Superfluid quantum criticality and the thermal evolution of neutron stars

Abstract

The neutron star starts to cool down shortly after its birth by emitting neutrinos. As it becomes cold enough, the Cooper pairs of neutrons are formed, triggering a superfluid transition. Previous studies on neutron superfluidity focused on finite-temperature transitions, with little attention paid to the potentially important quantum critical phenomena associated with superfluidity. Here, we provide the first theoretical analysis of superfluid quantum criticality, concentrating on its impact on neutron star cooling. Extensive calculations found that superfluidity occurs within a finite range of neutron star density $\rho$. The density serves as a nonthermal parameter for a superfluid quantum phase transition. In a broad quantum critical region, gapless neutrons are strongly coupled to the quantum critical fluctuations of the superfluid order parameter. We handle this coupling using both perturbation theory and renormalization group methods and find that it leads to non-Fermi liquid behavior, which yields a logarithmic $T\ln(1/T)$ correction to the neutron specific heat $c_{\mathrm{n}}\propto T$ and also dramatically alters the neutrino emissivity. Quantum critical phenomena emerge much earlier than the onset of superfluidity and persist throughout almost the entire lifetime of a neutron star. At low temperatures, these phenomena coexist with superfluidity in the neutron star interior but occupy different layers. We incorporate superfluid quantum criticality into the theoretical description of neutron star cooling and show that it substantially prolongs the thermal relaxation time. By varying the strength of superfluid fluctuations and other quantities, we obtain an excellent fit to the observed cooling data of a number of neutron stars. Our results indicate an intriguing correlation between superfluid quantum criticality and the thermal evolution of neutron stars.