Sizing the Universe with DESI Galaxy Sizes: Plain Fundamentals of Fundamental-Plane Lensing

Abstract

Weak gravitational lensing provides a powerful way to map cosmic structure, but most current measurements rely on galaxy shape distortions from deep imaging surveys and are affected by systematics such as intrinsic alignments, photometric-redshift uncertainties and shape-measurement biases. Here we present a spectroscopic galaxy-galaxy lensing magnification measurement using Fundamental-Plane (FP) size residuals, ${\delta }_r\equiv \Delta {\log }_{10}{R}_{\mathrm{e}}$, from 3.26 million DESI luminous red galaxy (LRG) sources behind DESI Bright Galaxy Survey lenses. The FP-like relation predicts the intrinsic sizes of LRGs from lensing-invariant quantities, including velocity dispersion ${\sigma }_0$ and surface brightness $I_{\mathrm{e}}$, with a scatter of about 0.06-0.07 dex. Lensing magnifies LRG sizes, giving the direct convergence response ${\delta }_r(\kappa )=\kappa /\ln 10$, but we show that the full lensing response is modified by magnification bias, because fitting $R_{\mathrm{e}}$ with $I_{\mathrm{e}}$ inevitably induces a magnitude dependence in ${\bar{\delta }}_r(m)$. After calibrating this response, we recover surface-density profiles with uncertainties comparable to those from individual Stage-III shear surveys using 5-20 million higher-redshift sources. The corresponding excess surface-density profiles agree with shear-based measurements. We further show that the estimator is robust to size-measurement uncertainties, with a convergence multiplicative bias only $\simeq -0.2$ times the size bias. FP lensing therefore provides a clean, spectroscopic and complementary probe of cosmic structure.

22 pages, 5+4 figures, submitted