Modeling the Variability of Active Galactic Nuclei by an Infinite Mixture of Ornstein–Uhlenbeck (OU) Processes

Abstract

Abstract We develop an infinite mixture model of Ornstein–Uhlenbeck (OU) processes for describing the optical variability of QSOs based on treating the variability as a stochastic process. This enables us to get the parameters of the power spectral densities (PSDs) on their brightness variations by providing more flexible description of PSDs than the models based on a single OU process (damped random walk (DRW). We apply this model to 67,507 variable objects extracted from Sloan Digital Sky Survey (SDSS) Stripe 82 photometric data and succeed in showing very high precision in identifying QSOs (∼99% levels in completeness and purity) among variable objects based only on their variability, by investigating on 9855 spectroscopically confirmed objects (7714 QSOs and 2141 stars) in the data of SDSS Data Release 12 (DR12), with sufficient and accurate multiple measurements of their brightness. By comparing our results with the values based on other models that are used in previous research, it is revealed that our model can be used as the most effective method for selecting QSOs from a variable object catalog, especially regarding completeness and purity. The main reason for improved identification rates is the ability of our model to separate clearly QSOs and stars, especially on the small fraction of QSOs with variabilities that can be described better than with the simple DRW model.