Abstract
A brief review is given of the current state of the problem of neutrino pair emission through neutral weak currents caused by the Cooper pairs breaking and formation (PBF) in superfluid baryon matter at thermal equilibrium. The cases of singlet-state pairing with isotropic superfluid gap and spin-triplet pairing with an anisotropic gap are analyzed with allowance for the anomalous weak interactions caused by superfluidity. It is shown that taking into account the anomalous weak interactions in both the vector and axial channels is very important for a correct description of neutrino energy losses through the PBF processes. The anomalous contributions lead to an almost complete suppression of the PBF neutrino emission in spin-singlet superfluids and strong reduction of the PBF neutrino losses in the spin-triplet superfluid neutron matter, which considerably slows down the cooling rate of neutron stars with superfluid cores.
Highlights
At the long cooling era, the evolution of a neutron star (NS) surface temperature crucially depends on the overall rate of neutrino emission out of the star
The superfluidity of nucleons in NSs strongly suppresses most mechanisms of neutrino emission operating in the nonsuperfluid nucleon matter but simultaneously strongly reduces the heat capacity and triggers the emission of neutrino pairs through neutral weak currents caused by the nucleon Cooper pair breaking and formation (PBF) processes in thermal equilibrium
This corresponds to the reduction factor of 0.76 with respect to the PBF emissivity previously obtained in [6], which led the authors to the conclusion that, within the minimal cooling paradigm, the closing of the vector channel of the PBF neutrino emission does not significantly affect the long-term cooling of NSs
Summary
At the long cooling era, the evolution of a neutron star (NS) surface temperature crucially depends on the overall rate of neutrino emission out of the star. The neutrino emissivity due to the PBF processes in the spin-singlet superfluid nucleon matter was first suggested and calculated by Flowers et al [3]. For more than three decades these ideas were a key ingredient in numerical simulations of NS evolution (e.g., [10,11,12]) After such a long period, it was unexpectedly found that the PBF emission of neutrino pairs is practically absent in a nonrelativistic spin-singlet superfluid liquid [13]. Later this result was confirmed in other calculations [14,15,16]. Since the complete calculations have been published repeatedly (e.g., [13, 27, 34]), I will briefly sketch the main steps of the derivation, referring the reader to the original papers for more detailed information
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