A Generalized Method for Measuring Weak Lensing Magnification With Weighted Number Counts

Abstract: We present a derivation of a generalized optimally-weighted estimator for the weak lensing magnification signal, including a calculation of errors. With this estimator, we present a local method for optimally estimating the local effects of magnification from weak gravitational lensing, using a comparison of number counts in an arbitrary region of space to the expected unmagnified number counts. We show that when equivalent lens and source samples are used, this estimator is simply related to the optimally-weighted correlation function estimator used in past work and vice-versa, but this method has the benefits that it can calculate errors with significantly less computational time, that it can handle overlapping lens and source samples, and that it can easily be extended to mass-mapping. We present a proof-of-principle test of this method on data from the CFHTLenS, showing that its calculated magnification signals agree with predictions from model fits to shear data. Finally, we investigate how magnification data can be used to supplement shear data in determining the best-fit model mass profiles for galaxy dark matter haloes. We find that at redshifts greater than z ~ 0.6, the inclusion of magnification can often significantly improve the constraints on the components of the mass profile which relate to galaxies' local environments relative to shear alone, and in high-redshift, low- and medium-mass bins, it can have a higher signal-to-noise than the shear signal.