We study thermal structure and evolution of magnetars as cooling neutron stars with a phenomenological heat source in a spherical internal layer. We focus upon effects of highly magnetized (>∼ 10¹⁴ G) envelopes composed of different chemical elements, from iron and ground-state nuclear matter to hydrogen or helium composition of the accreted material. We use updated strongly anisotropic thermal conductivity and the equation of state of matter in the neutron star outer crust as well as radiative opacities for partially ionized hydrogen in strong magnetic fields. We discuss the influence of magnetic field on the thermal structure of an isolated neutron star taking into account a combined effect of the thermal conductivity and neutrino emission in the outer crust. The cooling curves of magnetars with a dipole magnetic field are simulated for various locations of the heating layer, heating rates and magnetic field strengths. The joint effects of the super-strong magnetic fields and light-element composition noticeably improve the agreement between the model of outer-crust heating (at densities ρ <∼ 4 × 10¹¹ g cm^-3 and heat intensities W^∞ ∼ 10³⁶ - 10³⁷ erg s^-1) and current observational data on thermal luminosity of magnetars. These effects also marginally reconcile the model of an inner-crust heating with available estimates of the energy budget of neutron stars.

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