  The feature of the observed shadows and rings of an astrophysical black hole
(BH) may depend on its accretion flows and magnetic charge. We find that the
shadow radii and critical impact parameters of the Hayward BH are decreased
with the increase of the magnetic charge. Comparing the Schwarzschild BH with
the Hayward BH using the ray-tracing method, we show that the density and
deflection of lights increase with the magnetic charge, and the BH singularity
does not affect the generation of the shadow. Based on three optically thin
accretion flow models, the two-dimensional shadows in celestial coordinates are
derived. It is found that the shadow and photon ring luminosities of a Hayward
BH surrounded by infalling spherical accretion flow are dimmer than that of a
static spherical accretion flow. Taking three kinds of inner radii at which the
accretion flow stops radiating, we find that the observed luminosity of a
Hayward BH surrounded by a thin disk accretion flow is dominated by the direct
emission, and the photon ring emission has a weak influence on it. These
results suggest that the size of the observed shadow is related to the
space-time geometry, and the luminosities of both the shadows and rings are
affected by the accretion flow property and the BH magnetic charge.
