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

We consider the magnetic and spin evolution of isolated neutron starsassuming that the magnetic field is initially confined to the crust. Theevolution of the crustal field is determined by the conductive properties ofthe crust which, in its turn, depend on the thermal history of the neutronstar. Due to this fact, a study of the magnetic field decay may be a powerfuldiagnostic of the properties of matter in the core where the density is abovethe nuclear density. We treat the evolution of neutron stars for differentpossible equations of state and cooling scenarios (standard and, so called,accelerated cooling). The spin evolution is strongly influenced by the behaviour of the magneticfield. Assuming that the spin-down rate of the neutron star is determined bythe magnetodipole radiation, we calculated the evolutionary tracks of isolatedpulsars in the $B - \tau$ and $B-P$ planes, where $B$ and $P$ are the magneticfield and period, respectively, and $\tau$ is the spin-down age. The calculatedtracks are compared with observational data on the magnetic field and period ofpulsars. This comparison allows to infer the most suitable equations of stateof nuclear matter and cooling model and to determine the range of parameters ofthe original magnetic configurations of pulsars.Comment: 13 pages + 5 figures, uses epsf.st