Weak-Lensing Shear Response for Photometric Redshift-Based Tomographic Binning

Abstract

Dividing source galaxies into tomographic redshift bins is a cornerstone of modern weak gravitational lensing analyses, enabling measurements of the growth of cosmic structure and the nature of dark energy. In practice, these tomographic bins are defined using photometric redshift (photo-$z$) estimates. However, correlations between photo-$z$ estimates and weak lensing shear can introduce redshift-dependent selection biases in the measured shear signal; if left uncorrected, these biases distort the inferred amplitude and redshift evolution of the lensing signal, and in turn bias the measurement of the growth of cosmic structure across cosmic time. In this paper, we extend the analytical self-calibration for shear measurement (AnaCal) framework to account for photo-$z$-based selection biases in tomographic weak lensing analyses by propagating shear responses through the selection process. This approach eliminates the need for external image simulations to calibrate this correction. As a first sanity check on real data, we validate the photo-$z$ estimates derived from AnaCal fluxes on the Rubin Observatory Data Preview 1 dataset, and find that they reach photo-$z$ quality comparable to, and at high redshift slightly better than, the standard LSST estimates. We then validate the shear calibration on LSST-like image simulations with blending at the expected LSST Y10 depth, with two representative photo-$z$ algorithms -- a template-fitting method and a machine-learning method -- and show that the multiplicative shear bias induced by photo-$z$ selection remains within the LSST ten-year requirement $|m| < 3\times 10^{-3}$ across all five tomographic bins for both algorithms. These results establish AnaCal as a self-consistent pipeline for tomographic weak lensing science in upcoming LSST analyses.