The relationships between the effective surface temperature T eff and the internal temperature T b of nonmagnetized neutron stars with and without accreted envelopes are calculated for T eff > 5 × 10 4 K. We use updated equations of state and radiative opacities, and we improve considerably the electron conductive opacity. We examine various models of accreted layers (H, He, C, and O subshells produced by nuclear burning of accreted matter). The resulting T eff - T b relationship is remarkably insensitive to the details of the models and depends mainly on the accreted mass Δ M . For T eff > 10 5 K, the accreted matter is generally more heat transparent. Even a small accreted mass (Δ M ≳ 10 -13 M ☉ ) affects appreciably the cooling of a neutron star, leading to higher T eff at the neutrino cooling stage and to lower T eff at the subsequent photon stage. We illustrate this by simulating the standard cooling of neutron stars. The presence of accreted matter yields better agreement of our model cooling curves with the blackbody fits to the ROSAT spectral observations of cooling neutron stars, without invoking quark matter or superfluidity in the neutron star cores.
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Chabrier et al. (1997) studied this question.