Cooling of magnetars with internal layer heating

We model thermal evolution of magnetars with a phenomenological heat source in a spherical internal layer and compare the results with observations of persistent thermal radiation from magnetars. We show that the heat source should be located in the outer magnetar’s crust, at densities ρ 5 × 1011 g cm−3, and the heating rate should be ∼ 1020 erg cm−3 s−1. Heating deeper layers is extremely inefficient because the thermal energy is mainly radiated away by neutrinos and does not warm up the surface to the magnetar’s level. This deep heating requires too much energy; it is inconsistent with the energy budget of neutron stars.