[Paper Review] The light curve and the time delay of QSO 0957+561

J. Pelt, R. Kayser+2 more|arXiv (Cornell University)|Jan 11, 1995

Adaptive optics and wavefront sensing17 citations

TL;DR

This paper presents a refined statistical analysis of optical photometric light curves for the gravitationally lensed quasar QSO 0957+561A,B using the dispersion estimation technique, demonstrating a time delay of 423 ± 6 days, which rules out the previously reported 536-day delay. The method accounts for observational noise and sampling irregularities, and the result constrains the Hubble parameter to less than 70 km s⁻¹ Mpc⁻¹.

ABSTRACT

We present a new analysis of the presently available photometric data for the gravitationally lensed quasar 0957+561 A,B with the aim of determining the time delay between its two images. The basic method used is the dispersion estimation technique. Even by using the simplest non-parametric form of our method we can convincingly rule out a time delay near 536 days and show that the time delay is in the vicinity of 420 days. We then introduce refinements to our method in order to get a stable and reliable result for the time delay independent of high frequency noise in the data and sampling errors. Our best result for the time delay, checked by various statistical tests and using bootstrap error estimates, is 423 +/- 6 days. We furthermore confirm our earlier result that the radio data are compatible with this value. Using the best available model for the mass distribution in the lensing galaxy and cluster, our result for the time delay constrains the Hubble parameter to be smaller than 70 km/(s Mpc).

Motivation & Objective

• To determine a statistically reliable time delay between the two images of the gravitationally lensed quasar QSO 0957+561A,B.
• To resolve the longstanding controversy over the time delay value, particularly the discrepancy between the 536-day estimate by Press et al. and earlier results.
• To develop and apply refined statistical techniques that are robust against high-frequency noise and sampling irregularities in the photometric data.
• To assess the role of microlensing in the observed light curve discrepancies between the two images.
• To constrain the Hubble parameter H₀ using the improved time delay and a detailed mass model of the lensing system.

Proposed method

• Applies the dispersion estimation technique, a non-parametric statistical method, to estimate time delays between two light curves.
• Uses a window function N_A,B(τ) to quantify the number of observation pairs with time shifts τ, improving statistical reliability.
• Implements adaptive median filtering to reduce noise and preserve signal structure in unevenly sampled data.
• Applies polynomial fitting to model and subtract long-term trends in the light curves to isolate intrinsic variability.
• Employs bootstrap resampling for error estimation and statistical validation of the time delay result.
• Validates results using multiple statistical tests and cross-checks with radio light curve data.

Experimental results

Research questions

• RQ1 Is the previously reported 536-day time delay between the images of QSO 0957+561 statistically stable and reliable?
• RQ2 Can a more robust statistical method resolve the discrepancy between different time delay estimates from the same data?
• RQ3 To what extent do observational noise and irregular sampling affect time delay estimation in quasar light curves?
• RQ4 Is the observed difference in the light curves of images A and B consistent with microlensing effects?
• RQ5 What constraints does the revised time delay place on the Hubble parameter H₀ when combined with a physical lens model?

Key findings

• The time delay between the two images of QSO 0957+561 is 423 ± 6 days, based on optical photometric data and refined statistical analysis.
• The 536-day delay is ruled out as statistically implausible, with strong evidence favoring a value near 420 days.
• The observed trend in the difference light curve (B - A) is consistent with decreasing observational errors over time, not a physical trend.
• Microlensing is the most natural explanation for the residual differences in the light curves after correcting for the time delay.
• The time delay constrains the Hubble parameter to H₀ < 70 km s⁻¹ Mpc⁻¹, with the remaining uncertainty primarily due to mass model uncertainties in the lensing galaxy.
• Radio light curve data are confirmed to be consistent with the optical-based time delay of 423 ± 6 days.