Internal temperatures and cooling of neutron stars with accreted envelopes

The relationships between the effective surface (Teff ) and internal temperatures of neutron stars (NSs) with and without accreted envelopes are calculated for Teff > 5 × 104 K using new data on the equation of state and opacities in the outer NS layers. We examine various models of accreted layers (H, He, C, O shells produced by nuclear transformations in accreted matter). We employ new Opacity Library (OPAL) radiative opacities for H, He, and Fe. In the outermost NS layers, we implement the modern OPAL equation of state for Fe, and the Saumon-Chabrier equation of state for H and He. The updated thermal conductivities of degenerate electrons include the Debye-Waller factor for the electron-phonon scattering in solidified matter, while in liquid matter they include the contributions from electron-ion collisions (evaluated with non-Born corrections and with the ion structure factors in responsive electron background) and from the electron-electron collisions. For Teff < 105.5 K, the electron conduction in non-degenerate layers of the envelope becomes important, reducing noticeably the temperature gradient. The accreted matter further decreases this gradient at Teff > 105 K. Even a small amount of accreted matter (withmass>∼ 10−16M ) affects appreciably the NS cooling, leading to higher Teff at the neutrino cooling stage and to lower Teff at the subsequent photon stage.