  Weak lensing can be observed through a number of effects on the images of
distant 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 density
probe the convergence field. Both contain cosmological information. In this
paper we are concerned with the magnification of the size and magnitude of
individual galaxies as a probe of cosmic convergence. We develop a Bayesian
approach for inferring the convergence field 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 size-magnitude 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 magnification (similar to intrinsic alignments for shear) and
compute the expected gains in the Dark Energy Figure-of-Merit (FoM) from
combining magnification with shear for different scenarios regarding
systematics: when accounting for intrinsic alignments but no systematics on the
magnification signal, including magnification could improve the FoM by upto a
factor of ~2.5, whilst when accounting for physical systematics in both shear
and magnification we anticipate a gain between ~25% and ~65%. In addition to
the statistical gains, the fact that cosmic shear and magnification are subject
to different systematics makes magnification an attractive complement to any
cosmic shear analysis.
