  For testing different electron temperature ($T_{\rm e}$) prescriptions in
general relativistic magnetohydrodynamics (GRMHD) simulations through
observations, we propose to utilize linear polarization (LP) and circular
polarization (CP) images. We calculate the polarization images based on a
semi-Magnetically Arrested Disk (MAD) GRMHD model for various $T_{\rm e}$
parameters, bearing M87 in mind. We find an LP-CP separation in the images of
the low-$T_{\rm e}$ disk cases at 230 GHz; namely, the LP flux mainly
originates from downstream of the jet and the CP flux comes from the
counter-side jet, while the total intensity is maximum at the jet base. This
can be understood as follows: although the LP flux is generated through
synchrotron emission widely around the black hole, most of the LP flux from the
jet base does not reach the observer, since it undergoes Faraday rotation
($\propto T_{\rm e}^{-2}$) when passing through the outer cold disk and is thus
depolarized. Hence, only the LP flux from the downstream (not passing the cold
dense plasmas) can survive. Meanwhile, the CP flux is generated from the LP
flux by Faraday conversion ($\propto T_{\rm e}$) in the inner hot region.
Stronger CP flux is thus observed from the counter-side jet. Moreover, the
LP-CP separation is more enhanced at a lower frequency such as 86 GHz but is
rather weak at 43 GHz, since the media in the latter case is optically thick
for synchrotron self-absorption so that all the fluxes should come from the
photosphere. The same is true for cases with higher mass accretion rates and/or
larger inclination angles.
