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, Fvar, and excess variance, σ2XS, 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 σ2XS (or similarly Fvar) 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.

No abstract

By combining complementary monitoring observations spanning long, medium and short time scales, we have constructed power spectral densities (PSDs) of six Seyfert 1 galaxies. These PSDs span 4 orders of magnitude in temporal frequency, sampling variations on time scales ranging from tens of minutes to over a year. In at least four cases, the PSD shows a "break," a significant departure from a power law, typically on time scales of order a few days. This is similar to the behavior of Galactic X-ray binaries (XRBs), lower mass compact systems with breaks on time scales of seconds. NGC 3783 shows tentative evidence for a doubly-broken power law, a feature that until now has only been seen in the (much better-defined) PSDs of low-state XRBs. It is also interesting that (when one previously-observed object is added to make a small sample of seven), an apparently significant correlation is seen between the break time scale T and the putative black hole mass M BH , while none is seen between break time scale and luminosity. The data are consistent with the linear relation T = M BH /10 6.5 M ⊙ ; extrapolation over 6-7 orders of magnitude is in reasonable agreement with XRBs. All of this strengthens the case for a physical similarity between Seyfert 1s and XRBs.

We present ground-based optical photometric monitoring data for NGC 5548, part of an extended multiwavelength reverberation mapping campaign. The light curves have nearly daily cadence from 2014 January to July in nine filters (BVRI and ugriz). Combined with ultraviolet data from the Hubble Space Telescope and Swift, we confirm significant time delays between the continuum bands as a function of wavelength, extending the wavelength coverage from 1158 Å to the z band (∼ 9160 Å). We find that the lags at wavelengths longer than the V band are equal to or greater than the lags of high-ionization-state emission lines (such as He II λ1640 and λ4686), suggesting that the continuum-emitting source is of a physical size comparable to the inner broad-line region (BLR). The trend of lag with wavelength is broadly consistent with the prediction for continuum reprocessing by an accretion disk with τ ∝ λ 4/3 . However, the lags also imply a disk radius that is 3 times larger than the prediction from standard thin-disk theory, assuming that the bolometric luminosity is 10% of the Eddington luminosity (L = 0.1L Edd ). Using optical spectra from the Large Binocular Telescope, we estimate the bias of the interband continuum lags due to BLR emission observed in the filters. We find that the bias for filters with high levels of BLR contamination (∼ 20%) can be important for the shortest continuum lags, and likely has a significant impact on the u and U bands owing to Balmer continuum emission.

Recent intensive Swift monitoring of the Seyfert 1 galaxy NGC 5548 yielded 282 usable epochs over 125 days across six UV/optical bands and the X-rays. This is the densest extended AGN UV/optical continuum sampling ever obtained, with a mean sampling rate <0.5-day. Approximately daily HST UV sampling was also obtained. The UV/optical light curves show strong correlations (r max = 0.57 − 0.90) and the clearest measurement to date of interband lags. These lags are well-fit by a τ ∝ λ 4/3 wavelength dependence, with a normalization that indicates an unexpectedly large disk radius of ∼ 0.35 ± 0.05 lt-day at 1367Å, assuming a simple face-on model. The U-band shows a marginally larger lag than expected from the fit and surrounding bands, which could be due to Balmer continuum emission from the broad-line region as suggested by Korista and Goad. The UV/X-ray correlation is weaker (r max < 0.45) and less consistent over time. This indicates that while Swift is beginning to measure UV/optical lags in general agreement with accretion disk theory (although the derived size is larger than predicted), the relationship with X-ray variability is less well understood. Combining this accretion disk size estimate with those from quasar microlensing studies suggests that AGN disk sizes scale approximately linearly with central black hole mass over a wide range of masses.