From low- to high-frequency QPOs around the non-rotating hairy Horndeski black hole: Microquasar GRS 1915+105

Research on the Horndeski black hole, associated with the scalar hairy parameter, offers insights into enigmatic cosmic phenomena such as dark matter. Additionally, the numerical study of the GRS 1915+105 source, which exhibits continuous variability in X-ray observations, along with its physical properties and mechanisms behind Quasi-periodic oscillations (QPOs) frequencies, can contribute to observational studies. Motivated by this, we examine the variations in physical mechanisms around the non-rotating Horndeski black hole with Bondi-Hoyle-Lyttleton (BHL) accretion related to the scalar hair parameter and the resulting QPO frequencies. Numerical simulations have shown the formation of a shock cone around the black hole. With a decrease in the scalar hair parameter, the shock cone opening angle narrows due to the influence of the scalar field potential, and the stagnation point within the cone moves closer to the black hole horizon. With the changing scalar hair parameter, the simultaneous formation of the shock cone and bow shock is observed. Due to the intense increase in scalar potential, both the shock cone and bow shock disappeared, and a cavity surrounding the black hole forms in the area where the shock cone was. Additionally, QPO oscillations induced by the physical mechanisms observed in relation to the hair parameter are revealed through numerical simulations. A broad range of QPO frequencies is observed, from low to high frequencies, with resonance states like 3:2 occurring. The QPO frequencies determined numerically are compared with the observational results of the GRS 1915+105 source, demonstrating a match between the observations and numerical findings. From this, it is concluded that the shock cone, bow shock, and cavity are suitable physical mechanisms for generating QPOs for the GRS 1915+105 source. Lastly, we define the potential range of the spin parameter for the GRS 1915+105 source based on the agreement between observational and numerical results. It has also been found that for most of the QPOs obtained from numerical calculations to be consistent with observations, $h/M$ should be greater than −0.5.