  The observed rapid cooling of the Cassiopeia A neutron star can be
interpreted as being caused by neutron and proton transitions from normal to
superfluid and superconducting states in the stellar core. Here we present two
new Chandra ACIS-S Graded observations of this neutron star and measurements of
the neutron star mass M and radius R found from consistent fitting of both the
X-ray spectra and cooling behavior. This comparison is only possible for
individual nuclear equations of state. We test phenomenological superfluid and
superconducting gap models which mimic many of the known theoretical models
against the cooling behavior. Our best-fit solution to the Cassiopeia A data is
one in which the (M,R) = (1.44 Msun,12.6 km) neutron star is built with the
BSk21 equation of state, strong proton superconductor and moderate neutron
triplet superfluid gap models, and a pure iron envelope or a thin carbon layer
on top of an iron envelope, although there are still large observational and
theoretical uncertainties.
