Discriminating Accretion States via Rotational Symmetry in Simulated Polarimetric Images of M87

Polarized images of black holes have the potential to convey information about magnetic field morphology on event horizon scales. We describe a modal decomposition of linear polarized images into basis functions with varying polarization around a ring. We apply this decomposition to analyze ray traced images of general relativistic magnetohydrodynamics simulations of the Messier 87* (M87*) accretion flow. We show that the dimensionless Fourier coefficient associated with rotational symmetry, $\beta_2$, is a strong discriminator between accretion states for models of M87* that are consistent with the total intensity images produced by the Event Horizon Telescope (EHT). For simulated images viewed at the resolution of the EHT, we find that $|\beta_2|$ is greater than $0.2$ only for models with dynamically important magnetic fields in the accretion flow. We also find that higher black hole spins produce increasingly radial polarization patterns.