  Modeling of the shock cone formed around a static, hairy Horndeski black hole
with Bondi-Hoyle-Lyttleton (BHL) accretion has been conducted. We model the
dynamical changes of the shock cone resulting from the interaction of matter
with the Horndeski black hole. The effects of the scalar hair, the black hole
rotation parameter, and the impacts of the asymptotic speed have been examined.
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. After
h/M<-0.6, a visible change in the physical structure of the shock cone occurs.
On the other hand, it has been revealed that the asymptotic speed significantly
affects the formation of the shock cone. As h/M increases in the negative
direction and the asymptotic speed increases, the stagnation point moves 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, whereas 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_{\infty}/c< 0.4, all fundamental frequency modes are formed, while
at V_{\infty}/c=0.4, only the azimuthal mode is excited, and 1:2:3:4:...
resonance conditions occur. No QPOs have formed at V_{\infty}/c = 0.6. The
results obtained from numerical calculations have been compared with
theoretical studies for 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.
