Metacalibration of the cosmic magnification coefficient: Toward unbiased weak lensing reconstruction by counting galaxies

Weak lensing alters galaxy sizes and fluxes, influencing the clustering patterns of galaxies through cosmic magnification. This effect enables the reconstruction of weak lensing convergence $\stackrel{^}{\ensuremath{\kappa}}$ maps for Dark Energy Survey (DES) and Dark Energy Camera Legacy Survey (DECaLS) by linearly combining galaxy overdensities across magnitude bins in the $g$, $r$, and $z$ photometry bands (Qin et al.). In this study, we enhance the lensing reconstruction method by addressing biases in the magnification coefficient estimation, which arise from incomplete consideration of selection effects, especially those induced by photometric redshift (photo-$z$) selection. Using a random-forest-based photo-$z$ estimation for DECaLS and DES galaxies, we quantify the impact of photo-$z$ induced selection on magnification coefficient estimation. We characterize multiplicative bias by a factor $A$ such that $\stackrel{^}{\ensuremath{\kappa}}\ensuremath{\propto}A\ensuremath{\kappa}$, where $A$ measures the amplitude scaling of the reconstruction relative to the true convergence. Our results show that neglecting photo-$z$ selection introduces significant biases, with $A$ ranging from 0.4 to 3.5 depending on the survey, redshift, and magnitude cuts. By incorporating an improved magnification coefficient estimation that accounts for photo-$z$ selection, these biases are significantly reduced, with $A$ converging to $\ensuremath{\sim}1$ as the magnitude cuts approach optimal values. This improvement is consistently observed across DES and DECaLS datasets and redshift bins, despite differences in survey strategies and depths. These findings highlight the importance of addressing photo-$z$ induced selection to achieve unbiased weak lensing reconstructions and accurate cosmic magnification measurements.