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Weak lensing can be observed through a number of effects on the images ofdistant galaxies; their shapes are sheared, their sizes and fluxes (magnitudes)are magnified and their positions on the sky are modified by the lensing field.Galaxy shapes probe the shear field whilst size, magnitude and number densityprobe the convergence field. Both contain cosmological information. In thispaper we are concerned with the magnification of the size and magnitude ofindividual galaxies as a probe of cosmic convergence. We develop a Bayesianapproach for inferring the convergence field from a measured size, magnitudeand redshift and demonstrate that the inference on convergence requiresdetailed knowledge of the joint distribution of intrinsic sizes and magnitudes.We build a simple parameterised model for the size-magnitude distribution andestimate this distribution for CFHTLenS galaxies. In light of the measureddistribution, we show that the typical dispersion on convergence estimation is~0.8, compared to ~0.38 for shear. We discuss the possibility of physicalsystematics for magnification (similar to intrinsic alignments for shear) andcompute the expected gains in the Dark Energy Figure-of-Merit (FoM) fromcombining magnification with shear for different scenarios regardingsystematics: when accounting for intrinsic alignments but no systematics on themagnification signal, including magnification could improve the FoM by upto afactor of ~2.5, whilst when accounting for physical systematics in both shearand magnification we anticipate a gain between ~25% and ~65%. In addition tothe statistical gains, the fact that cosmic shear and magnification are subjectto different systematics makes magnification an attractive complement to anycosmic shear analysis.

Weak Lensing with Sizes, Magnitudes and Shapes