Polarization distribution in the image of a synchrotron emitting ring
  around regular black holes
  We have studied the polarized image of a synchrotron emitting ring around
regular Hayward black hole and Bardeen black hole, respectively. Each of them
carries a magnetic field itself in terms of gravity coupled to a nonlinear
electrodynamics. Our results show that the main features of the polarization
images of emitting rings are similar in these two regular black hole
spacetimes. With the increase of magnetic charge parameter, the polarization
intensity and electric vector position angle in the image plane increase in
both Hayward black hole and Bardeen black hole spacetimes. We also investigate
the differences of polarization intensity and electric vector position angle
between in the regular black hole spacetime and in the Schwarzschild case,
which indicates that the differences in the Hayward black hole spacetime are
smaller than those in the Bardeen black hole. We also find the effects of the
magnetic charge parameter on the Strokes $Q-U$ loops slightly larger in Bardeen
black hole spacetime. These information stored in the polarization image around
Hayward and Bardeen black holes could help us to understand regular black holes
and the gravity coupled a nonlinear electrodynamics.
