Extra Neutrino Emissivity of Neutron Stars under the Combined Condensation of Neutral and Charged Pions

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Abstract
Extra neutrino emissivity of neutron stars under the combined condensation of neutral and charged pions (CPC), which we call quasi-particle URCA process, is examined in a realistic approach. Here the isobar Δ(1232) degrees of freedom, baryon-baryon short-range correlations and p-wave form factors are considered consistently in the π-baryon and weak interaction vertices. Each role of neutral and charged pion condensate played in this process is clarified and a peculiar role of neutral pion condensate is emphasized. Our results show that quasi-particle URCA process is still dominant over other standard processes, e.g., the modified URCA process, while the emissivity is about one order of magnitude less than the one for the pure charged pion condensed case within a realistic approach.

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