Shadows and accretion disk images of charged rotating black hole in modified gravity theory

In this paper, we study the shadow and images of the accretion disk of Kerr-Newman (KN) black hole (BH) in modified gravity (MOG) theory by using backward ray-tracing method. And, the influence of spin parameter ($a$), charge ($Q$), and MOG parameter ($\alpha$) on the observed features of BHs are carefully addressed. Interestingly, as $\alpha$ increases, the flat edge of the BH's shadow gradually becomes more rounded, the size of shadow enlarges, and the deviation rate ($\delta s$) correspondingly decreases. By tracing the photon around BH, we observe that the trajectory of photon exhibits distortion behavior, i.e., the formation of two "tails" near the Einstein ring, which elongate as $a$ increases. For the accretion disk, it shows that the inner shadow expands with $\alpha$, while decreases with $Q$. The increase of $\alpha$ exhibits an increasing effect on redshift. At the same parameter level, $\alpha$ has a more obvious effect on inner shadow and image of BH by comparing with that of $Q$. Our study implies that both $\alpha$ and $Q$ have relatively significant effects on the image of the KN-MOG BH with the thin disk accretion, but the influence of $\alpha$ is much greater. So, this indicates that $\alpha$ plays a dominant role in this spacetime.