We present a quantitative analysis of superfluidity and superconductivity in dense matter from observations of isolated neutron stars in the context of the minimal cooling model .
Our new approach produces the best fit neutron triplet superfluid critical temperature , the best fit proton singlet superconducting critical temperature , and their associated statistical uncertainties .
We find that the neutron triplet critical temperature is likely 2.09 ^ { +4.37 } _ { -1.41 } \times 10 ^ { 8 } K and that the proton singlet critical temperature is 7.59 ^ { +2.48 } _ { -5.81 } \times 10 ^ { 9 } K. However , we also show that this result only holds if the Vela neutron star is not included in the data set .
If Vela is included , the gaps increase significantly to attempt to reproduce Vela ’ s lower temperature given its young age .
Further including neutron stars believed to have carbon atmospheres increases the neutron critical temperature and decreases the proton critical temperature .
Our method demonstrates that continued observations of isolated neutron stars can quantitatively constrain the nature of superfluidity in dense matter .