Mass measurements of AGNs from multi-Lorentzian models of X-ray variability.: I.: Sampling effects in theoretical models of the σrms2-MBH correlation

Recent X- ray variability studies suggest that the log of the square of the fractional rms variability amplitude, sigma(2)(rms), seems to correlate with the log of the AGN black holemass, M-BH, with larger black holes being less variable for a fixed time interval. This has motivated the theoretical modeling of the sigma(2)(rms)-M-BH correlation with the aim of constraining AGN masses based on X- ray variability. A viable approach to addressing this problem is to assume an underlying power spectral density with a suitable mass dependence, derive the functional form of the sigma(2)(rms)-M-BH correlation for a given sampling pattern, and investigate whether the result is consistent with the observations. For simplicity, previous studies, inspired by the similarities shared by the timing properties of AGN and X- ray binaries, have explored model power spectral densities characterized by broken power laws and ignored, in general, the distorting effects that the particular sampling pattern imprints in the observed power spectral density. Motivated by the latest timing results from X- ray binaries, obtained with RXTE, we propose that AGN broadband noise power spectra consist of a small number of Lorentzian components. This assumption allows one, for the first time, to fully account for sampling effects in theoretical models of X- ray variability in an analytic manner. We show that neglecting sampling effects when deriving the fractional rms from the model power spectral density can lead to underestimating it by a factor of up to 80% with respect to its true value for the typical sampling patterns used to monitor AGNs. We discuss the implications of our results for the derivation of AGN masses using theoretical models of the sigma(2)(rms)-M-BH correlation.