Revealing the Accretion Flow in M87*: Insights from Faraday Rotation

The Faraday rotation measure (RM) is a commonly used tool to trace electron number density and magnetic fields in hot accretion flows, particularly in low-luminosity accreting supermassive black holes. We focus on the nuclear region of M87, which was observed at 230 GHz (1.3 mm) by the Event Horizon Telescope in 2019. It remains unclear whether this emission originates from the accretion flow, the jet base, or both. To probe the presence of an accretion flow, we explore the scenario where the linearly polarized emission from the counter-jet, visible at 43 GHz (7 mm), is Faraday-rotated by the accretion flow. We calculate theoretical predictions for counter-jet polarization using analytical and numerical models. In all cases, we find a Faraday-thick flow at 43 GHz (7 mm), with $\mathrm{RM} \sim 10^6$ rad m$^{-2}$, and a polarization angle that follows a linear relationship with wavelength squared, consistent with external Faraday rotation. The more realistic model, which includes turbulence and magnetic field fluctuations, predicts that the polarization pattern should be time-dependent, and that the counter-jet emission is depolarized due to Faraday depth fluctuations across the accretion flow. Despite the Faraday thick regime and strong depolarization, the linear relationship persists, enabling us to constrain the flow's physical properties. Comparing the counter-jet and forward-jet linear polarization states should enable detection of M87's accretion flow and provide lower limits on electron density, magnetic field strength, and mass accretion rate.