Images of shadow and thin accretion disk around Bardeen black hole surrounded by perfect fluid dark matter

We investigate the shadow and optical appearance of Bardeen black hole (BH) immersed in perfect fluid dark matter (PFDM). Using EHT observations of M87* and Sgr A*, we constrain the DM parameter to a narrow range $b/M \sim \mathcal{O}(10^{-1}-10^{-2})$ for M87* and to $\mathcal{O}(10^{-2}-10^{-3})$ for Sgr A*. From these constraints we derive a rough prediction for the PFDM density near the shadow scale ($R_{\mathrm{sh}}\sim5M$): $\rho_{\mathrm{PFDM}} \sim 0.27$-$2.67\,\mathrm{g/cm^3}$ for Sgr A*, dropping to $\sim10^{-24}$-$10^{-25}\,\mathrm{g/cm^3}$ at 100 pc. Moreover, increasing $b$ substantially enlarges the photon sphere, impact parameter, shadow radius, and suppresses the observed disk brightness, while the magnetic charge $g$ produces only negligible corrections completely masked by PFDM on macroscopic scales. Subsequently, we investigate the primary/secondary images, flux, and redshift profiles for the PFDM-Bardeen BH using the Novikov-Thorne disk model, and compare these quantities with those of NFW, Dehnen-type and Moore DM BHs. The four BH types exhibit distinct densities at the shadow radius and at 100 pc, offering a potential distinguishing signature. Furthermore, for all DM BH models, blueshift appears in the primary image as inclination increases, while the secondary image remains redshift dominated even at high inclinations. Hence, if significant blueshifted emission were detected at low inclination, the predictions of these four DM models would be seriously challenged.