Dynamics of test particles around a Bardeen black hole surrounded by perfect fluid dark matter

We study the dynamics of (i) neutral test particles, (ii) magnetically charged test particles, and (iii) test magnetic dipole around a regular Bardeen black hole surrounded by perfect fluid dark matter (PFDM). It has been shown how the magnetic charge of the black hole and the parameter of the surrounding PFDM can influence the innermost stable circular orbit (ISCO) radius of a test particle. We have found that the ISCO radius is strongly affected as a consequence of the combined effect of the magnetic charge parameter and the perfect fluid dark matter. The black hole magnetic charge parameter $g$ and the combined effect of perfect fluid dark matter can mimic the black hole rotation parameter up to $a/M\ensuremath{\approx}0.9$. It has been observed that the ISCO for magnetic dipole disappears at the values exceeding the calculated upper value for the magnetic interaction parameter $\ensuremath{\beta}$. The upper limit decreases with the increase of both the dark matter and magnetic charge parameters. Finally, as an astrophysical application, we have analyzed degeneracy effects of spin of Kerr black holes and magnetic charge of regular Bardeen black holes for the different values of the dark matter parameter providing exactly the same value for ISCO radius of a magnetic dipole with the same value of the parameter $\ensuremath{\beta}=10.2$ of the magnetar called PSR J1745-2900 orbiting around supermassive black hole Sagittarius A*. It has been observed that the magnetic charge of the pure regular Bardeen black hole can mimic the spin of a Kerr black hole up to $a/M\ensuremath{\simeq}0.8085$, while upper limit for the magnetic charge which may provide ISCO for the magnetic dipole is ${g}_{\text{upper}}\ensuremath{\simeq}0.65M$. In the presence of PFDM with the parameter $\ensuremath{\alpha}=0.01(0.05)$, the upper limit for the magnetic charge decreases and equals to ${g}_{\text{upper}}\ensuremath{\simeq}0.62M$ ($0.548M$) and consequently mimicker value for the spin parameter of black hole lies in the range of $a/M\ensuremath{\in}(0.0106\textdiv{}0.8231)$ ($a/M\ensuremath{\in}(0.0816\textdiv{}0.8595)$). We also show that the same values of the spin of Kerr black hole and the magnetic charge of regular Bardeen black hole surrounded by PFDM provide the same values for the ISCO radius of the chosen magnetar.