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

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 $λ$ reduces both the size and brightness of the higher-order image, while increasing $θ$ 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 $λ$ than the RIAF model. While increasing $θ$ 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 $λ$ and $θ$, 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.

💡 Research Summary

This paper presents a comprehensive study of the shadow and polarization images of four‑dimensional Gauss‑Bonnet (GB) black holes surrounded by geometrically thick, optically thin accretion flows. Using a fully relativistic ray‑tracing code, the authors compute photon trajectories and radiative transfer for two representative disk models: a phenomenological radiatively inefficient accretion flow (RIAF‑like) model and the analytical Hou disk model based on the ballistic approximation accretion flow (BAAF). The GB coupling constant λ and the observer inclination angle θ are varied systematically to assess their impact on image morphology, brightness, and polarization structure.

Key theoretical ingredients include the static spherically symmetric GB metric obtained by rescaling the GB coupling and taking the D→4 limit, yielding the lapse function (F(r)=1+\frac{r^{2}}{2\lambda}\bigl