The Information Content of Quasar Variability Light Curves: How Well Can we Infer Stochastic Model Parameters?

2026-05-31

AI Summary

Traditional methods for fitting quasar light curves often fix the mean flux, leading to a severe underestimation of the uncertainty in the characteristic timescale parameter τ. Through information-theoretic analysis and simulations, this study demonstrates that photometric variability data contain substantially more information about the short-timescale fluctuation amplitude η than about τ, suggesting that research efforts should prioritize η. To this end, we develop an end-to-end hierarchical Bayesian regression model that directly infers η from raw light-curve data, thereby avoiding biases introduced by intermediate estimation steps. Combining the damped random walk (Ornstein–Uhlenbeck) process with mutual information quantification, we find that η decreases with increasing luminosity and rest-frame wavelength, and its decline with redshift is steeper than expected from cosmological time dilation alone, indicating intrinsically stronger variability in high-redshift quasars.

Abstract

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.

Problem

• quasar variability
• stochastic modeling
• Damped Random Walk
• parameter inference
• light curve analysis

Innovation

• Damped Random Walk
• information theory
• hierarchical Bayesian model
• quasar variability
• volatility parameter