Formed in the aftermath of gravitational core-collapse supernova explosions, neutron stars are the most compact observed stars. Their average density exceeds that found inside the heaviest atomic nuclei. Neutron stars are also endowed with the highest magnetic fields known, which can reach millions of billion times that of the Earth. According to our current understanding, a neutron star is stratified into distinct layers. The surface is probably covered by a metallic ocean. The solid layers beneath consist of a crystal lattice of pressure-ionized atoms embedded in a highly degenerate relativistic electron gas. With increasing density, nuclei become progressively more neutron rich until neutrons start to drip out of nuclei thus delimiting the boundary between the outer and inner regions of the crust, where neutron-proton clusters are immersed in a neutron liquid. At about half the density of heavy nuclei, the crust dissolves into a homogeneous liquid mixture of nucleons and leptons. Over the past years, we have developed a series of unified equations of state of dense matter in neutron stars, available on the European CompOSE database. Based on the nuclear energy-density functional theory, these equations of state provide a thermodynamically consistent treatment of all regions of the star and were calculated using functionals that were precision fitted to experimental and theoretical nuclear data. These equations of state were specifically developed to assess the role of nuclear uncertainties on neutron-star properties. Predictions will be compared to constraints inferred from the detection of the gravitational-wave signal GW170817 from a binary neutron-star merger and from observations of the electromagnetic counterparts. Constraints inferred from other observations will be also discussed.
