Optical variability of quasars: damped random walk Željko Ivezić, University of Washington with Chelsea MacLeod, U.S.

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1 Optical variability of quasars: damped random walk Željko Ivezić, University of Washington with Chelsea MacLeod, U.S. Naval Academy IAU Symposium 304, Yerevan, Armenia, October 7-12, 2013

2 OUTLINE Practically all quasars are variable (competing theories: Microlensing Bursts of Supernovae Accretion disk instabilities) Quasar variability is stochastic and consistent with damped random walk (DRW) Best-fit DRW parameters are correlated with physical parameters (luminosity, BH mass,...) SDSS has revolutionized studies of quasar variability; LSST will enable the next giant leap by providing millions of well-sampled light curves over a 10-year period...

3 Practically all quasars are variable! The fraction of variable objects in SDSS Stripe 82: With rms > 0.05 mag and g<20.5 The sample is dominated by quasars and RR Lyrae. Quasars and RR Lyrae have different variability properties: rms(g)/rms(r) Sesar et al. 2007

4 The variability time scales Time scale τ is defined via damped random walk (because not all variable sources are periodic) Quasars are easily distinguished from stars by their long time scales. Variability is even better than color selection! Case study: light curve data and proper motion data for over 1 million sources from SDSS Stripe 82 (all are publicly available) McLeod et al. 2011

5 Damped random walk For irregularly sampled data, best analyzed using the structure function, or alternatively by fitting individual light curves for the best-fit time scale τ and variability long-term variance (e.g. see Gaussian Processes in Numerical Recipes, or Kozłowski, S., et al. 2010, ApJ, 708, 927) m auto-correlation function t

6 Damped random walk For irregularly sampled data, statistical samples are best analyzed using the (model-independent) structure function Variability rms decreases with wavelength and increase with time Observing baseline of 10 years (SDSS) is sufficient to constrain variability time scale for the majority of quasars McLeod et al. 2012

7 Damped random walk also known as Ornstein-Uhlenbeck process and as CAR(1) process; it has exponentially decaying ACF and it is a Stochastic process with PSD(f) = 1/f 2 for f > 1/τ, and PSD(f)=const. for f < 1/τ flicker noise plus random walk 1/f for low f DRW RDW cannot be rejected (MacLeod+201x) (Zu+2012) 1/f 2 Kepler data: 1/f 3 for high frequencies i.e. 1/f 2 Random walk 1/τ short time scales (Mushotzky+2011)

8 Damped random walk fits to SDSS Stripe 82 Spectroscopy 3-parameter fits: DRW time scale, amplitude, and mean magnitude Using variability, one gets the same morphology in the g-r vs. u-g diagram as when using spectroscopy! amplitude McLeod et al. 2011

9 Redshift Distribution (g < 20.5) Var.-selected QSOs DR7 catalog (Schneider et al. 2010) Courtesy: S. F. Anderson Variability selection adds quasars at z 0.8, z 2.7 Variability is even better than color selection! redshift Chelsea MacLeod, 6/4/ The Optical Variability of Quasars as Seen by SDSS

10 Damped random walk What can be learned from fitting individual light curves? Mi Mi SF redshift SF Mi Mi τ redshift τ τ increases with wavelength and black hole mass, and is nearly constant with redshift and luminosity SF increases with decreasing luminosity and rest-frame wavelength, and without a correlation with redshift SF is correlated with black hole mass, independent of the anti-correlation with luminosity SF is anti-correlated with the Eddington ratio, which suggests a scenario where optical fluctuations are tied to variations in the accretion rate. MBH MBH McLeod et al. 2010

11 Quasar Variability: summary Competing theories for the origin of variability: Microlensing Bursts of Supernovae Accretion disk instabilities SDSS observations indicate rich information content and can already reject some models (MacLeod et al. 2010, 2011, 2012): Acc. disk: yes Text SNe: no! Variability is a tool, just like imaging, spectroscopy and multiwavelength X-ray to radio observations, for studying quasars. LSST data will be excellent for continuing such studies: millions of objects, thousands of precise measurements.

12 ACF( t) for y(t) damped random walk model for quasar light curve

13 Open source!