Neutron star properties and the equation of state for the core

Abstract

Context. Few unified equations of state for neutron star matter, in which core and crust are described using the same nuclear model, are available. However the use of non-unified equations of state with simplified matching between the crust and core has been shown to introduce uncertainties in the radius determination, which can be larger than the expected precision of the next generation of X-ray satellites. Aims. We aim to eliminate the dependence of the radius and mass of neutron stars on the detailed model for the crust and on the crust-core matching procedure. Methods. We solved the approximate equations of the hydrostatic equilibrium for the crust of neutron stars and obtained a precise formula for the radius that only depends on the core mass and radius, the baryon chemical potential at the core-crust interface, and at the crust surface. For a fully accreted crust one needs, additionally, the value of the total deep crustal heating per one accreted nucleon. Results. For typical neutron star masses, the approximate approach allows us to determine the neutron star radius with an error ∼0.1% (∼10 m, equivalent to a 1% inaccuracy in the crust thickness). The formalism applies to neutron stars with a catalyzed or a fully accreted crust. The difference in the neutron star radius between the two models is proportional to the total energy release due to deep crustal heating. Conclusions. For a given model of dense matter describing the neutron star core, the radius of a neutron star can be accurately determined independent of the crust model with a precision much better than the ∼5% precision expected from the next generation of X-ray satellites. This allows us to circumvent the problem of the radius uncertainty that may arise when non-unified equations of state for the crust and core are used.

New parameterization of the effective field theory motivated relativistic mean field model

“…The contributions of the crust EoS to the mass and the radius of the neutron star for a given central density are estimated using Ref. [39]. It is shown in Ref.…”

“…It is shown in Ref. [39] that the mass and radius of the core for a given central density together with the chemical potential at the core-crust transition density are enough to estimate reasonably well the thickness and the mass of the crust. We have used the core-crust transition density to be 0.074 fm −3 and the chemical potential at the transition point to be 951.72 MeV, which altogether results in the total maximum mass, M max = 2.03M ⊙ , and the corresponding radius R max = 11.03 km.…”

Analytical determination of the structure of the outer crust of a cold nonaccreted neutron star

“…The precision of Eqs. (30) and (31) for typical neutron-star masses and radii is a few % and less than 1% respectively [32]. These analytical approximations may actually be more accurate than the numerical solution of the full TOV Eqs.…”

Core-crust transition in neutron stars with finite-range interactions: The dynamical method

“…The total mass of the NS is M = M crust + M core . This approximate approach predicts the radius and mass of the crust with accuracy better than ∼ 1% in R crust and ∼ 5% in M crust for typical neutron star masses [59], while one circumvents the complex problem of computing the EOS of the crustal matter. Finally, to compute the crustal fraction of the moment of inertia we use the approximation given by [60][61][62], which allows one to express this quantity as…”