Time delays and stationarity in quasar light curves

TL;DR

This paper introduces a Bayesian Gaussian process framework for analyzing quasar light curves to infer time delays and test stationarity, accounting for microlensing effects and model uncertainties.

Contribution

It presents a novel Bayesian approach that separates non-stationary drift from stationary variability, enabling robust time delay inference and stationarity testing in quasar light curves.

Findings

Detected non-stationarity in two quasars, consistent with prior studies.

Identified optimal kernels for stochastic variability, including Markovian and non-Markovian types.

Ensured robustness of time delay estimates against model assumptions.

Abstract

We present a fully Bayesian framework for time delay inference and stationarity tests in quasar light curves using marginalised Gaussian processes. The model separates a deterministic, non-stationary drift (piecewise linear mean) from stationary stochastic variability (Mat\'ern and Spectral Mixture kernels), and jointly models multiple images with per-image microlensing. Bayesian evidence and parameter posteriors are obtained via nested sampling and marginalised over model choices. Applied to the quasars WFI J2033 - 4723, B 1608 + 656, and HE 0435 - 1223, we find strong evidence for non-stationarity in B 1608 + 656 and HE 0435 - 1223, while WFI J2033 - 4723 is consistent with stationarity. The stochastic component favours an Markovian exponential kernel for B 1608 + 656 and a non-Markovian Mat\'ern-$\frac32$ kernel for WFI J2033 - 4723 and HE 0435 - 1223. Multi-length-scale Spectral Mixture kernels are disfavoured. Time delays are shown to be robust to model assumptions and consistent with prior work within the error. We further identify and mitigate a likelihood pathology which biases toward large delays, providing a practical nested sampling convergence protocol.