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The active galactic nucleus (AGN) RE J1034+396 displays the most significantX-ray Quasi-Periodic Oscillation (QPO) detected so far. We perform a detailedspectral-timing analysis of our recent simultaneous XMM-Newton, NuSTAR andSwift observations. We present the energy dependence of the QPO's frequency,rms, coherence and phase lag, and model them together with the time-averagedspectra. Our study shows that four components are required to fit all thespectra. These components include an inner disc component (diskbb), two warmcorona components (CompTT-1 and CompTT-2), and a hot corona component(nthComp). We find that diskbb, CompTT-2 (the hotter but less luminouscomponent) and nthComp all contain the QPO signal, while CompTT-1 only exhibitsstochastic variability. By fitting the lag spectrum, we find that the QPO indiskbb leads CompTT-2 by 679 s, and CompTT-2 leads nthComp by 180 s. By onlyvarying the normalizations, these components can also produce good fits to thetime-averaged and variability spectra obtained from previous observations whenQPOs were present and absent. Our multi-wavelength study shows that thedetectability of the QPO does not depend on the contemporaneous mass accretionrate. We do not detect a significant Iron K{\alpha} emission line, or anysignificant reflection hump. Finally, we show that the rms and lag spectra inthe latest observation are very similar to the 67 Hz QPO observed in themicro-quasar GRS 1915+105. These new results support the physical analogybetween these two sources. We speculate that the QPO in both sources is due tothe expansion/contraction of the vertical structure in the inner disc.

Re-observing the NLS1 Galaxy RE J1034+396. II. New Insights on the Soft X-ray Excess, QPO and the Analogy with GRS 1915+105