Shadow and Polarized Images of Schwarzschild-MOG Black Hole Illuminated by Thick Accretion Disk

Recent EHT polarimetric observations provide a powerful probe of near-horizon physics and modified gravity. We investigate the shadow and polarization images of a static Schwarzschild-MOG black hole illuminated by geometrically thick, optically thin accretion flows. Adopting a phenomenological model and the Hou disk model, and solving null geodesics and relativistic radiative transfer, we study how the MOG parameter, inclination angle, anisotropic synchrotron emission, and flow geometry affect the total intensity and linear polarization. It is found that the MOG parameter mainly enlarges and brightens higher-order photon rings and broadens the shadow, while the inclination angle breaks axial symmetry and enhances polarized emission inside the shadow. The Hou disk model suppresses off-equatorial radiative interference and localizes polarization signals within higher-order rings. Electric vector position angle (EVPA) patterns are mostly azimuthal but vary rapidly near lensed images. These results provide theoretical diagnostics for constraining MOG with EHT/ngEHT polarimetric observations.