We present the first constraint on the Faraday rotation measure (RM) at submillimeter wavelengths for the nucleus of M87. By fitting the polarization position angles (χ) observed with the Submillimeter Array at four independent frequencies around 230 GHz and interpreting the change in χ as a result of external Faraday rotation associated with accretion flow, we determine the RM of the M87 core to be between -7.5 × 105 and 3.4 × 105 rad m-2. Assuming a density profile of the accretion flow that follows a power-law distribution and a magnetic field that is ordered, radial, and has equipartition strength, the limit on the RM constrains the mass accretion rate to be below 9.2 10-4 M ⊙ yr-1 at a distance of 21 Schwarzschild radii from the central black hole. This value is at least two orders of magnitude smaller than the Bondi accretion rate, suggesting significant suppression of the accretion rate in the inner region of the accretion flow. Consequently, our result disfavors the classical advection-dominated accretion flow and prefers the adiabatic inflow-outflow solution or convection-dominated accretion flow for the hot accretion flow in M87.
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