The remarkable X-ray variability of IRAS 13224-3809-I. The variability process

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 1.5Ms 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 similar to 10(-7) Hz and consists of multiple peaked components: a low-frequency break at similar to 10(-5) Hz, with slope alpha < 1 down to low frequencies, and an additional component breaking at similar to 10(-3) Hz. Using the high-frequency break, we estimate the black hole mass MBH = [0.5-2] x 10(6)M(circle dot) and mass accretion rate in Eddington units,. m Edd greater than or similar to 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 x 10(-4) Hz; modelled with a Lorentzian the feature has Q similar to 8 and an rms similar to 3 per cent. We discuss the implication of these results for accretion of matter on to black holes.