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

Abstract

Research on the optical appearance of black holes, both in general relativity and modified gravity, has been in full swing since the Event Horizon Telescope Collaboration announced photos of M87$^{*}$ and Sagittarius A$^{*}$. Nevertheless, limited attention has been given to the impact of tilted accretion disks on black hole images. This paper investigates the $230$ GHz images of non-rotating hairy black holes illuminated by tilted, thin accretion disks in Horndeski gravity with the aid of a ray tracing method. The results indicate that reducing the scalar hair parameter effectively diminishes image luminosity and extends both the critical curve and the inner shadow. This trend facilitates the differentiation between hairy black holes and Schwarzschild black holes. Furthermore, we observe that the inclination of the tilted accretion disk can mimic the observation angle, consequently affecting image brightness and the morphology of the inner shadow. In specific parameter spaces, the disk inclination has the ability to shift the position of the light spot in the images of hairy black holes. This finding may provide potential theoretical evidence for the formation of three flares at different positions in the Sagittarius A$^{*}$ image. Additionally, by examining the images of hairy black holes surrounded by two thin accretion disks, we report the obscuring effect of the accretion environment on the inner shadow of the black hole.Comment: 26 pages, 14 figure