Circular-orbit dynamics and QPO constraints in static Einstein–scalar–Gauss–Bonnet black holes

Abstract Einstein–scalar–Gauss–Bonnet (EsGB) gravity provides a physically motivated framework for testing strong-field deviations from the Schwarzschild geometry through scalar hair. We study neutral-particle circular motion and high-frequency quasi-periodic oscillations (HF-QPOs) in static EsGB black holes described by a continued-fraction metric with a single dimensionless deformation parameter $$p$$ p on the Schwarzschild-connected quadratic-coupling branch. We determine the effective potential, circular-orbit energy and angular momentum, characteristic radii, and orbital and radial epicyclic frequencies, and apply the relativistic precession model to twin-peak QPO data from XTE J1550–564, GRO J1655–40, GRS 1915+105, and M82 X-1. A source-by-source Markov chain Monte Carlo (MCMC) analysis shows that the observed frequency pairs can be reproduced within their uncertainties and that the radial epicyclic frequency carries the main model-level sensitivity to $$p$$ p . However, a controlled prior-sensitivity analysis using uniform and truncated Gaussian priors finds that the marginal posterior of $$p$$ p closely follows the adopted prior for all four sources. This reflects the intrinsic underconstraint of fitting three correlated parameters $$(M,p,r)$$ ( M , p , r ) to two measured frequencies. The inferred intervals therefore represent model-dependent compatibility regions rather than an independent measurement or preferred value of the EsGB deformation. The static results provide a baseline for future rotating and multi-observable tests.