Weak Lensing Magnification Reconstruction with the Modified Internal Linear Combination Method

Measuring weak lensing cosmic magnification signal is very challenging due to the overwhelming intrinsic clustering in the observed galaxy distribution. In this paper, we modify the Internal Linear Combination (ILC) method to reconstruct the lensing signal with an extra constraint to suppress the intrinsic clustering. To quantify the performance, we construct a realistic galaxy catalogue for the LSST-like photometric survey, covering $20\,000\ \deg^2$ with mean source redshift at $z_s\sim 1$. We find that the reconstruction performance depends on the width of the photo-z bin we choose. Due to the correlation between the lensing signal and the source galaxy distribution, the derived signal has smaller systematic bias but larger statistical uncertainty for a narrower photo-z bin. We conclude that the lensing signal reconstruction with the Modified ILC method is unbiased with a statistical uncertainty $<5\%$ for bin width $\Delta z^P = 0.2$.