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