Spectral Representations of Neutron-Star Equations of State

Methods are developed for constructing spectral representations of cold (barotropic) neutron-star equations of state. These representations are faithful in the sense that every physical equation of state has a representation of this type, and conversely every such representation satisfies the minimal thermodynamic stability criteria required of any physical equation of state. These spectral representations are also efficient, in the sense that only a few spectral coefficients are generally required to represent neutron-star equations of state quiet accurately. This accuracy and efficiency is illustrated by constructing spectral fits to a large collection of “realistic” neutron-star equations of state.

💡 Research Summary

The paper introduces a novel spectral parameterisation for cold (barotropic) neutron‑star equations of state (EOS), addressing long‑standing difficulties associated with traditional tabular or polynomial representations. In a barotropic EOS the pressure p is a single‑valued function of the energy density ε, p = p(ε). Physical EOS must satisfy basic thermodynamic stability: the pressure must increase monotonically with ε and the adiabatic index Γ = (ε + p)/p · dp/dε must remain positive. Conventional approaches enforce these constraints by hand, often requiring high‑order polynomials or dense tables, which can introduce non‑physical oscillations and are computationally expensive.

The authors propose to expand the adiabatic index Γ(ε) in a spectral series after mapping the relevant density interval onto the unit interval