Light Echoes in Kerr Geometry: A Source of High-Frequency QPOs from Random X-Ray Bursts

We propose that high-frequency quasi-periodic oscillations (HFQPOs) can be produced from randomly formed X-ray bursts (flashes) by plasma interior to the ergosphere of a rapidly rotating black hole. We show by direct computation of their orbits that the photons comprising the observed X-ray light curves, if due to a multitude of such flashes, are significantly affected by the black hole's dragging of inertial frames; the photons of each such burst arrive to an observer at infinity in multiple (double or triple), distinct "bunches" separated by a roughly constant time lag of Δ t_lag/M ≃ 14, regardless of the bursts' azimuthal position. We argue that every other such "bunch" represents photons that follow trajectories with an additional orbit around the black hole at the photon circular orbit radius (a photon "echo"). The presence of this constant lag in the response function of the system leads to a QPO feature in its power density spectra, even though the corresponding light curve consists of a totally stochastic signal. This effect is by and large due to the black hole spin and is shown to gradually diminish as the spin parameter a decreases or the radial position of the burst moves outside the static limit surface (ergosphere). Our calculations indicate that for a black hole with Kerr parameter of a/M = 0.99 and mass of M = 10 M_☉, the QPO is expected at a frequency of ν_QPO ∼ 1.3–1.4 kHz. We discuss the plausibility and observational implications of our model results, as well as its limitations.