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Astron. Astrophys. 343, 650-660 (1999)

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5. Conclusions

We have reconsidered the neutrino emission rate due to Cooper pairing of nucleons in the neutron star cores (Sect. 2). We have presented the results in the form convenient for practical implications in three cases: (A) singlet-state 1S0 pairing, (B) triplet-state 3P2 pairing with zero projection of the Cooper pair momentum ([FORMULA]) onto quantization axis, and (C) triplet-state pairing with maximum ([FORMULA]) momentum projection. For the singlet-state pairing of neutrons, our results agree with those by Flowers et al. (1976). For the triplet-state pairing our consideration is original. Notice an essential difference of the Cooper-pair neutrino emissivities for singlet and triplet-state superfluids and also for neutrons and protons. In Sect. 3 we have analysed the efficiency of the Cooper-pair neutrino emission at different densities in the neutron star cores as compared with the traditional neutrino production mechanisms including a powerful direct Urca process allowed at high densities. Contrary to the non-superfluid cores where the main neutrino emission is produced either by the modified or by the direct Urca processes (depending on equation of state and density), very different neutrino mechanisms can dominate in the superfluid cores at certain temperatures T and superfluid critical temperatures [FORMULA] and [FORMULA]. In particular, neutrinos produced by pairing of neutrons can be very important if [FORMULA]. The importance of these neutrinos in the standard and rapid cooling of the neutron stars has been analysed in Sect. 4. We show that, under certain conditions, neutrinos provided by pairing of neutrons can greatly accelerate both standard and enhanced cooling of middle-age neutron stars (t= [FORMULA]-[FORMULA] yr). In particular, the accelerated standard cooling can mimic rapid cooling of the stars. The Cooper-pair neutrinos modify the cooling curves and enable us to explain observations of thermal radiation of several neutron stars by one cooling curve at once. This confirms the potential ability (Page & Applegate, 1992) to constrain the fundamental parameters of superdense matter in the neutron star cores, the critical temperatures of neutron and proton superfluids, by comparing theory and observation of neutron stars.

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© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999