Comparison of Equations of State for Neutron Stars with First-Order Phase Transitions: A Qualitative Study

TL;DR

This study compares two methods for modeling first-order phase transitions in neutron star equations of state, emphasizing thermodynamic consistency and the ability to accurately capture the star's mass-radius relation.

Contribution

It introduces and evaluates the randomized speed-of-sound interpolation approach as a more thermodynamically consistent method for EoS modeling.

Findings

Speed of sound method ensures chemical potential continuity.

Polytropic interpolation can cause causality issues.

Speed of sound approach better captures softer mass-radius spectra.

Abstract

The equation of state is fundamental in describing matter under the extreme conditions characteristic of neutron stars and is central to advancing our understanding of dense matter physics. A critical challenge, however, lies in accurately modelling first-order phase transitions while ensuring thermodynamic consistency and aligning with astrophysical observations. This study explores two frameworks for constructing EoSs with first-order phase transitions: the polytropic interpolation method and the randomized speed-of-sound interpolation approach. It is found that the mass-radius relation and pressure vs. energy density relation are blind towards the thermodynamic consistency check. The polytropic interpolation method can exhibit discontinuities in the chemical potential for first-order phase transition, raising concerns regarding potential causality violations and thermodynamic inconsistencies. In contrast, the speed of sound interpolation approach ensures continuity in the chemical potential, offering a more thermodynamically consistent and reliable framework. Moreover, the sound speed method effectively captures the softer segment of the mass-radius spectrum, a capability not achieved by the consistent piecewise-polytropic approach due to its monotonic stiffness constraints. The speed of sound definition involving number density and chemical potential reveals the thermodynamic inconsistency, making it a more consistent and robust definition. These findings underscore the importance of thermodynamic consistency in EoS construction and highlight the advantages of the randomized speed-of-sound method for modelling phase transitions in dense matter.