enhancement is provided by direct Urca process [@lpph91; @pplp92] in nucleon (or nucleon-hyperon) matter. It is a sequence of two reactions (a beta decay and beta capture) forbidden in the outer core by momentum conservation. It is allowed in the inner core for the matter with rather high ($\ga$11–13%) proton fraction (for EOSs with large symmetry energy of nuclear matter). If it is forbidden but the matter contains pion condensate, neutrino emission is enhanced (although weaker) by direct-Urca-type reactions involving quasinucleons $\widetilde{\rm N}$ (superpositions of n and p) in pion-condensed matter. If pion condensate is absent, but kaon condensate available, neutrino emission is enhanced (even more weaker) by direct-Urca-like process involving baryonic quasiparticles $\widetilde{\rm B}$ in kaon condensed matter. Nearly the same enhancement is expected due to the direct Urca process involving d and u quarks in quark matter. The processes in the inner core (Table \[tab-nucore-fast\]) can amplify the neutrino emission by 2–7 orders of magnitude and lead to fast cooling. It is also possible that the neutrino emission in the inner core is not enhanced.

The emissivity $Q_\nu(\rho,T)$ of slow and fast neutrino processes in nonsuperfluid matter can be written as $$Q_{\rm slow}= Q_{\rm s}\, T_9^8,\qquad
   Q_{\rm fast}= 