Q_{\rm f}\, T_9^6,
\label{Qnu}$$ where $T_9=T/(10^9~{\rm K})$, while $Q_{\rm s}$ and $Q_{\rm f}$ are slowly varying functions of $\rho$ (Tables \[tab-nucore-slow\] and \[tab-nucore-fast\]). Thus, the neutrino luminosities of massive and low-mass stars (with and without inner core) can be very different. For instance, in a young massive star, where the direct Urca is open and the core temperature is $T=10^9$ K, $L_\nu$ is as huge as $\sim 10^{46}$ erg s$^{-1}$. In a low-mass star at the same $T$, $L_\nu$ would be $\sim 7$ orders of magnitude lower. In both cases $L_\nu$ rapidly decreases when the star cools. For instance, one has $L_\nu \sim 10^{34}$ erg s$^{-1}$ for a low-mass star at $t\sim10$ kyr.

#### Neutrino emission in superfluid cores

Nucleons, hyperons, and quarks in dense matter can be in superfluid state (e.g., [@ls01], also see [@yls99; @yp04] for references). This superfluidity occurs via Cooper pairing of particles owing to an attractive component of their interaction (with the appearance of a gap in the particle energy spectrum near the Fermi level). Systematic simulations of cooling superfluid neutron stars were triggered by a remarkable paper of Page and Applegate [@pa92]. Superfluidity of any particles is characterized by its own density dependent critical 