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Magnetic and spin evolution of isolated neutron stars with the crustal magnetic field

We consider the magnetic and spin evolution of isolated neutron stars assuming that the magnetic field is initially confined to the crust. The evolution of the crustal field is determined by the conductive properties of the crust which, in its turn, depend on the thermal history of the neutron star. Due to this fact, a study of the magnetic field decay may be a powerful diagnostic of the properties of matter in the core where the density is above the nuclear density. We treat the evolution of neutron stars for different possible equations of state and cooling scenarios (standard and, so called, accelerated cooling). The spin evolution is strongly influenced by the behaviour of the magnetic field. Assuming that the spin-down rate of the neutron star is determined by the magnetodipole radiation, we calculated the evolutionary tracks of isolated pulsars in the $B - τ$ and $B-P$ planes, where $B$ and $P$ are the magnetic field and period, respectively, and $τ$ is the spin-down age. The calculated tracks are compared with observational data on the magnetic field and period of pulsars. This comparison allows to infer the most suitable equations of state of nuclear matter and cooling model and to determine the range of parameters of the original magnetic configurations of pulsars.