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.
