Polarimetric differences between Schwarzschild and Kerr black holes in active galactic nuclei

Abstract

If the linear polarization of the optical emission of active galactic nuclei (AGNs) arises in magnetized accretion disk (the Milne problem), the degree of polarization should depend strongly on the spin of the central black hole. For the same black hole luminosities and masses, the polarization is substantially higher for rotating Kerr than for non-rotating Schwarzschild black holes. Statistically, this means that the majority of AGNs displaying appreciable linear polarization should have Kerr black holes. The spin dependence of the polarization is due to the fact that the radius of the innermost stable circular orbit risco depends on the spin—this radius is three gravitational radii for a Schwarzschild black hole, and a factor of six smaller for a rapidly rotating black hole. This means that the magnetic field in the region of emergence of the optical emission, which decreases with distance from risco, is higher for a non-rotating than for a rapidly rotating black hole. This higher magnetic field gives rise to strong Faraday depolarization, explaining the effect considered here.