  The equation of state (EOS) of dense matter has been a long-sought goal of
nuclear physics. Equations of state generate unique mass versus radius (M-R)
relations for neutron stars, the ultra-dense remnants of stellar evolution. In
this work, we determine the neutron star mass-radius relation and, based on
recent observations of both transiently accreting and bursting sources, we show
that the radius of a 1.4 solar mass neutron star lies between 10.4 and 12.9 km,
independent of assumptions about the composition of the core. We show, for the
first time, that these constraints remain valid upon removal from our sample of
the most extreme transient sources or of the entire set of bursting sources;
our constraints also apply even if deconfined quark matter exists in the
neutron star core. Our results significantly constrain the dense matter EOS and
are, furthermore, consistent with constraints from both heavy-ion collisions
and theoretical studies of neutron matter. We predict a relatively weak
dependence of the symmetry energy on the density and a value for the neutron
skin thickness of lead which is less than 0.20 fm, results that are testable in
forthcoming experiments.
