Weak lensing with sizes, magnitudes and shapes

Weak lensing can be observed through a number of eects on the images of distant galaxies; their shapes are sheared, their sizes and uxes (magnitudes) are magnied and their positions on the sky are modied by the lensing eld. Galaxy shapes probe the shear eld whilst size, magnitude and number density probe the convergence eld. Both contain cosmological information. In this paper we are concerned with the magnication of the size and magnitude of individual galaxies as a probe of cosmic convergence and address three key questions: given a size, magnitude and redshift, how do we estimate the convergence eld? What is the intrinsic distribution of sizes and magnitudes for a typical lensing survey and how does the shape of this distribution determine our ability to infer convergence? For the observed size-magnitude distribution, how much additional information might we expect to extract from magnication in addition to cosmic shear? We develop a Bayesian approach for inferring the convergence eld from a measured size, magnitude and redshift and demonstrate that the inference on convergence requires detailed knowledge of the joint distribution of intrinsic sizes and magnitudes. We build a simple parameterised model for the sizemagnitude distribution and estimate this distribution for CFHTLenS galaxies. In light of the measured distribution, we show that the typical dispersion on convergence estimation is 0:8, compared to 0:38 for shear. We discuss the possibility of physical systematics for magnication (similar to intrinsic alignments for shear) and compute the expected gains in the Dark Energy Figure-of-Merit (FoM) from combining magnication with shear for dierent