Analytical representations of unified equations of state for neutron-star matter

Abstract: Context. A unified equation of state (EoS) should describe the crust and the core of a neutron star using the same physical model. The Brussels-Montreal group has recently derived a family of such EoSs based on the nuclear energy-density functional theory with generalized Skyrme effective forces, fitted to the available mass data. At the same time, these forces were constrained to reproduce microscopic calculations of homogeneous neutron matter based on realistic two- and three-nucleon forces. Aims. We represent basic physical characteristics of the latest Brussels-Montreal EoS models by analytical expressions to facilitate their inclusion in astrophysical simulations. Methods. We consider three EoS models, which significantly differ by stiffness: BSk19, BSk20, and BSk21. For each of them we constructed two versions of the EoS parametrization. In the first version, pressure P and gravitational mass density \rho are given as functions of the baryon number density n_b. In the second version, P, \rho, and n_b are given as functions of pseudo-enthalpy, which is useful for two-dimensional calculations of stationary rotating configurations of neutron stars. In addition to the EoS, we derived analytical expressions for several related quantities that are required in neutron-star simulations: number fractions of electrons and muons in the stellar core, nucleon numbers per nucleus in the inner crust, and equivalent radii and shape parameters of the nuclei in the inner crust. Results. We obtain analytical representations for the basic characteristics of the models of cold dense matter, which are most important for studies of neutron stars. We demonstrate the usability of our results by applying them to calculations of neutron-star mass-radius relations, maximum and minimum masses, thresholds of direct Urca processes, and the electron conductivity in the neutron-star crust.

• The paper presents analytical representations of three unified neutron-star equations of state (BSk19, BSk20, and BSk21) derived from nuclear energy-density functional theory.
• It introduces detailed parametric expressions for pressure, mass density, and baryon number density that ensure smooth transitions across the star’s crust and core.
• The analytical models reveal distinct stiffness characteristics among the EoSs, providing practical tools for accurately computing neutron-star mass-radius relationships and stability limits.

Analytical Representations of Unified Equations of State for Neutron-Star Matter

The paper authored by Potekhin et al. provides a comprehensive analysis of three unified equations of state (EoSs) for neutron-star matter, labeled as BSk19, BSk20, and BSk21. These EoSs were formulated using the nuclear energy-density functional theory, incorporating generalized Skyrme effective forces. The main objective of the study was to create analytical representations of these EoSs to facilitate their implementation in astrophysical simulations, with a specific focus on modeling the structure and behavior of neutron stars.

Objectives and Scope

The foundational basis of the research lies in establishing a unified EoS that consistently describes both the crust and core of a neutron star using a singular physical model. To achieve this, the paper presents analytical fitting expressions for basic physical characteristics of the EoSs derived from nuclear energy-density functionals. These functionals were meticulously constrained to experimental mass data and realistic calculations for homogeneous neutron matter. Potekhin et al. provided a two-version parametrization for each EoS, detailing pressure, mass density, and baryon number density as functions of selected variables. The aim is to support rapid and precise modeling of rotating neutron stars and other astrophysical phenomena.

Methodological Approach

The methodological approach includes an extensive fitting of the BSk models to available experimental data and microscopic calculations of neutron matter. Each EoS exhibits varying stiffness, with distinct characteristics analyzed through derived analytical expressions. The authors report successful analytical representation of the EoSs in terms of barotropic relations, transitioning seamlessly through major neutron-star domains—outer crust, inner crust, and core.

The transition from tabulated values to analytic functions involves intricate parametrizations, ensuring continuity and thermodynamical consistency. These parametrizations circumvent typical numerical errors associated with transitions at interfaces like crust-core regions.

Key Findings

1. EoS Models: The paper distinguishes between EoS models by their stiffness characteristics—BSk19 being the softest and BSk21 the stiffest. The precise fitting to experimental mass data allows these models to provide reliable descriptions across various densities encountered in neutron stars.
2. Maximum Mass and Stability: The analytical expressions derived facilitate the evaluation of neutron-star mass-radius relationships, revealing maximum and minimum mass limits. The EoS for BSk20 allows a maximum mass of 2.16 solar masses, whereas BSk21 reaches slightly higher. The authors note superluminal behavior of EoSs under certain conditions signaling an upper limit for density applicability.
3. Implementation in Astrophysical Simulations: The introduction of pseudo-enthalpy as a variable aids in simulating rapidly rotating stars, offering computational advantages and enhancing accuracy compared to direct table-based methods. The analytical expressions thereby enable efficient computation of dynamic stability properties and direct Urca process thresholds.
4. Density and Composition in Crust: Analytical expressions provide insights into the distribution of electrons, muons, and nucleons within the neutron-star core and crust, essential for thermal evolution modeling. The composition's continuity across interfaces supports the stability of numerical neutron-star models.

Implications and Future Directions

By rendering the BSk models into easily implementable forms, the paper poses significant implications for astrophysical inquiry into neutron stars. The unified treatment across vast density ranges offers potential to enhance theories related to neutron-star cooling, pulsar timing, and gravitational wave events. Additionally, comparisons with empirical data from neutron-star observations will further validate these models.

Future research includes extending this analytical approach to incorporate hyperonic and quark matter influences, capturing a more comprehensive picture of highly dense matter behavior. Furthermore, as observational technologies advance, these models stand to be pivotal in predicting astrophysical phenomena with increasing accuracy.

In summary, Potekhin et al.'s research contributes indispensable tools for neutron-star studies, presenting robust models that address internal consistency and offer clear pathways for future exploration in high-density astrophysical contexts.