Determining the Nature of Super Fluidity and Superconductivity in Dense Matter from Neutron Star Observations

I present a quantitative analysis that utilizes observations of neutron stars to constrain the magnitude of the neutron superfluid gap and the proton superconducting gap in dense matter. In the context of the minimal cooling model, the most likely range for the neutron triplet superfluid gap is $2.09^{+4.37}_{-1.41} \times 10^{8}$ K and the most likely range for the the proton singlet superconducting gap is $7.59^{+2.48}_{-5.81} \times 10^{9}$ K. In a second analysis, I confirm these basic predictions for the gaps and additionally determine the mass and envelope composition of the neutron stars in our data set. This analysis shows that some neutron stars are likely more massive and thus cool by the direct Urca process. It also shows that the minimal cooling model may not be the best explanation of neutron star cooling observations. Finally, these quantitative results show that further observations of neutron star cooling will continue to provide constraints on both the equation of state and the transport properties of dense matter.