Power density spectra of modes of orbital motion in strongly curved space–time: obtaining the observable signal

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High frequency quasi-periodic oscillations (HF QPOs) appear in the X-ray variability of several accreting low-mass binaries. In a series of works it was suggested that these QPOs may have connection to inhomogeneities orbiting close to an inner edge of the accretion disc. In this paper we explore the appearance of an observable signal generated by small radiating circular hot spots moving along quasi-elliptic trajectories close to the innermost stable circular orbit in the Schwarzschild spacetime. Our consideration takes into account the capabilities of observatories that have been operating in the past two decades represented by the Rossi X-ray Timing Explorer (RXTE) and the proposed future instruments represented by the Large Observatory for X-ray Timing (LOFT). For these purposes we choose such model parameters that lead to lightcurves comparable to those observed in Galactic black hole sources, in particular the microquasar GRS 1915+105. We find that when a weak signal corresponding to the hot-spot Keplerian frequency is around the limits of the RXTE detectability, the LOFT observations can clearly reveal its first and second harmonics. Moreover, in some specific situations the radial epicyclic frequency of the spot can be detected as well. Finally, we also compare the signal produced by the spots to the signal produced by axisymmetric epicyclic disc-oscillation modes and discuss the key differences that could be identified via the proposed future technology. We conclude that the ability to recognize the harmonic content of the signal can help to distinguish between the different proposed physical models.