Photon ring polarimetry with next-generation black hole imaging I. M87*

The near-horizon region of a black hole impacts linear (LP) and circular polarization (CP) through strong lensing of photons, adding large-scale symmetries and anti-symmetries to the polarized image. To probe the signature of lensing in polarimetry, we utilise a geometric model of concentric, Gaussian rings of equal radius to investigate the transition in the Fourier plane at which the photon ring signal begins to dominate over the direct image. We find analytic, closed-form expressions for the transition radii in total intensity, LP, and CP, wherein the resultant formulae are composed of ratios of tunable image parameters, with the overall "scale" set primarily by the thickness of the direct image. Using these formulae, we compute the transition radii for time-averaged images of M87* simulations at 230 GHz, studying both Magnetically Arrested Disc (MAD) and Standard and Normal Evolution (SANE) configurations for various spin and electron heating models. We compare geometric values to radii obtained directly from the simulations through a coherent averaging scheme. We find that nearly all MAD models have a photon ring-dominated CP signal on long baselines shorter than the Earth diameter at 230 GHz. Across favored models for the M87* accretion flow identified by EHT polarimetric constraints, we quantify the sensitivity and antenna size requirements for the next-generation EHT and the Black Hole Explorer orbiter to detect these features. We find that the stringent requirements for CP favour explorations using long baselines on the ground, while LP remains promising on Earth-space baselines.