Combined Long and Short Timescale X-ray Variability of NGC4051 with RXTE and XMM-Newton

We present a comprehensive examination of the X-ray variability of the narrow line Seyfert 1 (NLS1) galaxy NGC4051. We combine over 6.5 years of frequent monitoring observations by RXTE with a >100ks continuous observation by XMM-Newton and so present a powerspectral density (PSD) covering an unprecedented frequency range of over 6.5 decades from <1e-8 to >1e-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 find a break in the PSD at a frequency u_{B}=8e-4 Hz. If u_{B} scales linearly with mass then, assuming a black hole (BH) mass of 10 M_solar for Cyg X-1, we imply a BH mass of 3e-5 M_solar in NGC4051, which is consistent with the recently reported reverberation mapped value. Hence NGC4051 is emitting at sim30% L_{Edd}. We note that the higher energy photons lag the lower energy ones and 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 similar to that of GBHs and suggests a radial distribution of frequencies and photon energies with higher energies and higher frequencies being associated with smaller radii [ABRIDGED].