  One of the major uncertainties in the dense matter equation of state has been
the nuclear symmetry energy. The density dependence of the symmetry energy is
important in nuclear astrophysics, as it controls the neutronization of matter
in core-collapse supernovae, the radii of neutron stars and the thicknesses of
their crusts, the rate of cooling of neutron stars, and the properties of
nuclei involved in r-process nucleosynthesis. We show that fits of nuclear
masses to experimental masses, combined with other experimental information
from neutron skins, heavy ion collisions, giant dipole resonances and dipole
polarizabilities, lead to stringent constraints on parameters that describe the
symmetry energy near the nuclear saturation density. These constraints are
remarkably consistent with inferences from theoretical calculations of pure
neutron matter, and, furthermore, with astrophysical observations of neutron
stars. The concordance of experimental, theoretical and observational analyses
suggests that the symmetry parameters S_v and L are in the range 29.0 - 32.7
MeV and 40.5 - 61.9 MeV, respectively, and that the neutron star radius, for a
1.4 M_sun star, is in the narrow window 10.7 km < R < 13.1 km (90% confidence).
We can also set tight limits to the size of neutron star crusts and the
fractional moment of inertia they contain, as well as the overall moment of
inertia and quadrupole polarizability of 1.4 M_sun stars. Our results also have
implications for the disk mass and ejected mass of compact mergers involving
neutron stars.
