Analytical models of neutron star envelopes

The thermal structure of neutron star envelopes is investigated using approximate analytical formulae. In the degenerate layers the thermal structure equation is solved exactly for electron-dominated heat transport. In the nondegenerate layers it is shown that if the opacity is a power-law function of density and temperature, then the T(rho) profiles lie along curves of constant thermal conductivity. The two solutions are matched at intermediate densities to give an approximate relation between the heat flux and the core temperature of the neutron star. The dependence on various uncertain factors is found explicitly, allowing a detailed understanding of the physical processes that control the heat flux. The possible significance of the results to cooling calculations that take into account strong magnetic fields is discussed.