Mass Measurements of AGNs from Multi‐Lorentzian Models of X‐Ray Variability. I. Sampling Effects in Theoretical Models of the \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\…

Recent X-ray variability studies suggest that the log of the square of thefractional rms variability amplitude, rms^2, seems to correlate with the log ofthe AGN black-hole mass, M_BH, with larger black holes being less variable fora fixed time interval. This has motivated the theoretical modeling of therms^2-M_BH correlation with the aim of constraining AGN masses based on X-rayvariability. A viable approach to addressing this problem is to assume anunderlying power spectral density with a suitable mass dependence, derive thefunctional form of the rms^2-M_BH correlation for a given sampling pattern, andinvestigate whether the result is consistent with the observations. Forsimplicity, previous studies, inspired by the similarities shared by the timingproperties of AGN and X-ray binaries, have explored model power spectraldensities characterized by broken power laws. and ignored, in general, thedistorting effects that the particular sampling pattern imprints in theobserved power spectral density. Motivated by the latest timing results fromX-ray binaries, obtained with RXTE, we propose that AGN broad-band noisespectra consist of a small number of Lorentzian components. This assumptionallows, for the first time, to fully account for sampling effects intheoretical models of X-ray variability in an analytic manner. We show that,neglecting sampling effects when deriving the fractional rms from the modelpower 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 tomonitor AGN. We discuss the implications of our results for the derivation ofAGN masses using theoretical models of the rms^2-M_BH correlation. (Abridged)Comment: The Astrophysical Journal, in press, 11 pages, 6 figure