The Information Content of Quasar Variability Light Curves: How Well Can we Infer Stochastic Model Parameters?
Quasar variability, driven by multi-scale physical processing within a relativistic accretion disk, is commonly modelled with stochastic time series models. The simplest of these is the Damped Random Walk (DRW), also known as the Ornstein-Uhlenbeck (OU) process. Here, we demonstrate that, when fitting such a model to quasar light curve data, the mean of the light curve, $μ$, should not be fixed (which is the typical approach), as this leads to overconfident inferences about the variability timescale $τ$, with substantially underestimated uncertainties. However, the short term volatility parameter $η$ is typically very well constrained from short light curves. Through simulations, we compute information theoretic quantities such as the conditional entropy and the mutual information, confirming that light curves provide much more information about $η$ than about $τ$. As a result, we recommend that future quasar variability studies focus on $η$ rather than $τ$. To demonstrate this approach, we fit a hierarchical Bayesian regression model for $η$ as a function of bolometric luminosity and rest wavelength to a dataset of 570 light curves measured over decades. We perform the fit using a likelihood function that uses the light curves directly, rather than using intermediate $η$ values from individual light curve fits. We find that volatility decreases as a function of both bolometric luminosity and rest wavelength. The volatility also decreases more steeply with redshift than time dilation alone would suggest, pointing to an increase in intrinsic volatility as quasars evolve over cosmic time.