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

¹ Centre de Recherche Astrophysique de Lyon, Université de Lyon, Université Lyon 1, Observatoire de Lyon, École Normale Supérieure de Lyon, CNRS, UMR 5574, 9 avenue Charles André, 69230 Saint-Genis Laval, France
e-mail: palex@astro.ioffe.ru
² Ioffe Physical-Technical Institute, Politekhnicheskaya 26, 194021 St. Petersburg, Russia
³ Isaac Newton Institute of Chile, St. Petersburg Branch, 198504 St. Petersburg, Russia
⁴ Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles, CP-226, 1050 Brussels, Belgium
⁵ Département de Physique, Université de Montréal, Montréal ( Québec ) H3C 3J7, Canada

Received: 15 April 2013
Accepted: 23 September 2013

Abstract

Context. An equation of state (EoS) of dense nuclear matter is a prerequisite for studies of the structure and evolution of compact stars. A unified 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 that have been fitted with great precision to essentially all 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 ρ are given as functions of the baryon number density n_b. In the second version, P, ρ, 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.