COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses XI. Techniques for time delay measurement in presence of microlensing

TL;DR

This paper introduces three novel numerical methods for accurately measuring time delays in gravitationally lensed quasars, accounting for microlensing effects, and provides a framework for estimating uncertainties and biases in these measurements.

Contribution

It presents three new point estimators designed to handle extrinsic variability in light curves, improving the robustness of time delay measurements in gravitational lensing studies.

Findings

The estimators effectively handle microlensing-induced variability.

Empirical bias and uncertainty estimates improve measurement reliability.

Methods are validated with simulated light curves closely resembling real data.

Abstract

Measuring time delays between the multiple images of gravitationally lensed quasars is now recognized as a competitive way to constrain the cosmological parameters, and it is complementary with other cosmological probes. This requires long and well sampled optical light curves of numerous lensed quasars, such as those obtained by the COSMOGRAIL collaboration. High-quality data from our monitoring campaign call for novel numerical techniques to robustly measure the delays, as well as the associated random and systematic uncertainties, even in the presence of microlensing variations. We propose three different point estimators to measure time delays, which are explicitly designed to handle light curves with extrinsic variability. These methods share a common formalism, which enables them to process data from n-image lenses. Since the estimators rely on significantly contrasting ideas, we expect them to be sensitive to different bias sources. For each method and data set, we empirically estimate both the precision and accuracy (bias) of the time delay measurement using simulated light curves with known time delays that closely mimic the observations. Finally, we test the self-consistency of our approach, and we demonstrate that our bias estimation is serviceable. These new methods, including the empirical uncertainty estimator, will represent the standard benchmark for analyzing the COSMOGRAIL light curves.