Shadows and Polarization Images of a Four-dimensional Gauss-Bonnet Black Hole Irradiated by a Thick Accretion Disk

Abstract

We adopt a general relativistic ray-tracing approach to study the shadows and polarization images of spherically symmetric Gauss-Bonnet (GB) black holes enveloped by geometrically thick accretion flows. Specifically, we adopt a phenomenological RIAF-like model and an analytical Hou disk model. In the RIAF-like model, increasing the GB coupling parameter $\lambda$ reduces both the size and brightness of the higher-order image, while increasing $\theta$ alters the shape of the higher-order image and obscures the horizon's outline. The main difference between isotropic and anisotropic emission is that the latter produce distortion of the high-order image in the vertical direction, leading to an elliptical morphology. For the Hou disk model, due to specific regions being geometrically thinner with the conical approximation, the high-order images are narrower with the increase in $\lambda$ than the RIAF model. While increasing $\theta$ enhances the brightness of the direct images outside the higher-order images, but hardly changes the size of the higher-order images, which is in sharp contrast to the RIAF model. Meanwhile, the Hou disk produces polarization patterns that trace the brightness configuration and are affected by $\lambda$ and $\theta$, reflecting the intrinsic structure of spacetime. These results illustrate that intensity and polarization in thick-disk models provide probes of GB black holes and near-horizon accretion dynamics.