Magnetars as cooling neutron stars with internal heating
  We study thermal structure and evolution of magnetars as cooling neutron stars with a phenomenological heat source in a spherical internal layer. We explore the location of this layer as well as the heating rate that could explain high observable thermal luminosities of magnetars and would be consistent with the energy budget of neutron stars. We conclude that the heat source should be located in an outer magnetar's crust, at densities rho < 5e11 g/cm^3, and should have the heat intensity of the order of 1e20 erg/s/cm^3. Otherwise the heat energy is mainly emitted by neutrinos and cannot warm up the surface. 
A.D. Kaminker (1), D.G. Yakovlev (1), A.Y. Potekhin (1), N. Shibazaki   (2), P.S. Shternin (1), O.Y. Gnedin (3) ((1) Ioffe I...