A pitfall of piecewise-polytropic equation of state inference

TL;DR

This paper investigates how the choice of prior distribution affects the inference of the dense matter equation of state from observations of compact stars, highlighting sensitivities in Bayesian analysis.

Contribution

It demonstrates that EOS parameter inference is sensitive to prior definitions on mass-radius versus interior matter parameters, especially for piecewise-polytropic models.

Findings

EOS inferences depend on prior choices in Bayesian analysis.

Prior definition on mass-radius space influences EOS parameter estimates.

Implications for astrophysical dense matter research are discussed.

Abstract

The only messenger radiation in the Universe which one can use to statistically probe the Equation of State (EOS) of cold dense matter is that originating from the near-field vicinities of compact stars. Constraining gravitational masses and equatorial radii of rotating compact stars is a major goal for current and future telescope missions, with a primary purpose of constraining the EOS. From a Bayesian perspective it is necessary to carefully discuss prior definition; in this context a complicating issue is that in practice there exist pathologies in the general relativistic mapping between spaces of local (interior source matter) and global (exterior spacetime) parameters. In a companion paper, these issues were raised on a theoretical basis. In this study we reproduce a probability transformation procedure from the literature in order to map a joint posterior distribution of Schwarzschild gravitational masses and radii into a joint posterior distribution of EOS parameters. We demonstrate computationally that EOS parameter inferences are sensitive to the choice to define a prior on a joint space of these masses and radii, instead of on a joint space interior source matter parameters. We focus on the piecewise-polytropic EOS model, which is currently standard in the field of astrophysical dense matter study. We discuss the implications of this issue for the field.