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 improvement in the constraint on the mass is an order of magnitude better if FP residuals are included. Furthermore, we find that the mass estimator is robust to selection effects. 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 $\sigma_{\kappa,\mathrm{eff}}=0.183$. We discuss the improvements to our FP model necessary to make this formalism a practical companion to shear analyses in weak lensing surveys.