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

Abstract We study linear polarization of the accretion disks around black holes with a dark matter halo. The interaction of the black hole with the dark matter is modeled by considering an exact solution to the Einstein equations which describe 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 less than $$1\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> from the isolated Schwarzschild black hole for a range of magnetic field configurations. For indirect images the deviation increases by an order of magnitude but still remains under $$10\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>10</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> for small inclination angles corresponding to the galactic targets M87* and SgrA*. This makes detection of the dark matter impact on the polarized emissions from accretion disks extremely challenging in the near future.