Polarized equatorial emission and hot spots around black holes with a dark matter halo

Abstract: We study the linear polarization of the accretion disk around black holes with a dark matter halo. The interaction of the black hole with the dark matter is modelled by considering an exact solution to the Einstein equations which describes a superposition of the Schwarzschild black hole with a Hernquist-type matter distribution. We simulate the observable polarization of a magnetized fluid ring orbiting around the black hole and evaluate the influence of the dark matter halo on its properties for physical parameters compatible with the dark matter distribution in galaxies. The polarization intensity and direction of the direct images deviate with less than $1\%$ from the isolated Schwarzschild black hole for a range of magnetic field configurations. For the indirect images the deviation increases with an order of magnitude but still remains under $10\%$ for small inclination angles corresponding to the galactic targets M87* and Sgr A*. This makes the detection of the dark matter impact on the polarized emission from the accretion disk extremely challenging in the near future.