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 magnifica
tion 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.
We present a galaxy group-finding algorithm, the Photo-z Probability Peaks (P3) algorithm, optimized for locating small galaxy groups using photometric redshift data by searching for peaks in the signal-to-noise of the local overdensity of galaxies i
n a three-dimensional grid. This method is an improvement over similar two-dimensional matched-filter methods in reducing background contamination through the use of redshift information, allowing it to accurately detect groups at lower richness. We present the results of tests of our algorithm on galaxy catalogues from the Millennium Simulation. Using a minimum S/N of 3 for detected groups, a group aperture size of 0.25 Mpc/h, and assuming photometric redshift accuracy of sigma_z = 0.05 it attains a purity of 84% and detects ~295 groups/deg.^2 with an average group richness of 8.6 members. Assuming photometric redshift accuracy of sigma_z = 0.02, it attains a purity of 97% and detects ~143 groups/deg.^2 with an average group richness of 12.5 members. We also test our algorithm on data available for the COSMOS field and the presently-available fields from the CFHTLS-Wide survey, presenting preliminary results of this analysis.
