1p and $1.61\, {\mbox{$M_\odot$}}$ for 2p. Unfortunately, neither EOS nor $T_{\rm c}(\rho)$ are known and the “weighing” procedure is ambiguous. Nevertheless, as a rule, the ambiguity does not destroy the mass ordering of cooling stars. For instance, the Vela pulsar is expected to be more massive than RX J0822–4300. Moreover, one can invert the scheme and state that had the mass of one or several cooling neutron stars been measured, one could constrain the EOS and $T_{\rm c}(\rho)$.

One can construct many other models of cooling neutron stars consistent with the data. One can take other EOSs in the core \[with other direct Urca thresholds $\rho_{\rm D}$ and functions $T_{\rm c}(\rho)$\]. For instance, one can assume the presence of strong neutron superfluidity and normal protons (because cooling curves are nearly symmetric [@gusakovetal04a] with respect to exchanging neutron and proton $T_{\rm c}(\rho)$ profiles).

The direct Urca threshold can also be broadened by nuclear effects (e.g., of pion polarization; see [@schaabetal96] and references therein) or by superstrong magnetic fields $\ga 3 \times 10^{15}$ G [@by99] in a nonsuperfluid neutron star core.

Levels of slow and fast neutrino emission
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![(a) Schematic density dependence of the neutrino emissivity in a neutron star core 