Polarization Signatures of Rotating Black Holes in Perfect Fluid Dark Matter Spacetimes

Abstract

Motivated by horizon-scale polarization observations of M87^{*}, we investigate polarized emission from rotating black holes (BHs) immersed in a perfect fluid dark matter (PFDM) background. Fully relativistic ray tracing is utilized to examine how the polarization structure jointly depends on magnetic-field geometry, higher-order imaging, and the PFDM intensity parameter k. We show that, for a given k value, magnetic configurations with a polar component naturally produce a continuous spiral pattern in the electric vector position angle (EVPA), while the large-scale EVPA morphology remains primarily controlled by the magnetic-field topology. Variations in k affect light propagation and polarization transport near the horizon, leading to corresponding changes in EVPA deflection and polarized intensity around the photon ring. A decomposition of the total polarized image further reveals that higher-order images provide localized yet non-negligible corrections near the ring. Compared with the polarization characteristics of M87^{*} inferred by the EHT, image-domain quantities such as |m|_{\rm net} and \argβ_2 indicate that PFDM induces systematic shifts relative to the pure Kerr BH case, lowering the net linear polarization fraction and modifying the large-scale polarization phase. Overall, PFDM acts as an additional strong-gravity ingredient that systematically reorganizes the horizon-scale polarization structure, suggesting that surrounding dark matter can leave observable imprints on black hole polarization signatures.