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We analyze the time variability of the X-ray emission of RE J1034+396 -- anactive galactic nucleus with the first firm detection of a quasi-periodicoscillations (QPO). Based on the results of a wavelet analysis, we find a driftin the QPO central frequency. The change in the QPO frequency correlates withthe change in the X-ray flux with a short time delay. The data specificallysuggest a linear dependence between the QPO period and the flux, and this givesimportant constraints on the QPO models. In particular, it excludes explanationin terms of the orbiting hot spot model close to a black hole. Linearstructures such as shocks, spiral waves, or very distant flares are favored.

The model constraints from the observed trends for the quasi-periodic oscillation in RE J1034+396