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  • Open Access

Time delays and stationarity in quasar light curves

Namu Kroupa1,2,3,*, David Yallup2,4, and Will Handley2,4

  • 1Astrophysics Group, Cavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
  • 2Kavli Institute for Cosmology, Madingley Road, Cambridge CB3 0HA, United Kingdom
  • 3Engineering Laboratory, University of Cambridge, Cambridge CB2 1PZ, United Kingdom
  • 4Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, United Kingdom

  • *Contact author: nk544@cam.ac.uk
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Phys. Rev. D 113, 063549 – Published 19 March, 2026

DOI: https://doi.org/10.1103/87nn-klh9

Abstract

We present a fully Bayesian framework for time delay inference and stationarity tests in quasar light curves using marginalized Gaussian processes. The model separates a deterministic, nonstationary drift (piecewise linear mean) from stationary stochastic variability (Matérn and Spectral Mixture kernels), and jointly models multiple images with per-image microlensing. Bayesian evidence and parameter posteriors are obtained via nested sampling and marginalized over model choices. Applied to the quasars WFI J2033–4723, B 1608+656, and HE 0435–1223, we find strong evidence for nonstationarity in B 1608+656 and HE 0435–1223, while WFI J2033–4723 is consistent with stationarity. The stochastic component favors an Markovian exponential kernel for B 1608+656 and a non-Markovian Matérn-32 kernel for WFI J2033–4723 and HE 0435–1223. Multilength-scale Spectral Mixture kernels are disfavored. 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.

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Phys. Rev. D 113, 063549– Published 19 March, 2026
  • Received 29 October 2025
  • Accepted 23 February 2026
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