  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.
