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

Abstract

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi mathvariant="normal">Λ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>˜</mml:mo> </mml:mrow> </mml:mover> <mml:mo>≤</mml:mo> <mml:mn>720</mml:mn> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mrow> <mml:mi>chirp</mml:mi> </mml:mrow> </mml:msub> </mml:math> , which is measured very accurately, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi mathvariant="normal">Λ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>˜</mml:mo> </mml:mrow> </mml:mover> </mml:math> , which contains important information on the EOS. Hence, when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mrow> <mml:mi>chirp</mml:mi> </mml:mrow> </mml:msub> </mml:math> is measured in future detections, our relation can be used to set tight constraints on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi mathvariant="normal">Λ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>˜</mml:mo> </mml:mrow> </mml:mover> </mml:math> .