  Observation of the bright Seyfert 1 galaxy RE J1034+396 is believed to
demonstrate a drift of the central period of the Quasi Periodic Oscillation
(QPO) linearly correlated with the temporary X-ray luminosity. We show, using a
specific scenario of the oscillation mechanism in black hole accretion disc,
that modeling such correlated trends puts very strong constraints on the nature
of this oscillation and the characteristic features of the hot flow in Active
Galactic Nuclei (AGN). In our model, QPO oscillations are due to the
oscillations of the shock formed in the low angular momentum hot accretion
flow, and the variation of the shock location corresponds to the observed
changes in the QPO period and the X-ray flux. In this scenario, change in the
shock location caused by perturbation of the flow angular momentum is
compatible with the trends observed in RE J1034+396, whereas the perturbation
of the specific flow energy results in too strong flux response to the change
of the oscillation period. Using a complete general relativistic framework to
study the accretion flow in the Kerr metric, we discuss the role of the black
hole spin in the period drift. Future missions are expected to bring more
active galaxies with time-resolved quasi-periodic oscillations so similar
quantitative study for other QPO scenarios will be necessary.
