MODELING THE TIME VARIABILITY OF SDSS STRIPE 82 QUASARS AS A DAMPED RANDOM WALK

By C. MacLeod, vZeljko Ivezi'c, C. Kochanek, S. Kozłowski, B. Kelly, E. Bullock, A. Kimball, B. Sesar, D. Westman, K. Brooks and 3 more. 2010

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We model the time variability of ∼9000 spectroscopically confirmed quasars in SDSS Stripe 82 as a damped random walk (DRW). Using 2.7 million photometric measurements collected over 10 yr, we confirm the results of Kelly et al. and Kozłowski et al. that this model can explain quasar light curves at an impressive fidelity level (0.01–0.02 mag). The DRW model provides a simple, fast (O(N) for N data points), and powerful statistical description of quasar light curves by a characteristic timescale (τ) and an asymptotic rms variability on long timescales (SF∞). We searched for correlations between these two variability parameters and physical parameters such as luminosity and black hole mass, and rest-frame wavelength. Our analysis shows SF∞ to increase with decreasing luminosity and rest-frame wavelength as observed previously, and without a correlation with redshift. We find a correlation between SF∞ and black hole mass with a power-law index of 0.18 ± 0.03, independent of the anti-correlation with luminosity. We find that τ increases with increasing wavelength with a power-law index of 0.17, remains nearly constant with redshift and luminosity, and increases with increasing black hole mass with a power-law index of 0.21 ± 0.07. The amplitude of variability is anti-correlated with the Eddington ratio, which suggests a scenario where optical fluctuations are tied to variations in the accretion rate. However, we find an additional dependence on luminosity and/or black hole mass that cannot be explained by the trend with Eddington ratio. The radio-loudest quasars have systematically larger variability amplitudes by about 30%, when corrected for the other observed trends, while the distribution of their characteristic timescale is indistinguishable from that of the full sample. We do not detect any statistically robust differences in the characteristic timescale and variability amplitude between the full sample and the small subsample of quasars detected by ROSAT. Our results provide a simple quantitative framework for generating mock quasar light curves, such as currently used in LSST image simulations.

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/189f8ea3dd3099ef6cc99081932ab945c1e6f852

