[Paper Review] Time delay controversy on QSO 0957+561 not yet decided

J. Pelt, W. Hoff+3 more|arXiv (Cornell University)|Jan 11, 1994

Cardiac Imaging and Diagnostics19 citations

TL;DR

This paper re-analyzes optical and radio light curves of the gravitational lens system QSO 0957+561 A,B using a non-parametric dispersion estimation method that avoids windowing effects by considering only alternating neighboring pairs from the two images. It finds a time delay of (415 ± 32) days from optical data and (409 ± 23) days from radio data, concluding that the radio result is more reliable due to reduced sensitivity to data perturbations and less windowing bias.

ABSTRACT

We present a new analysis of previously published optical and radio data sets of the gravitationally lensed quasar 0957+561 A,B with the aim of determining the time delay between its two images. We use a non-parametric estimate of the dispersion of the combined data set where, however, we only make use of alternating neighbours in order to avoid windowing effects. From the optical data a time delay of (415 $\pm$ 32) days and from the radio data a delay of (409 $\pm$ 23) days is suggested. We demonstrate a considerable sensitivity of different delay estimation procedures against the removal of only a few observational data points or against smoothing or detrending of the original data sets. The radio data give us formally a slightly more precise value for the time delay than the optical data. Also, due to the lack of windowing effects, the result obtained for the radio data can be considered as somewhat more reliable than the delay determined from the optical data.

Motivation & Objective

• To re-evaluate the time delay between the two images of the gravitationally lensed quasar QSO 0957+561 A,B using optical and radio light curves.
• To address the controversy over conflicting time delay estimates, which range from 376 to 657 days, by applying a robust statistical method.
• To minimize windowing effects in time delay estimation by using only alternating neighboring pairs from the two light curves.
• To assess the sensitivity of time delay estimates to data perturbations, smoothing, and detrending, particularly in the context of unevenly sampled data.
• To compare the reliability of optical and radio data for time delay determination, given differing sensitivities to data processing choices.

Proposed method

• Uses a non-parametric dispersion estimation method to compute the scatter in the combined light curve after time-shifting one image by trial delays τ.
• Applies a selection window G(δ, ti, tj) to include only pairs of observations with time lags ≤ δ, reducing trend-induced bias.
• Estimates dispersion using only alternating neighboring pairs (one from image A, one from image B) to avoid strong windowing effects that bias minima at τ = (n+0.5) years.
• Employs a subsampling approach based on neighboring observations (y_i, y_{i+1}) to estimate error dispersion without assuming a parametric trend model.
• Uses the formula S²(δ) = [Σ G(δ, ti, tj)(yi - yj)²] / [2 × Σ G(δ, ti, tj)] to compute dispersion for each δ, with δ chosen to balance trend bias and sampling error.
• Validates results by comparing with PRHa and PRHb procedures and testing sensitivity to data removal, smoothing, and detrending.

Experimental results

Research questions

• RQ1 What is the true time delay between the two images of QSO 0957+561 A,B, given conflicting prior estimates?
• RQ2 How do windowing effects from uneven sampling influence time delay estimation, and can they be mitigated?
• RQ3 Why do different statistical methods yield such divergent time delay results, especially around 415 and 536 days?
• RQ4 Which data set—optical or radio—provides a more robust and reliable time delay estimate?
• RQ5 How sensitive are time delay estimates to minor data manipulations such as smoothing, detrending, or removal of a few points?

Key findings

• The optical data yield a time delay of (415 ± 32) days, consistent with earlier estimates but sensitive to data processing choices.
• The radio data yield a time delay of (409 ± 23) days, with higher formal precision than the optical result.
• The radio result is considered more reliable due to reduced sensitivity to data perturbations and absence of strong windowing effects.
• The study demonstrates significant sensitivity of time delay estimates to the removal of just a few data points or to smoothing and detrending procedures.
• The dispersion spectrum D²(τ) shows a minimum at τ ≈ 409–415 days, but the presence of multiple minima in window functions complicates interpretation.
• The choice of δ in the dispersion estimator affects bias and variance trade-off, with an optimal δ balancing trend bias and sampling error.