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In this paper, we investigate the shadows and rings of the charged Horndeskiblack hole illuminated by accretion flow that is both geometrically andoptically thin. We consider two types of accretion models: spherical andthin-disk accretion flow. We find that in both types of models, the size of thecharged Horndeski black hole shadow decreases with the increase of the charge,and it decreases more slowly for the Reissner-Nordstr\"om (RN) black hole. Inthe spherical accretion flow model, we find that the increase of the charge ofHorndeski black hole brightens the light ring around it, and it brightens moresignificantly in comparison with RN black hole. Due to the Doppler effect, thecharged Horndeski black holes with accretion flow of radial motion have darkershadows than those with the static accretion flow, but the size of the shadowis not affected by accretion flow motion. In the thin disk-shaped accretionflow model, we find that the brightness of the light ring around the chargedHorndeski black hole is dominated by the direct emission from the accretionflow, and the contribution from lensed rings is relatively small, and that fromthe photon rings is negligible. We also find that the ring brightness decreasesas the charge of Horndeski black hole increases, and the decrease is moresignificant than that in the RN black hole case. Moreover, the radiationposition of the accretion flow can affect the shadow size and the ringbrightness of the charged Horndeski black hole.

Investigating shadow images and rings of the charged Horndeski black hole illuminated by various thin accretions