We present a comprehensive examination of the X-ray variability of the narrow line Seyfert 1 ( NLS1 ) galaxy NGCÂ 4051 , one of the most variable AGN in the sky .
We combine over 6.5 years of frequent monitoring observations by RXTE with a > 100 Â ks continuous observation by XMM-Newton and so present an overall 2-10 keV powerspectral density ( PSD ) covering an unprecedent frequency range of over 6.5 decades from < 10 ^ { -8 } to > 10 ^ { -2 } Hz .
The combined RXTE and XMM-Newton PSD is a very good match to the PSD of the galactic black hole binary system ( GBH ) Cyg X-1 when in a ‘ high ’ , rather than ‘ low ’ , state providing the first definite confirmation of an AGN in a ‘ high ’ state .
We also find that a bending powerlaw , rather than a sharply broken powerlaw , besides being more physical , is a much better description of the high state PSD of Cyg X-1 and is also a better description of the PSD of NGC 4051 .

At low frequencies the PSD of NGCÂ 4051 has a slope of -1.1 bending , at a frequency \nu _ { B } = 8 ^ { +4 } _ { -3 } \times 10 ^ { -4 } Hz , to a slope of \alpha _ { H } \sim - 2 .
Although \nu _ { B } does not depend on photon energy , \alpha _ { H } is steeper at lower energies .
If \nu _ { B } scales with mass , we imply a black hole mass of 3 ^ { +2 } _ { -1 } \times 10 ^ { 5 } M _ { \odot } in NGCÂ 4051 , which is consistent with the recently reported reverberation value of 5 ^ { +6 } _ { -3 } \times 10 ^ { 5 } M _ { \odot } .
Hence NGCÂ 4051 is emitting at \sim 30 \% ~ { } L _ { Edd } .

NGCÂ 4051 follows the same rms-flux relationship as GBHs , consistent with higher Fourier frequencies being associated with smaller radii .

From the cross-powerspectra and cross-correlation functions between XMM-Newton lightcurves in different energy bands , we note that the higher energy photons lag the lower energy ones .
We also note that the lag is greater for variations of longer Fourier period and increases with the energy separation of the bands .
Variations in different wavebands are very coherent at long Fourier periods but the coherence decreases at shorter periods and as the energy separation between bands increases .
This behaviour is again similar to that of GBHs , and of MCG-6-30-15 , and suggests a radial distribution of frequencies and photon energies with higher energies and higher frequencies being associated with smaller radii .

Combining our observations with observations from the literature we find it is not possible to fit all AGN to the same linear scaling of break timescale with black hole mass .
However broad line AGN are consistent with a linear scaling of break timescale with mass from Cyg X-1 in its low state and NLS1 galaxies scale better with Cyg X-1 in its high state .
We suggest that the relationship between black hole mass and break timescale is a function of at least one other underlying parameter which may be accretion rate or black hole spin or both .