A Framework for Measuring Weak-Lensing Magnification Using the Fundamental Plane

TL;DR

This paper introduces a formalism and code for measuring weak-lensing magnification using the fundamental plane of elliptical galaxies, improving mass and redshift error constraints in galaxy-galaxy lensing studies.

Contribution

It develops a new formalism and a modular code to utilize FP residuals for joint estimation of foreground mass and background redshift errors, enhancing weak lensing magnification measurements.

Findings

Combining FP residuals with number counts improves mass and photo-z error constraints.

The method constrains the lens mass to 17.0% accuracy, better than 27.7% with counts alone.

Effective size noise for a $10^{14}M_\odot$ lens is $\sigma_{\kappa, ext{eff}}=0.250$.

Abstract

Galaxy-galaxy lensing is an essential tool for probing dark matter halos and constraining cosmological parameters. While galaxy-galaxy lensing measurements usually rely on shear, weak-lensing magnification contains additional constraining information. Using the fundamental plane (FP) of elliptical galaxies to anchor the size distribution of a background population is one method that has been proposed for performing a magnification measurement. We present a formalism for using the FP residuals of elliptical galaxies to jointly estimate the foreground mass and background redshift errors for a stacked lens scenario. The FP residuals include information about weak-lensing magnification $\kappa$, and therefore foreground mass, since to first order, nonzero $\kappa$ affects galaxy size but not other FP properties. We also present a modular, extensible code that implements the formalism using emulated galaxy catalogs of a photometric galaxy survey. We find that combining FP information with observed number counts of the source galaxies constrains mass and photo-z error parameters significantly better than an estimator that includes number counts only. In particular, the constraint on the mass is 17.0\% if FP residuals are included, as opposed to 27.7\% when only number counts are included. The effective size noise for a foreground lens of mass $M_H=10^{14}M_\odot$, with a conservative selection function in size and surface brightness applied to the source population, is $\sigma_{\kappa,\mathrm{eff}}=0.250$. We discuss the improvements to our FP model necessary to make this formalism a practical companion to shear analyses in weak lensing surveys.