On characterizing the variability properties of X-ray light curves from active galaxies

We review some practical aspects of measuring the amplitude of variability in `red noise' light curves typical of those from active galactic nuclei (AGN). The quantities commonly used to estimate the variability amplitude in AGN light curves, such as the fractional rms variability amplitude, F_var, and excess variance, σ²_XS, are examined. Their statistical properties, relationship to the power spectrum and uses for investigating the nature of the variability processes are discussed. We demonstrate that σ²_XS (or similarly F_var) shows large changes from one part of the light curve to the next, even when the variability is produced by a stationary process. This limits the usefulness of these estimators for quantifying differences in variability amplitude between different sources or from epoch to epoch in one source. Some examples of the expected scatter in the variance are tabulated for various typical power spectral shapes, based on Monte Carlo simulations. The excess variance can be useful for comparing the variability amplitudes of light curves in different energy bands from the same observation. Monte Carlo simulations are used to derive a description of the uncertainty in the amplitude expected between different energy bands (due to measurement errors). Finally, these estimators are used to demonstrate some variability properties of the bright Seyfert 1 galaxy Markarian 766. The source is found to show a strong, linear correlation between rms amplitude and flux, and to show significant spectral variability.