Images from disk and spherical accretions of Bardeen black hole surrounded by perfect fluid dark matter

Abstract: In this paper, we investigate the shadow and optical appearance of the Bardeen black hole surrounded by perfect fluid dark matter (PFDM) illuminated by various static accretions. First, we find that as the dark matter parameter $\left|α\right|$ increases, the fundamental characteristic quantities of the black hole, the event horizon $r_h$, the photon sphere radius $r_{ph}$, and the critical impact parameter $b_{ph}$ all increase, while the peak of the effective potential $V_{\text{eff}}$ decreases and shifts toward the direction of increasing $r$. In contrast, the magnetic charge parameter $g$ suppresses $r_h$, $r_{ph}$, and $b_{ph}$, while increases the peak of $V_{\text{eff}}$ and shifts it toward the direction of decreasing $r$. This indicates a competing effect between the dark matter parameter $\left|α\right|$ and the magnetic charge parameter $g$ on the fundamental properties of the black hole. Furthermore, we use the EHT observational data to constrain the dark matter parameters $α$ and find that the constraint range given by the supermassive black hole SgrA* is stricter than that of the black hole M87*. Finally, the black hole images are studied based on different accretion models, and it is found that both dark matter parameters $α$ and accretion models significantly influence the black hole images. For larger dark matter parameters $\left|α\right|$, the inner shadow or central faint illuminating region of the Bardeen black hole surrounded by PFDM is larger but the bright ring of the image is fainter. This provides a potential method for us to distinguish between classical Bardeen black holes and Bardeen black holes surrounded by PFDM. These preliminary results may provide some clues for future investigations of dark matter using black hole shadows and images.