Abstract. An equation of state (EOS) of neutron star matter, describing both the neutron star crust and the liquid core, is calculated. It is based on the effective nuclear interaction SLy of the Skyrme type, which is particularly suitable for the application to the calculation of the properties of very neutron rich matter (Chabanat et al. 1997(Chabanat et al. , 1998. The structure of the crust, and its EOS, is calculated in the T = 0 approximation, and under the assumption of the ground state composition. The crust-core transition is a very weakly first-order phase transition, with relative density jump of about one percent. The EOS of the liquid core is calculated assuming (minimal) npeµ composition. Parameters of static neutron stars are calculated and compared with existing observational data on neutron stars. The minimum and maximum masses of static neutron stars are 0.094 M and 2.05 M , respectively. Effects of rotation on the minimum and the maximum mass of neutron stars are briefly discussed.

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%e show that the direct URCA process can occur in neutron stars if the proton concentration exceeds some critical value in the range (11 -15)%. The proton concentration, which is determined by the poorly

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.

The uncertainties in neutron star radii and crust properties due to our limited knowledge of the equation of state are quantitatively analyzed. We first demonstrate the importance of a unified microscopic description for the different baryonic densities of the star. If the pressure functional is obtained matching a crust and a core equation of state based on models with different properties at nuclear matter saturation, the uncertainties can be as large as ∼30 % for the crust thickness and 4% for the radius. Necessary conditions for causal and thermodynamically consistent matchings between the core and the crust are formulated and their consequences examined. A large set of unified equations of state for purely nucleonic matter is obtained based on twenty-four Skyrme interactions and nine relativistic mean-field nuclear parametrizations. In addition, for relativistic models fifteen equations of state including a transition to hyperonic matter at high density are presented. All these equations of state have in common the property of describing a 2M star and of being causal within stable neutron stars. Spans of ∼3 and ∼4 km are obtained for the radius of, respectively, 1.0M and 2.0M stars. Applying a set of nine further constraints from experiment and ab initio calculations the uncertainty is reduced to ∼1 and 2 km, respectively. These residual uncertainties reflect lack of constraints at large densities and insufficient information on the density dependence of the equation of state near the nuclear matter saturation point. The most important parameter to be constrained is shown to be the symmetry energy slope L. Indeed, this parameter exhibits a linear correlation with the stellar radius, which is particularly clear for small mass stars around 1.0M . The other equation-of-state parameters do not show clear correlations with the radius, within the present uncertainties. Potential constraints on L, the neutron star radius, and the equation of state from observations of thermal states of neutron stars are also discussed. The unified equations of state are made available in the Supplemental Materials and via the CompOSE database.

We review the main neutrino emission mechanisms in neutron star crusts and cores. Among them are the well-known reactions such as the electron-positron annihilation, plasmon decay, neutrino bremsstrahlung of electrons colliding with atomic nuclei in the crust, as well as the Urca processes and neutrino bremsstrahlung in nucleon-nucleon collisions in the core. We emphasize recent theoretical achievements, for instance, band structure effects in neutrino emission due to scattering of electrons in Coulomb crystals of atomic nuclei. We consider the standard composition of matter (neutrons, protons, electrons, muons, hyperons) in the core, and also the case of exotic constituents such as the pion or kaon condensates and quark matter. We discuss the reduction of the neutrino emissivities by nucleon superfluidity, as well as the specific neutrino emission produced by Cooper pairing of the superfluid particles. We also analyze the effects of strong magnetic fields on some reactions, such as the direct Urca process and the neutrino synchrotron emission of electrons. The results are presented in the form convenient for practical use. We illustrate the effects of various neutrino reactions on the cooling of neutron stars. In particular, the neutrino emission in the crust is critical in setting the initial thermal relaxation between the core and the crust. Finally, we discuss the prospects of exploring the properties of supernuclear matter by confronting cooling simulations with observations of the thermal radiation from isolated neutron stars.