Simultaneous fitting of neutron star structure and cooling data

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.

Figure 1

All panels except (d) show results with and without Vela. For display purposes, simulations with and without Vela are fixed to have the same overall normalization. Panel (a): 95% credible intervals for the neutron and proton density profiles for ${}^{208}\mathrm{Pb}$. Panel (b): 95% credible intervals for the mass-radius curves. Panel (c): histograms for the maximum value of the proton singlet and neutron triplet gaps. Panel (d): Histograms for the other two gap parameters for neutrons and protons for the analysis excluding Vela. Panel (e): Histograms for the central proton fraction of 1.4, 1.7, or 2.0 ${\mathrm{M}}_{\odot }$ neutron stars. Panel (f): Posterior mass distributions for the seven QLMXB neutron stars or the 14 isolated cooling neutron stars (or 15 stars when Vela is included).

Figure 2

The 95% credible intervals for the luminosity-age curves for different neutron star masses and different amounts of light elements in the neutron star envelope (parameterized by $\eta$), along with the luminosity and age values obtained from observations which were used in this work. Vela (labeled “0833”) is not included in the model results but the data point is included in the figure for comparison.

Figure 3

The 95% credible intervals for the luminosity-age curves for different neutron star masses and different amounts of light elements in the neutron star envelope (parameterized by $\eta$), along with the luminosity and age values obtained from observations which were used in this work. Vela (labeled “0833”) is included in the model results.