Low-luminosity active galactic nuclei (LLAGNs) are believed to be powered by an accretion-jet model, consisting of an inner advection-dominated accretion flow (ADAF), an outer truncated standard thin disk, and a jet. But model degeneracy still exists in this framework. For example, the X-ray emission can originate from either the ADAF or jet. The aim of the present work is to check these models with the Faraday rotation measure (RM) observations recently detected for two LLAGNs, M87 and 3C 84, in the sub-mm band. For M87, we find that the RM predicted by the model in which the X-ray emission originates from the ADAF is larger than the observed upper limit of RM by over two orders of magnitude, while the model in which the X-ray emission originates from the jet predicts a RM lower than the observed upper limit. For 3C 84, the sub-mm emission is found to be dominated by the jet component, while the Faraday screen is attributed to the ADAFs. This scenario can naturally explain the observed {it external} origin of the RM and why RM is found to be stable during a two-year interval although the sub-mm emission increases at the same period.
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