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Citations in the corpus

A systematic search for close supermassive black hole binaries in the Catalina Real-time Transient Survey (2015, methodology): “For each light curve, we set bτ to its median value and use the rest frame CAR(1) fitting functions determined by MacLeod et al. (2010): log f = A+B log ( λRF 4000Å ) + C(Mi + 23) +D log ( MBH 109M ) where (A,B,C,D) = (−0.51,−0.479, 0.131, 0.18) for f = SF∞ and (A,B,C,D) = (2.4, 0.17, 0.03, 0.21)…”
AN ALTERNATIVE APPROACH TO MEASURING REVERBERATION LAGS IN ACTIVE GALACTIC NUCLEI (2010, methodology): “MacLeod et al. (2010) then apply the model to ∼ 9,000 spectroscopically identified quasars in SDSS Stripe 82.”
REVERBERATION MEASUREMENTS OF THE INNER RADIUS OF THE DUST TORUS IN 17 SEYFERT GALAXIES (2014, background): “…UV-optical continuum emission, which has been demonstrated to be a good statistical model for AGN variability (e.g., Kelly et al. 2009; Koz lowski et al. 2010; MacLeod et al. 2010, 2012; Zu et al. 2013), and also assumes a top hat transfer function in the transfer equation of reverberation mapping.”
THE STRUCTURE OF THE BROAD-LINE REGION IN ACTIVE GALACTIC NUCLEI. I. RECONSTRUCTED VELOCITY-DELAY MAPS (2012, methodology): “This method models the continuum with a damped random walk (DRW) model that has been demonstrated to be a good statistical model of AGN variability (e.g., Kelly et al. 2009; Koz lowski et al. 2010; MacLeod et al. 2010; MacLeod et al. 2012; Zu et al. 2012).”
The Sloan Digital Sky Survey Reverberation Mapping Project: Hα and Hβ Reverberation Measurements from First-year Spectroscopy and Photometry (2017, methodology): “The DRW model is observed to be a good description of quasar variability within the time regime relevant to our study (e.g., Kelly et al. 2009; Koz lowski et al. 2010; Koz lowski 2016; MacLeod et al. 2010, 2012), and so is an effective prior to describe the light curve between observations.”
Generating artificial light curves: revisited and updated (2013, background): “• The detection of variability in large catalogues and surveys (Bauer et al. 2009; Villforth et al. 2010; MacLeod et al. 2010; Primini et al. 2011), as well as for the detection of the smallest variability time-scales embedded in a data set (e.g. Aharonian et al. 2007).”
A physical model of the broad-band continuum of AGN and its implications for the UV/X relation and optical variability (2018, methodology): “This matches MNRAS 000, 1–14 (2018) to some of the trends seen in systematic surveys of AGN variability e.g., SDSS Stripe 82 (MacLeod et al. 2010), but there is more variability seen in high Eddington fraction AGN than predicted.”
STELLAR VELOCITY DISPERSION MEASUREMENTS IN HIGH-LUMINOSITY QUASAR HOSTS AND IMPLICATIONS FOR THE AGN BLACK HOLE MASS SCALE (2013, methodology): “The continuum is modeled as an autoregressive process using a damped random walk (DRW) model, which has shown to be a good statistical model of quasar variability (Gaskell & Peterson 1987; Kelly et al. 2009; Koz lowski et al. 2010; MacLeod et al. 2010; Zu et al. 2013).”
THE SDSS-IV EXTENDED BARYON OSCILLATION SPECTROSCOPIC SURVEY: QUASAR TARGET SELECTION (2015, background): “…distinguish them from stars of similar colors (e.g., van den Bergh et al. 1973; Hawkins 1983; Cimatti et al. 1993; Rengstorf et al. 2004a,b; Claeskens et al. 2006; Sesar et al. 2007; Koz lowski et al. 2010; MacLeod et al. 2010; Schmidt et al. 2010; Palanque-Delabrouille et al. 2011, 2013a, 2015).”
THE MAN BEHIND THE CURTAIN: X-RAYS DRIVE THE UV THROUGH NIR VARIABILITY IN THE 2013 ACTIVE GALACTIC NUCLEUS OUTBURST IN NGC 2617 (2013, methodology): “For example, Kelly et al. (2009) argue that the DRW time scale could be related to the thermal time scale of the disk, while MacLeod et al. (2010) note that the scalings of both the DRW time scale and amplitude with wavelength, black hole mass, and luminosity all seem too weak compared to the…”
IS QUASAR OPTICAL VARIABILITY A DAMPED RANDOM WALK? (2012, methodology): “The DRW model can be equivalently parameterized by τ and the asymptotic amplitude of the SF (SF∞ = √ 2σ, MacLeod et al. 2010), or τ and the slope of the SF on short time scales (σ̂ = √ 2σ2/τ , Kelly et al. 2009).”
A DESCRIPTION OF QUASAR VARIABILITY MEASURED USING REPEATED SDSS AND POSS IMAGING (2011, methodology): “We focus our description on the quasars with multiple observations (similar to MacLeod et al. 2010; 2011).”
False periodicities in quasar time-domain surveys (2016, methodology): “The means of each lognormal prior were set based on the geometric mean τ of 200 d from quasar samples in MacLeod et al. (2010), Kozłowski et al. (2010) and Andrae et al. (2013), and to give σ T = (cτ/2)1/2 ∼ 0.1 mag.”
A systematic search for changing-look quasars in SDSS (2015, background): “…3 hours to 8 years and provide well-sampled 5-band light curves for an unprecedented number of quasars (see Sesar et al. 2007; Schmidt et al. 2010; Ai et al. 2010; MacLeod et al. 2010; Meusinger et al. 2011; Butler & Bloom 2011, for examples of quasar variability studies based on S82 photometry).”
Modelling reverberation mapping data – II. Dynamical modelling of the Lick AGN Monitoring Project 2008 data set (2013, methodology): “…that we use is the same as a continuous-time first-order autoregressive process (CAR(1)), which has been found to be a good model for larger samples of AGN light curves (Kelly, Bechtold & Siemiginowska 2009; Kozłowski et al. 2010; MacLeod et al. 2010; Zu, Kochanek & Peterson 2011; Zu et al. 2013).”
A Population of Short-Period Variable Quasars from PTF as Supermassive Black Hole Binary Candidates (2016, methodology): “For instance, MacLeod et al. (2010) analysed light curves from SDSS Stripe82, which have long baselines and relatively sparse sampling and found that τ is overestimated for a fraction of their light curves (e.g., see their Fig.”
LSST: From Science Drivers to Reference Design and Anticipated Data Products (2008, methodology): “29 • A study of quasar variability using accurate, multicolor light curves for a few million quasars, leading to constraints on the accretion physics and nuclear environments (de Vries, Becker & White 2003; Vanden Berk et al. 2004, MacLeod et al. 2010).”