Bayesian Analysis of Quasar Lightcurves with a Running Optimal Average: New Time Delay Measurements of COSMOGRAIL Gravitationally Lensed Quasars

TL;DR

This paper introduces a Bayesian method using the running optimal average (ROA) to analyze quasar lightcurves, accurately measuring time delays and detecting microlensing effects, with applications in gravitational lensing studies.

Contribution

The paper presents a novel Bayesian ROA-based approach for modeling quasar lightcurves, enabling precise time delay measurements and robust outlier handling, validated with simulations and real data.

Findings

ROA method accurately measures quasar time delays

Comparison shows ROA results align with existing methods

Detected microlensing effects in COSMOGRAIL data

Abstract

We present a new method of modelling time-series data based on the running optimal average (ROA). By identifying the effective number of parameters for the ROA model, in terms of the shape and width of its window function and the times and accuracies of the data, we enable a Bayesian analysis, optimising the ROA width, along with other model parameters, by minimising the Bayesian Information Criterion (BIC) and sampling joint posterior parameter distributions using MCMC methods. For analysis of quasar lightcurves, our implementation of ROA modelling can measure time delays among lightcurves at different wavelengths or from different images of a lensed quasar and, in future work, be used to inter-calibrate lightcurve data from different telescopes and estimate the shape and thus the power-density spectrum of the lightcurve. Our noise model implements a robust treatment of outliers and error-bar adjustments to account for additional variance or poorly-quantified uncertainties. Tests with simulated data validate the parameter uncertainty estimates. We compare ROA delay measurements with results from cross-correlation and from JAVELIN, which models lightcurves with a prior on the power-density spectrum. We analyse published COSMOGRAIL lightcurves of multi-lensed quasar lightcurves and present the resulting measurements of the inter-image time delays and detection of microlensing effects.