  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.
