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

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.