Bayesian inferences on covariant density functionals from multimessenger astrophysical data: The impacts of likelihood functions of low density matter constraints

TL;DR

This study compares Gaussian and uniform likelihood functions in Bayesian inference for nuclear matter and compact star properties, finding nearly identical results for mass-radius relations but significant variations in some nuclear matter coefficients.

Contribution

It introduces a uniform likelihood function with Gaussian normalization for direct comparison and analyzes its impact on astrophysical and nuclear matter inferences.

Findings

Mass-radius relations are nearly identical across methods.

Significant variation in isoscalar channel coefficients.

Minimal variation in isovector channel coefficients.

Abstract

We systematically investigate how the choice between Gaussian and uniform likelihood functions in Bayesian inference affects the inferred bulk properties of compact stars and nuclear matter within covariant density functional-based equations of state. To enable direct comparison between the two approaches, we designed the uniform likelihood function with a Gaussian-equivalent normalization factor and marginalization behavior. Across three representative astrophysical scenarios, both approaches yield nearly identical mass-radius relations, density-pressure relations, and overlapping 95.4\% confidence level regions. Although our inference analysis is carried out using parameters of the density functional, we subsequently determine the associated nuclear matter characteristic coefficients derived from the Taylor expansion of the energy density around the saturation density. We observe significant variation in the predicted isoscalar channel coefficients (e.g., the nuclear incompressibility) across different astrophysical scenarios, while the isovector channel (e.g., the slope of symmetry energy) exhibits only minimal variation.