Neutrino Emission from Cooper Pairs and Minimal Cooling of Neutron Stars

The minimal cooling paradigm for neutron star cooling assumes that enhanced cooling due to neutrino emission from any direct Urca process, due either to nucleons or to exotica such as hyperons, Bose condensates, or deconfined quarks, does not occur. This scenario was developed to replace and extend the so-called standard cooling scenario to include neutrino emission from the Cooper pair breaking and formation processes that occur near the critical temperature for superfluid/superconductor pairing. Superfluidity is generally expected to exist in the neutron star interior, and Cooper-pair neutrino emission processes, which operate through both vector and axial channels, can dominate cooling in the minimal model. Neutron stars that have observed temperatures that are too low for their age than in the minimal cooling model for any combination of its parameters will imply that enhanced cooling is occurring. Previous studies showed that the observed temperatures of young, cooling, isolated neutron stars with ages between 10 and 10 years, with the possible exception of the pulsar in the supernova remnant CTA 1, are consistent with predictions of the minimal cooling paradigm as long as the neutron P2 pairing gap present in the stellar core is of moderate size. Recently, it has been found that Cooper-pair neutrino emission from the vector channel is suppressed by a large factor, of order 10, compared to the original estimates that violated vector current conservation. We show that Cooper-pair neutrino emission remains, nevertheless, an efficient cooling mechanism through the axial channel. As a result, the elimination of neutrino emission from Cooperpaired nucleons through the vector channel has only minor effects on the long-term cooling of neutron stars within the minimal cooling paradigm. We further quantify precisely the effect of the size of the neutron P2 gap and demonstrate that consistency between observations and the minimal cooling paradigm requires that the critical temperature Tc for this gap covers a range of values between T c < ∼ 0.2× 10 K up to T c > ∼ 0.5× 10 K in the core of the star. This range of values guarantees that the Cooper-pair neutrino emission is operating efficiently in stars with ages between 10 to 10 years, leading to the coldest predicted temperatures for young neutron stars. In addition, it is required that young neutron stars have heterogenous envelope compositions: some must have lightelement compositions and others must have heavy-element compositions. Unless these two conditions are fulfilled, about half of the observed young cooling neutron stars are inconsistent with the minimal cooling paradigm and provide evidence for the existence of enhanced cooling. Subject headings: Dense matter — equation of state — neutrinos — stars: neutron