Assessment of stochastic and deterministic models of 6304 quasar lightcurves from SDSS Stripe 82

Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
e-mail: andrae@mpia-hd.mpg.de

Received: 21 February 2013
Accepted: 2 April 2013

Abstract

The optical lightcurves of many quasars show variations of tenths of a magnitude or more on timescales of months to years. This variation often cannot be described well by a simple deterministic model. We perform a Bayesian comparison of over 20 deterministic and stochastic models on 6304 quasi-steller object (QSO) lightcurves in SDSS Stripe 82. We include the damped random walk (or Ornstein-Uhlenbeck [OU] process), a particular type of stochastic model, which recent studies have focused on. Further models we consider are single and double sinusoids, multiple OU processes, higher order continuous autoregressive processes, and composite models. We find that only 29 out of 6304 QSO lightcurves are described significantly better by a deterministic model than a stochastic one. The OU process is an adequate description of the vast majority of cases (6023). Indeed, the OU process is the best single model for 3462 lightcurves, with the composite OU process/sinusoid model being the best in 1706 cases. The latter model is the dominant one for brighter/bluer QSOs. Furthermore, a non-negligible fraction of QSO lightcurves show evidence that not only the mean is stochastic but the variance is stochastic, too. Our results confirm earlier work that QSO lightcurves can be described with a stochastic model, but place this on a firmer footing, and further show that the OU process is preferred over several other stochastic and deterministic models. Of course, there may well exist yet better (deterministic or stochastic) models, which have not been considered here.