Imaging and polarization patterns of various thick disks around Kerr-MOG black holes

We investigate the imaging and polarization properties of Kerr-MOG black holes surrounded by geometrically thick accretion flows. The MOG parameter $\alpha$ introduces deviations from the Kerr metric, providing a means to test modified gravity in the strong field regime. Two representative accretion models are considered: the phenomenological radiatively inefficient accretion flow (RIAF) and the analytical ballistic approximation accretion flow (BAAF). Using general relativistic radiative transfer, we compute synchrotron emission and polarization maps under different spins, MOG parameters, inclinations, and observing frequencies. In both models, the photon ring and central dark region expand with increasing $\alpha$, whereas frame dragging produces pronounced brightness asymmetry. The BAAF model predicts a narrower bright ring and distinct polarization morphology near the event horizon. By introducing the net polarization angle $\chi_{\text{net}}$ and the second Fourier mode $\angle\beta_2$, we quantify inclination- and frame-dragging-induced polarization features. Our results reveal that both $\alpha$ and spin significantly influence the near-horizon polarization patterns, suggesting that high-resolution polarimetric imaging could serve as a promising probe of modified gravity in the strong field regime.