Extensive X-ray variability studies of NGC 7314 using long XMM-Newton observations

We present a detailed X-ray variability study of the low mass Active Galactic Nuclei (AGN) NGC 7314 using the two newly obtained XMM-Newton observations ($140$ and $130$ ks), together with two archival data sets of shorter duration ($45$ and $84$ ks). The relationship between the X-ray variability characteristics and other physical source properties (such as the black hole mass) are still relatively poorly defined, especially for low-mass AGN. We perform a new, fully analytical, power spectral density (PSD) model analysis method, which will be described in detail in a forthcoming paper, that takes into consideration the spectral distortions, caused by red-noise leak. We find that the PSD in the $0.5-10$ keV energy range, can be represented by a bending power-law with a bend around $6.7\times10^{-5}$ Hz, having a slope of $0.51$ and $1.99$ below and above the bend, respectively. Adding our bend time-scale estimate, to an already published ensemble of estimates from several AGN, supports the idea that the bend time-scale depends linearly only on the black hole mass and not on the bolometric luminosity. Moreover, we find that as the energy range increases, the PSD normalization increases and there is a hint that simultaneously the high frequency slope becomes steeper. Finally, the X-ray time-lag spectrum of NGC 7314 shows some very weak signatures of relativistic reflection, and the energy resolved time-lag spectrum, for frequencies around $3\times10^{-4}$ Hz, shows no signatures of X-ray reverberation. We show that the previous claim about ks time-delays in this source, is simply an artefact induced by the minuscule number of points entering during the time-lag estimation in the low frequency part of the time-lag spectrum (i.e. below $10^{-4}$ Hz).