Meta-Calibration of the Cosmic Magnification Coefficient: Toward Unbiased Weak Lensing Reconstruction by Counting Galaxies

TL;DR

This paper improves weak lensing convergence map reconstruction by correcting biases in the magnification coefficient caused by photometric redshift selection effects, leading to more accurate cosmic magnification measurements.

Contribution

The study introduces a method to account for photo-$z$ selection biases in magnification coefficient estimation, enhancing the accuracy of weak lensing reconstructions from DES and DECaLS data.

Findings

Neglecting photo-$z$ selection biases causes significant deviations in convergence map amplitude.

Incorporating photo-$z$ selection effects reduces bias, bringing the amplitude closer to unity.

Method is effective across different surveys, redshifts, and magnitude cuts.

Abstract

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 $\hat{\kappa}$ maps for DES and DECaLS by linearly combining galaxy overdensities across magnitude bins in the $g$, $r$, and $z$ photometry bands \citep{Qin+,Qin2+}. 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. Our results show that neglecting photo-$z$ selection introduces significant biases in the magnification coefficient, leading to deviations in the reconstructed convergence map amplitude $A$, with values 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 $\sim 1$ 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. Our findings highlight the importance of addressing photo-$z$ induced selection to achieve unbiased weak lensing reconstructions and accurate cosmic magnification measurements.