Parameter constraints on Horndeski rotating black hole through quasiperiodic oscillations

Abstract: In this paper, we perform small perturbations around the circular timelike orbit in the equatorial plane of the Horndeski rotating black hole, and analyze the effects of Horndeski hair on the three fundamental frequencies of the epicyclic oscillations. Since this operation can model the quasiperiodic oscillations (QPOs) phenomena of the surrounding accretion disc, we then employ the MCMC simulation to fit the theoretical results with three QPO events, including GRO J1655-40, XTE J1859+226 and H1743-322, and constrain the characteristic radius $r$, black hole mass $M$ and spinning parameter $a$, and the Horndeski hair parameter $h$. Our constraint on the Horndeski hair parameter is much tighter than QPOs simulation from the existed accretion models, suggesting slight deviation from classical Kerr black hole.