  Using a model for the equation of state and composition of dense matter and
the magnitude of singlet proton superconductivity and triplet neutron
superfluidity, we perform the first simultaneous fit of neutron star masses and
radii determined from observations of quiescent low-mass x-ray binaries and
luminosities and ages determined from observations of isolated neutron stars.
We find that the Vela pulsar strongly determines the values inferred for the
superfluid/superconducting gaps and the neutron star radius. We find,
regardless of whether or not the Vela pulsar is included in the analysis, that
the threshold density for the direct Urca process lies between the central
density of 1.7 and 2 solar mass neutron stars. We also find that two solar mass
stars are unlikely to cool principally by the direct Urca process because of
the suppression by neutron triplet superfluidity.
