  We consider configurations consisting of a gravitating nonlinear spinor field
$\psi$, with a nonlinearity of the type $\lambda\left(\bar\psi\psi\right)^2$,
minimally coupled to Maxwell and Proca fields through the coupling constants
$Q_M$ [U(1) electric charge] and $Q_P$, respectively. In order to ensure
spherical symmetry of the configurations, we use two spin-$1/2$ fields having
opposite spins. By means of numerical computations, we find families of
equilibrium configurations with a positive Arnowitt-Deser-Misner (ADM) mass
described by regular zero-node asymptotically flat solutions for static Maxwell
and Proca fields and for stationary spinor fields. For the case of the Maxwell
field, it is shown that, with increasing charge $Q_M$, the masses of the
objects increase and diverge as the charge tends to a critical value. For
negative values of the coupling constant $\lambda$, we demonstrate that, by
choosing physically reasonable values of this constant, it is possible to
obtain configurations with masses comparable to the Chandrasekhar mass and with
effective radii of the order of kilometers. It enables us to speak of an
astrophysical interpretation of such systems, regarding them as charged Dirac
stars. In turn, for the system with the Proca field, it is shown that the mass
of the configurations also grows with increasing both $|\lambda|$ and the
coupling constant $Q_P$. Although in this case the numerical calculations do
not allow us to make a definite conclusion about the possibility of obtaining
masses comparable to the Chandrasekhar mass for physically reasonable values of
$\lambda$, one may expect that such masses can be obtained for certain values
of free parameters of the system under consideration.
