We present an analysis of the high frequency X-ray variability of NGC 4051 ( M _ { BH } \sim 1.7 \times 10 ^ { 6 } \thinspace M _ { \odot } ) based on a series of XMM-Newton observations taken in 2009 with a total exposure of \sim 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 \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } } } 10 ^ % { -2 } Hz , above the frequency of the innermost stable circular orbit ( ISCO ) around the black hole ( \nu _ { ISCO } \sim 10 ^ { -3 } -10 ^ { -2 } Hz , depending on the black hole spin parameter j ) .
This is equivalent to probing frequencies \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } } } 1 kHz in a stellar mass ( M _ { BH } \sim 10 \thinspace M _ { \odot } ) 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 \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } } } 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 energised 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 \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } } 2 per cent rms in the 3 \times 10 ^ { -3 } -0.1 Hz range , and \sim 5 - 10 per cent in the 10 ^ { -4 } -3 \times 10 ^ { -3 } Hz range .
We compare these results to the known properties of accreting stellar mass black holes in X-ray binaries , with the aim further of developing a ‘ black hole unification ’ scheme .