at $T=10^9$ K assuming very slow neutrino emission in the outer core and three scenarios of fast emission in the inner core. (b), (c), and (d): Ranges of $T_{\rm s}^\infty$ (hatched) for the three types of fast emission compared with observations (see text for details). []{data-label="exotica"}](yakfig4.ps){width="\textwidth"}

After several examples we can turn to a general analysis.

One can show that it is sufficient to lower the neutrino luminosity due to the modified Urca process in a low-mass star by a factor of $\sim 30-100$ to explain observations of stars hottest for their age. This low neutrino luminosity can be produced by nucleon-nucleon bremsstrahlung. The modified Urca process can be reduced by nucleon superfluidity, as in the above examples (Figs. \[cool4\]c and d).

The level of fast neutrino emission in high-mass stars is less certain. To analyze it, let us consider (Fig. \[exotica\]) three typical levels appropriate to the direct Urca process in nucleon/hyperon matter; to pion-condensed matter; and kaon-condensed matter. A schematic picture of the neutrino emissivity profiles through the stellar core for these scenarios is presented in Fig. \[exotica\]a.

Fig. \[exotica\]b shows the ranges of $T_{\rm s}^\infty$ (hatched regions) which can be explained by the theory assuming the scenario 