The rapid X-ray variability of NGC 4051

We present an analysis of the high-frequency X-ray variability of NGC 4051 (M-BH similar to 1.7 x 106 M-circle dot) based on a series of XMM-Newton observations taken in 2009 with a total exposure of similar to 570 ks (EPIC pn). These data reveal the form of the power spectrum over frequencies from 10-4 Hz, below the previously detected power spectral break, to greater than or similar to 10-2 Hz, above the frequency of the innermost stable circular orbit (ISCO) around the black hole (nu(ISCO) similar to 10-3-10-2 Hz, depending on the black hole spin parameter j). This is equivalent to probing frequencies of greater than or similar to 1 kHz in a stellar mass (M-BH similar to 10 M-circle dot) black hole binary system. The power spectrum is a featureless power law over the region of the expected ISCO frequency, suggesting no strong enhancement or change in the variability at the fastest orbital period in the system. Despite the huge amplitude of the flux variations between the observations (peak-to-peak factor of greater than or similar to 50), the power spectrum appears to be stationary in shape and varies in amplitude at all observed frequencies following the previously established linear rms-flux relation. The rms-flux relation is offset in flux by a small and energy-dependent amount. The simplest interpretation of the offset is in terms of a very soft spectral component that is practically constant (compared to the primary source of variability). One possible origin for this emission is a circumnuclear shock energized by a radiatively driven outflow from the central regions and emitting via inverse-Compton scattering of the central engine's optical-UV continuum (as inferred from a separate analysis of the energy spectrum). A comparison with the power spectrum of a long XMM-Newton observation taken in 2001 gives only weak evidence for non-stationarity in power spectral shape or amplitude. Despite being among the most precisely estimated power spectra for any active galaxy, we find no strong evidence for quasi-periodic oscillations (QPOs) and determine an upper limit on the strength of a plausible QPO of less than or similar to 2 per cent rms in the 3 x 10-3 -0.1 Hz range and similar to 5-10 per cent in the 10-4 -3 x 10-3 Hz range. We compare these results to the known properties of accreting stellar mass black holes in X-ray binaries, with the further aim of developing a 'black hole unification' scheme.