  In April 2017, the Event Horizon Telescope observed the shadow of the
supermassive black hole at the core of the elliptical galaxy Messier 87. While
the original image was constructed from measurements of the total intensity,
full polarimetric data were also collected, and linear polarimetric images are
expected in the near future. We propose a modal image decomposition of the
linear polarization field into basis functions with varying azimuthal
dependence of the electric vector position angle. We apply this decomposition
to images of ray traced general relativistic magnetohydrodynamics simulations
of the Messier 87 accretion disk. For simulated images that are physically
consistent with previous observations, the magnitude of the coefficient
associated with rotational symmetry, $\beta_2$, is a useful discriminator
between accretion states. We find that at 20 $\mu$as resolution, $|\beta_2|$ is
greater than 0.2 only for models of disks with horizon-scale magnetic pressures
large enough to disrupt steady accretion. We also find that images with a more
radially directed electric vector position angle correspond to models with
higher black hole spin. Our analysis demonstrates the utility of the proposed
decomposition as a diagnostic framework to improve constraints on theoretical
models.
