LAUSR

We present a detailed X-ray timing analysis of the highly variable narrow-line Seyfert 1 (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 techniques in order to understand the underlying variability process. The source flux is not distributed lognormally, as expected for all types of 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, and 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≳1m˙Edd≳1⁠. The broad-band power spectral density (PSD) and accretion rate make IRAS 13224–3809 a likely analogue of very high/intermediate-state black hole X-ray binaries. The non-stationarity is manifest in the PSD with the normalization 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 7 × 10−4 Hz; modelled with a Lorentzian the feature has Q ∼ 8 and an rms ∼3 per cent. We discuss the implication of these results for accretion of matter on to black holes.