Magnification Bias Estimators for Realistic Surveys: an Application to the BOSS Survey

TL;DR

This paper introduces a new method to estimate magnification bias in galaxy surveys, applying it to SDSS BOSS data, and discusses its implications for future surveys and modeling.

Contribution

We develop a finite difference-based estimator for magnification bias that accounts for shape dependence and redshift evolution, with application to SDSS BOSS data.

Findings

Measured magnification biases for CMASS and LOWZ samples.

Quantified redshift evolution of magnification bias within samples.

Provided publicly available code for the estimator.

Abstract

In addition to the intrinsic clustering of galaxies themselves, the spatial distribution of galaxies observed in surveys is modulated by the presence of weak lensing due to matter in the foreground. This effect, known as magnification bias, is a significant contaminant to analyses of galaxy-lensing cross-correlations and must be carefully modelled. We present a method to estimate the magnification bias in spectroscopically confirmed galaxy samples based on finite differences of galaxy catalogues while marginalizing over errors due to finite step size. We use our estimator to measure the magnification biases of the CMASS and LOWZ samples in the SDSS BOSS galaxy survey, analytically taking into account the dependence on galaxy shape for fiber and PSF magnitudes, finding $\alpha_{\rm CMASS} = 2.71 \pm 0.02$ and $\alpha_{\rm LOWZ} = 2.45 \pm 0.02$ and quantify modelling uncertainties in these measurements. Finally, we quantify the redshift evolution of the magnification bias within the CMASS and LOWZ samples, finding a difference of up to a factor of three between the lower and upper redshift bounds for the former. We discuss how to account for this evolution in modelling and its interaction with commonly applied redshift-dependent weights. Our method should be readily-applicable to upcoming surveys and we make our code publicly available as part of this work.