Orbital models of high-frequency quasi-periodic oscillations observed in Galactic microquasars and their predictions

High sensitivity X-ray observations of compact objects provide a unique tool to investigate strong-field gravity and give direct access to measurements of black hole (BH) masses and spins. The most promising methods of measuring the BH parameters are either through fitting the X-ray spectral continuum or the relativistically broadened iron lines, or by studying relativistic time-scale X-ray variability, in particular, through the theory of twin-peak high-frequency quasi-periodic oscillations (HF QPOs). We study frequencies of axisymmetric and non-axisymmetric epicyclic modes of accretion disc oscillations and explore the influence of pressure forces present in the disc. We discuss implications following from our consideration for models of 3:2 HF QPOs observed in X-ray fluxes of accreting BHs. Our results have consequences for estimations of BH spin in the three Galactic microquasars, namely GRS 1915+105, GRO J1655-40, and XTE J1550-564. The specific behaviour of the predicted QPO frequencies implies highly testable predictions. These predictions can be explored using the large amount of high-time-resolution data, which is expected to become available with the next generation of X-ray instruments, such as the LAD (Large Area Detector), previously proposed for Large Observatory for X-ray Timing (LOFT), and presently considered for other future X-ray missions (The enhanced X-ray Timing and Polarimetry mission, eXTP).