Bondi-Hoyle-Lyttleton Accretion around the Rotating Hairy Horndeski Black Hole

We model the dynamical changes of the disk and shock cone resulting from the interaction of matter with the Horndeski black hole, at where the scalar field and spacetime has a strong interaction. The effects of the scalar hair, the black hole rotation parameter, and the impacts of the asymptotic speed have been examined, revealing the influence of these parameters on the shock cone and the trapped QPO modes within the cone. Numerical calculations have shown that the hair paramete significantly affects the formation of the disk and the shock cone. As the absolute value of the hair parameter increases, the matter in the region of the shock cone is observed to move away from the black hole horizon. The rate of matter expulsion increases as $h/M$ changes. As h/M increases in the negative direction and the asymptotic speed increases, the stagnation point is getting closer to the black hole horizon. When the value of the hair parameter changes, the rest-mass density of the matter inside the cone decreases, while the opposite is observed with the asymptotic speed. Additionally, the formed shock cone has excited QPO modes. The deformation of the cone due to the hair parameter has led to a change or complete disappearance of the QPOs. Meanwhile, at asymptotic speeds of V∞/c< 0.4, all fundamental frequency modes are formed, while at V∞/c=0.4, only the azimuthal mode is excited, and 1:2:3:4:... resonance conditions occur. No QPOs have formed at V∞/c = 0.6. The results obtained from numerical calculations have been compared with theoretical studies for the M87^*, and it has been observed that the possible values of h/M found in the numerical simulations are consistent with the theory. Additionally, the results have been compared with those for the GRS 1915+105 black hole, and the hair parameters corresponding to the observed frequencies have been determined.