Abstract
Compact gravitating configurations consisting of strongly magnetized spinor fluid are studied. The latter is described by an effective equation of state which is obtained in the limit of large values of the coupling constant of a nonlinear spinor field. Regular static asymptotically flat solutions describing configurations with finite sizes (Dirac stars) are found. Mass-radius relations for stars with masses of the order of the Chandrasekhar mass and radii comparable with sizes of neutron stars are constructed. The structure of a dipole magnetic field modeled in the form of an axisymmetric poloidal magnetic field created by toroidal electric currents is investigated. The energy density of the magnetic field is assumed to be much smaller than that of the spinor fluid. The radial and tangential components of the magnetic field strength are computed. It is shown that their distributions along the radius of the configurations are similar to those of neutron stars.