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Research on the optical appearance of black holes, both in general relativityand modified gravity, has been in full swing since the Event Horizon TelescopeCollaboration announced photos of M87$^{*}$ and Sagittarius A$^{*}$.Nevertheless, limited attention has been given to the impact of tiltedaccretion disks on black hole images. This paper investigates the $230$ GHzimages of non-rotating hairy black holes illuminated by tilted, thin accretiondisks in Horndeski gravity with the aid of a ray tracing method. The resultsindicate that reducing the scalar hair parameter effectively diminishes imageluminosity and extends both the critical curve and the inner shadow. This trendfacilitates the differentiation between hairy black holes and Schwarzschildblack holes. Furthermore, we observe that the inclination of the tiltedaccretion disk can mimic the observation angle, consequently affecting imagebrightness and the morphology of the inner shadow. In specific parameterspaces, the disk inclination has the ability to shift the position of the lightspot in the images of hairy black holes. This finding may provide potentialtheoretical evidence for the formation of three flares at different positionsin the Sagittarius A$^{*}$ image. Additionally, by examining the images ofhairy black holes surrounded by two thin accretion disks, we report theobscuring effect of the accretion environment on the inner shadow of the blackhole.

Influences of tilted thin accretion disks on the optical appearance of hairy black holes in Horndeski gravity