The physics of neutron star crusts is vast, involving many different research fields, from nuclear and condensed matter physics to general relativity. This review summarizes the progress, which has been achieved over the last few years, in modeling neutron star crusts, both at the microscopic and macroscopic levels. The confrontation of these theoretical models with observations is also briefly discussed.

We present a new Skyrme-Hartree-Fock-Bogoliubov nuclear-mass model in which the contact-pairing force is constructed from microscopic pairing gaps of symmetric nuclear matter and neutron matter calculated from realistic two- and three-body forces, with medium-polarization effects included. With the pairing being treated more realistically than in any of our earlier models, the rms deviation with respect to essentially all the available mass data falls to 0.581 MeV, the best value ever found within the mean-field framework. Since our Skyrme force is also constrained by the properties of pure neutron matter, this new model is particularly well suited for application to astrophysical problems involving a neutron-rich environment, such as the elucidation of the r process of nucleosynthesis, and the description of supernova cores and neutron-star crusts.

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.

Large pulsar frequency glitches are generally interpreted as sudden transfers of angular momentum between the neutron superfluid permeating the inner crust and the rest of the star. Despite the absence of viscous drag, the neutron superfluid is strongly coupled to the crust due to nondissipative entrainment effects. These effects are shown to severely limit the maximum amount of angular momentum that can possibly be transferred during glitches. In particular, it is found that the glitches observed in the Vela pulsar require an additional reservoir of angular momentum.

We construct three new Hartree-Fock-Bogoliubov (HFB) mass models, labeled HFB-19, HFB-20, and HFB-21, with unconventional Skyrme forces containing t 4 and t 5 terms, i.e., density-dependent generalizations of the usual t 1 and t 2 terms, respectively. The new forces underlying these models are fitted respectively to three different realistic equations of state of neutron matter for which the density dependence of the symmetry energy ranges from the very soft to the very stiff, reflecting thereby our present lack of complete knowledge of the high-density behavior of nuclear matter. All unphysical instabilities of nuclear matter, including the transition to a polarized state in neutron-star matter, are eliminated with the new forces. At the same time the new models fit essentially all the available mass data with rms deviations of 0.58 MeV and give the same high-quality fits to measured charge radii that we obtained in earlier models with conventional Skyrme forces. Being constrained by neutron matter, these new mass models, which all give similar extrapolations out to the neutron drip line, are highly appropriate for studies of the r process and the outer crust of neutron stars. Moreover, the underlying forces, labeled BSk19, BSk20 and BSk21, respectively, are well adapted to the study of the inner crust and core of neutron stars. The new family of Skyrme forces thus opens the way to a unified description of all regions of neutron stars.

We calculate the maximum mass of neutron stars for three different equations of state (EOS) based on generalized Skyrme functionals that are simultaneously fitted to essentially all the 2003 nuclear mass data (the rms deviation is 0.58 MeV in all three cases) and to one or other of three different equations of state of pure neutron matter, each determined by a different many-body calculation using realistic two-and three-body interactions but leading to significantly different degrees of stiffness at the high densities prevailing in neutron-star interiors. The observation of a neutron star with mass 1.97 ± 0.04 M ⊙ eliminates the softest of our models (BSk19), but does not discriminate between BSk20 and BSk21. However, nuclear-mass measurements that have been made since our models were constructed strongly favor BSk21, our stiffest functional.

Publisher's Note: Neutron conduction in the inner crust of a neutron star in the framework of the band theory of solids [Phys. Rev. C 85, 035801 (2012)]N. Chamel

The theory of the nuclear energy-density functional is used to provide a unified and thermodynamically consistent treatment of all regions of cold non-accreting neutron stars. In order to assess the impact of our lack of complete knowledge of the density dependence of the symmetry energy on the constitution and the global structure of neutron stars, we employ four different functionals. All of them were precision fitted to essentially all the nuclear-mass data with the Hartree-Fock-Bogoliubov method and two different neutron-matter equations of state based on realistic nuclear forces. For each functional, we calculate the composition, the pressure-density relation, and the chemical potentials throughout the star. We show that uncertainties in the symmetry energy can significantly affect the theoretical results for the composition and global structure of neutron stars. To facilitate astrophysical applications, we construct analytic fits to our numerical results.