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

Abstract By employing ray-tracing techniques, we investigate the shadow images of rotating Bardeen black holes surrounded by perfect fluid dark matter. We consider two models for the background light source, namely the celestial light source and thin accretion disk model. For the celestial light source model, the main focus is on the impact of variations in the relevant parameters and observational inclination angle on the shape and size of the black hole shadow. The results indicate that an increase in the magnetic charge $$\mathcal {G}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> </mml:math> leads to a reduction in the shadow’s deformation, whereas an increase in the dark matter parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> produces the opposite effect. For the thin accretion disk model, the optical appearance of the black hole strongly depends on the radiative properties of the accretion disk, as well as the observational inclination angle and the spacetime parameters. As the observational inclination angle increases, the observed flux of both direct and lensed images shifts toward the lower region of the image. It is evident that an increase in $$\mathcal {G}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> </mml:math> results in a reduction of both the shadow area and the photon ring, and an increase in $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> exhibits a similar influence. In addition, we examined the redshift effect of the image, the results show that the redshift dominates at low inclination angles, while the blueshift effect emerges significantly at higher inclination angles. These results for the rotating Bardeen black hole surrounded by perfect fluid dark matter could serve as observational signatures to distinguish it from other black hole models.