Constraints on Scalar--Tensor--Vector Gravity Theory Parameters Inferred from Quasiperiodic Oscillations

We study circular geodesics of neutral test particles in the static charged solution of Scalar--Tensor--Vector Gravity (STVG), and we use the twin kilohertz quasiperiodic oscillations (QPOs) of twelve accreting compact objects to bound its parameters. Starting from the effective potential we obtain closed forms for the specific energy, the specific angular momentum and the Keplerian angular velocity, and from these the radial and vertical epicyclic frequencies. The horizon, photon sphere, shadow radius and innermost stable circular orbit are given in closed form as well, and each one reduces to the RN and Schwarzschild value in the appropriate limit. Null geodesics are integrated numerically and show how the enhanced coupling widens the capture cross section while leaving the logarithmic divergence of the deflection angle at the photon sphere intact. Within the RP model we then run Metropolis--Hastings MCMC simulations on the QPO pairs of eight neutron stars and four microquasars, comparing the Schwarzschild spacetime, the RN spacetime, STVG with vanishing charge and the full STVG solution. The best fits are obtained mainly for the charged solutions in the neutron star sample, while all four models describe the black hole sample equally well. We show that the orbital dynamics depends on the mass M, the coupling α and the charge Q only through the two combinations =(1+α)M and squared=(1+α)(αM squared+Q squared), which accounts for the multimodal posteriors found in the neutron star sample and sets a model-independent limit on what QPO timing alone can measure. The astrophysical implications of these bounds, in particular for inferred masses above the Tolman--Oppenheimer--Volkoff limit, are discussed in detail.