independent (except near the very surface). At the later neutrino-transparent stage the star cools via neutrino emission from its interior and via heat transport to the surface and subsequent photon thermal emission.

Neutron star cooling is described by general relativistic equations [@thorne77] of heat diffusion inside the star with neutrino energy sources and surface photon emission. The solution gives the distribution of the temperature $T$ inside the star versus time $t$, and the effective surface temperature $T_{\rm s}(t)$. To simplify computations, one divides [@gpe83] the neutron star into the interior region and the outermost heat-blanketing envelope \[extended to densities $\rho \le \rho_{\rm b} \sim (10^{10}-10^{11})$ g cm$^{-3}$\]. The thermal structure of the blanketing envelope is studied separately in the stationary, plane-parallel approximation, that relates $T_{\rm s}$ to the temperature $T_{\rm b}$ at $\rho=\rho_{\rm b}$. The diffusion equations are then solved in the interior ($\rho \geq \rho_{\rm b}$).

The thermal photon luminosity of the star is $ L_\gamma = 4 \pi \sigma R^2 T^4_{\rm s}(t)$, where $R$ is the circumferential stellar radius. Both, $L_\gamma$ and $T_{\rm s}$, refer to a locally-flat reference frame on the stellar surface. A distant observer detects the “apparent” luminosity $L_\gamma^\infty = L_\gamma (1 - r_{\rm g}/R)$ 