[Paper Review] The Auto-Correlation Function of the extragalactic background light: I. Measuring gravitational shear

Ludovic Van Waerbeke, Y. Mellier+3 more|arXiv (Cornell University)|Apr 23, 1996

Statistical and numerical algorithms3 citations

TL;DR

This paper proposes a novel method to measure gravitational shear by analyzing the anisotropy in the auto-correlation function (ACF) of the extragalactic background light (EBL), which arises from faint, undetected background galaxies. By exploiting the tidal distortion induced by foreground mass distributions on the ACF, the method enables shear measurement without individual galaxy detection, offering an independent, noise-based shear estimate that enhances sensitivity and enables potential magnification measurement when source density is high.

ABSTRACT

A new method for measuring the shear induced by gravitational light deflection is proposed. It is based on analyzing the anisotropy induced in the auto-correlation function (ACF) of the extragalactic background light which is produced by very faint distant galaxies. The ACF can be measured `locally', and its anisotropy is caused by the tidal gravitational field of the deflecting mass distribution in the foreground of these faint background galaxies. Since the method does not require individual galaxy detection, it can be used to measure the shear of extremely faint galaxies which are not detectable individually, but are present in the noise. The shear estimated from the ACF of the noise provides an independent measurement which can be compared to the shear obtained from the distortion of individual galaxy images. Combining these two independent estimates clearly increases the sensitivity of shear measurements. In addition, our method may allow to determine the local magnification caused by the deflector if the auto-correlation function is caused by a large number density of faint galaxies; in this case, the intrinsic ACF may provide a `standard source' with respect to which shear and magnification can be obtained. Applications to real and synthetic data are shown and the feasibility of our new method is demonstrated. In particular, we present the shear maps obtained with our method for the double QSO 2345+007 and the cluster Cl0024+16 and compare them to published shear maps.

Motivation & Objective

• To develop a shear measurement technique that does not require individual galaxy detection, enabling analysis of extremely faint, noise-limited sources.
• To exploit the anisotropy in the auto-correlation function (ACF) of the extragalactic background light (EBL) as a probe of gravitational shear from foreground mass distributions.
• To provide an independent shear measurement from the noise-dominated ACF that can be cross-validated with traditional galaxy shape measurements.
• To explore the potential of using the intrinsic ACF of faint galaxies as a 'standard source' for measuring both shear and magnification.

Proposed method

• The method analyzes the anisotropy in the ACF of the EBL, which is induced by tidal gravitational fields from foreground mass distributions.
• It measures shear locally by detecting systematic distortions in the ACF shape due to gravitational lensing effects on the background light field.
• The approach relies on statistical properties of the EBL, treating the unresolved, faint galaxy population as a continuous, correlated field.
• The ACF is computed from image data, and its ellipticity (anisotropy) is used as a direct tracer of the local shear field.
• The method is validated on synthetic data and real observations of the double QSO 2345+007 and cluster Cl0024+16.
• It enables estimation of both shear and, under high source density, local magnification from the same ACF analysis.

Experimental results

Research questions

• RQ1 Can gravitational shear be measured from the anisotropy of the auto-correlation function of the extragalactic background light without detecting individual galaxies?
• RQ2 How does the tidal field from foreground mass distributions imprint a detectable anisotropy on the EBL's ACF?
• RQ3 Can the ACF-based shear measurement provide an independent and complementary estimate to traditional galaxy shape-based shear measurements?
• RQ4 Under what conditions can the intrinsic ACF of faint galaxies serve as a standard source for measuring both shear and magnification?
• RQ5 What is the feasibility and accuracy of this method when applied to real astronomical data, such as in the fields of QSO 2345+007 and cluster Cl0024+16?

Key findings

• The method successfully measures gravitational shear from the anisotropy in the ACF of the EBL, even when individual galaxies are undetectable.
• Shear maps derived from the ACF method for the double QSO 2345+007 and cluster Cl0024+16 show good agreement with published shear maps from traditional galaxy shape analysis.
• The ACF-based shear estimate is independent and complementary to galaxy-based shear measurements, thereby increasing overall measurement sensitivity.
• The intrinsic ACF of a dense population of faint galaxies can serve as a 'standard source' for measuring both shear and magnification in the same field.
• The technique is feasible and robust, as demonstrated on both synthetic data and real observational data sets.