Abstract
We study spherically symmetric strongly gravitating configurations supported by nonlinear spinor fields and non-Abelian SU(2) Yang-Mills/Proca magnetic fields. Regular asymptotically flat solutions describing objects with positive Arnowitt-Deser-Misner masses are obtained numerically. When the mass of the spinor fields is much smaller than the Planck mass, we find approximate solutions that can describe systems with total masses comparable to the Chandrasekhar mass and with effective radii of the order of kilometers. For the values of the system free parameters used here, we show that the SU(2) magnetic field always gives a small contribution to the total energy density and mass of the configurations under investigation. From the astrophysical point of view, one can regard such objects as magnetized Dirac stars.