Polarization images of accretion flow around supermassive black holes: imprints of toroidal field structure

With unprecedented angular resolution, the Event Horizon Telescope (EHT) has opened a new era of black holes. We have previously calculated the expected polarization images of M87* with the EHT observations in mind. There, we demonstrated that circular polarization (CP) images, as well as the linear polarization (LP) maps, can convey quite useful information to us, such as the flow structure and magnetic field configuration around the black hole. In this paper, we make new predictions for the cases in which disk emission dominates over jet emission, bearing Sgr A* in mind. Here we set the proton-to-electron temperature ratio of the disk component to be Tp/Te $\sim$ 2 so as to suppress jet emission relative to emission from accretion flow. As a result, we obtain ring-like images and triple-forked images around the black hole for face-on and edge-on cases, respectively. We also find significant CP components in the images ($\gtrsim 10\%$ in fraction), both with positive and negative signs, amplified through the Faraday conversion, not sensitively depending on the inclination angles. Furthermore, we find a "separatrix" in the CP images, across which the sign of CP is reversed and on which the LP flux is brightest, that can be attributed to the helical magnetic field structure in the disk. These results indicate that future full polarization EHT images are a quite useful tracer of the magnetic field structure. We also discuss to what extent we will be able to extract information regarding the magnetic field configurations, under the scattering in the interstellar plasma, in future EHT polarimetric observations of Sgr A*.