2009ApJ...707.1131P

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. Previous studies showed that the observed temperatures of young, cooling, isolated neutron stars with ages between 10² and 10⁵ yr, 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 ³ 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 the order of 10^–3, 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 Cooper-paired 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 ³ P₂ gap and demonstrate that consistency between observations and the minimal cooling paradigm requires that the critical temperature T_c for this gap covers a range of values between T ^min_ c_≲ 0.2x10⁹ up to T ^max_c≳ 0.5x10⁹ 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 10³ to 10⁵ yr, leading to the coldest predicted temperatures for young neutron stars. In addition, it is required that young neutron stars have heterogeneous envelope compositions: some must have light-element 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.