two additional results. First, an inverse correlation between the normalized central number density, n c,TOV/n s , and the radius of a maximally massive star, R TOV. Second, and most importantly, it has confirmed the relation between the chirp mass and the binary tidal deformability. The importance of this result is that it relates  chirp , which is measured very accurately, and Λ ˜ , which contains important information on the EOS. Hence, when  chirp is measured in future detections, our relation can be used to set tight constraints on Λ ˜ .

Ab-initio QCD Calculations Impact the Inference of the Neutron-star-matter Equation of State

“…The majority of these EoS-inference setups have used different parametric (Hebeler et al 2013;Tews et al 2018;Capano et al 2020;Dietrich et al 2020;Miller et al 2020;Raaijmakers et al 2020;Al-Mamun et al 2021;Huth et al 2022;Lim & Holt 2022) or nonparametric extensions (Landry & Essick 2019;Essick et al 2020;Landry et al 2020;Essick et al 2021;Miller et al 2021) of the CET EoS to NS star densities n ∼ 5-10n s . There are also fewer works that additionally include the fundamental, high-density QCD constraint and interpolate through the full density range from 1.1n s to 40n s (Kurkela et al 2014;Annala et al 2018;Most et al 2018;Annala et al 2020;Altiparmak et al 2022;Annala et al 2022;Jiang et al 2023).…”

Two-flavor Color Superconducting Quark Stars May Not Exist

“…We mention here that there are several alternative models discussed in the literature for HESS J1731-347, such as (hybrid) neutron stars (Brodie & Haber 2023;Huang et al 2024;Kubis et al 2023;Laskos-Patkos et al 2024;Li & Sedrakian 2023;Tsaloukidis et al 2023), and dark-matteradmixed neutron stars (Routaray et al 2023;Sagun et al 2023). In practice, measuring the mass and radius of compact stars is an extremely challenging task (see further discussions in, e.g., Brandes et al 2023;Jiang et al 2023;. We eagerly anticipate more updated results in the near future, especially as models for atmosphere, distance, and other factors continue to develop.…”

On the Maximum Mass and Oblateness of Rotating Neutron Stars with Generic Equations of State

“…for mass ratios q > 0.73. The constraints from these astrophysical observations are imposed as sharp cutoffs on the EOS ensemble, which, as shown by Jiang et al (2023), leads to good agreement of the important central part of the PDF obtained from a more expensive Bayesian analysis. Finally, we impose a lower bound ( ) -…”