Observational features of the rotating Bardeen black hole surrounded by perfect fluid dark matter

By employing ray-tracing techniques, we investigate the shadow images of rotating Bardeen black holes surrounded by perfect fluid dark matter. In this work, two models are considered for the background light source, namely the celestial light source model and the thin accretion disk model. Regarding the celestial light source, the investigation focuses on the impact of variations in relevant parameters and observed inclination on the contour and size of the shadow. For the thin accretion disk model, the optical appearance of a black hole is evidently contingent upon the radiative properties exhibited by the accretion disk, as well as factors such as observed inclination and relevant parameters governing spacetime. With an increasing observation inclination, the observed flux of direct and lensed images of the accretion disk gradually converge towards the lower region of the image, while an increase in the dark matter parameter $a$ significantly expands the region encompassing both direct and lensed images. Furthermore, the predominant effect is redshift at lower observation angles, whereas the blueshift effect only becomes apparent at higher observation angles. Simultaneously, the increase in the observation inclination will amplify the redshift effect, whereas an increase in the magnetic charge $\mathcal{G}$, rotation parameter $a$ and the absolute value of dark matter parameter $\alpha$ will attenuate the redshift effect observed in the image. These observations of a rotating Bardeen black hole surrounded by perfect fluid dark matter could provide a convenient way to distinguish it from other black hole models.