Variability

In this work, we compared many deterministic and stochastic models in order to statistically study which model describes QSO light curves most successfully. As a result, we confirmed that a stochastic model is preferred over other models. The work is published in A&A (Andrae+ 2013).

Abstract from Andrae+ 2013: "The optical light curves 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-stellar object (QSO) light curves 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 light curves 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 light curves, 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 light curves show evidence that not only the mean is stochastic but the variance is stochastic, too. Our results confirm earlier work that QSO light curves 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."

[ Five example QSO light curves with the OU process fitting. The dashed line shows the time-evolution of the mean values. The grey shadings areas are the 1, 2, and 3σ intervals, respectively (Figure 4. from Andrae+ 2013) ]