We present a detailed X-ray timing analysis of the highly variable NLS1
galaxy, IRAS 13224-3809. The source was recently monitored for 1.5 Ms with
XMM-Newton which, combined with 500 ks archival data, makes this the best
studied NLS1 galaxy in X-rays to date. We apply standard time- and
Fourier-domain in order to understand the underlying variability process. The
source flux is not distributed lognormally, as would be expected for accreting
sources. The first non-linear rms-flux relation for any accreting source in any
waveband is found, with rms∝flux2/3. The light
curves exhibit significant strong non-stationarity, in addition to that caused
by the rms-flux relation, and are fractionally more variable at lower source
flux. The power spectrum is estimated down to ∼10−7 Hz and consists of
multiple peaked components: a low-frequency break at ∼10−5 Hz, with
slope α<1 down to low frequencies; an additional component breaking at
∼10−3 Hz. Using the high-frequency break we estimate the black hole
mass MBH=[0.5−2]×106M⊙, and mass accretion rate
in Eddington units, m˙Edd≳1. The non-stationarity is
manifest in the PSD with the normalisation of the peaked components increasing
with decreasing source flux, as well as the low-frequency peak moving to higher
frequencies. We also detect a narrow coherent feature in the soft band PSD at
0.7 mHz, modelled with a Lorentzian the feature has Q∼8 and an
rms∼3 %. We discuss the implication of these results for
accretion of matter onto black holes