We present the first constraint on Faraday rotation measure ( RM ) at submillimeter wavelengths for the nucleus of M 87 .
By fitting the polarization position angles ( \chi ) observed with the SMA at four independent frequencies around \sim 230 GHz and interpreting the change in \chi as a result of external Faraday rotation associated with accretion flow , we determine the rotation measure of the M 87 core to be between - 7.5 \times 10 ^ { 5 } and 3.4 \times 10 ^ { 5 } 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 rotation measure constrains the mass accretion rate \dot { M } to be below 9.2 \times 10 ^ { -4 } M _ { \odot } yr ^ { -1 } at a distance of 21 Schwarzchild 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 ( ADAF ) and prefers the adiabatic inflow-outflow solution ( ADIOS ) or convection-dominated accretion flow ( CDAF ) for the hot accretion flow in M 87 .