Modeling the Time Variability of SDSS Stripe 82 Quasars as a Damped Random Walk

Abstract

We model the time variability of ∼9,000 spectroscopically confirmed quasars in SDSS Stripe 82 as a damped random walk. Using 2.7 million photometric measurements collected over 10 years, we confirm the results of Kelly et al. (2009) and Koz lowski et al. (2010) that this model can explain quasar light curves at an impressive fidelity level (0.01-0.02 mag). The damped random walk model provides a simple, fast [O(N ) for N data points], and powerful statistical description of quasar light curves by a characteristic time scale (τ ) and an asymptotic rms variability on long time scales (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 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 time scale is indistinguishable from that of the full sample. We do not detect any statistically robust differences in the characteristic time scale 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.

Using AGN Variability Surveys to explore the AGN-Galaxy Connection

“…spectroscopic, color selection, UV excess) displaying significant optical variability when observed over several years (Schmidt et al 2010). The optical/IR flux changes occur 386 Vicki L. Sarajedini on timescales of months to years and have been well fit with damped random walk models indicating a characteristic timescale for variability and maximum amplitude at long time intervals (MacLeod et al 2010). Variability in AGN is likely due to instabilities in the accretion disk (e.g.…”

“…Variability in AGN is likely due to instabilities in the accretion disk (e.g. Li & Cao 2008) and has been found to correlate with several AGN parameters such as bolometric luminosity, wavelength and black hole mass (MacLeod et al 2010;Zuo et al 2012). In addition, intrinsically fainter AGN are found to have a higher amplitude of variability (Trevese et al 1994;Wilhite et al 2008) making variability selection particularly well-suited for identifying faint AGN.…”

The correlations between optical variability and physical parameters of quasars in SDSS Stripe 82

“…A sample of 9254 variable quasars is obtained from cross-matching the spectroscopic confirmed SDSS DR7 quasars (Schneider et al 2010;Shen et al 2011) and a sample of 67507 variable sources in SDSS Stripe 82, which lies along the celestial equator in the Southern Galactic Hemisphere (22h 24m < α J2000 < 04h 08m, −1.27 • < δ J2000 < +1.27 • , ∼ 290 deg 2 ) and have repeated photometric observations (at least 4 per band, with a median of 10) measured in up to 10 years in the u ′ g ′ r ′ i ′ z ′ system (Fukugita et al 1996;MacLeod et al 2010;Ivezić et al 2007;Sesar et al 2007). Black hole masses, bolometric luminosities and Eddington ratios are obtained from the quasar catalog in Shen et al (2011), where the black hole masses of quasars were settled by fiducial virial mass estimates: Hβ (Vestergaard & Wilkes 2006) estimates for z < 0.7, [MgII] (Shen & Kelly 2010) estimates for 0.7 ≤ z < 1.9 and CIV] (Vestergaard & Wilkes 2006) estimates for z ≥ 1.9.…”

A degeneracy in DRW modelling of AGN light curves

“…The damped random walk (DRW) model is an increasingly successful method of quantifying the variability of active galactic nuclei (AGNs; Kelly et al 2009;Koz lowski et al 2010;MacLeod et al 2010;Zu et al 2011Zu et al , 2013. Kelly et al (2009) introduce DRW as an underlying stochastic process leading to AGN variability, also known as the continuous-time first order autoregressive process [CAR(1)] or Ornstein-Uhlenbeck process (Uhlenbeck & Ornstein 1930).…”

“…Kelly et al (2009) introduce DRW as an underlying stochastic process leading to AGN variability, also known as the continuous-time first order autoregressive process [CAR(1)] or Ornstein-Uhlenbeck process (Uhlenbeck & Ornstein 1930). The model has two parameters, the time-scale τ after which the light curve becomes uncorrelated and the modified amplitudeσ (Koz lowski et al 2010) or asymptotic amplitude SF∞ (MacLeod et al 2010). These two parameters show correlations with the physical parameters of AGNs, such as the black hole mass, luminosity, Eddington ratio, and rest-frame wavelength.…”