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.

中文翻译：

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使用基面测量弱透镜放大率的框架

星系-星系透镜是探测暗物质晕和约束宇宙学参数的重要工具。虽然星系-星系透镜测量通常依赖于剪切力，但弱透镜放大率包含额外的约束信息。使用椭圆星系的基本平面 (FP) 来锚定背景种群的大小分布是一种已被提议用于执行放大测量的方法。我们提出了一种使用椭圆星系的 FP 残差来联合估计堆叠透镜场景的前景质量和背景红移误差的形式。FP 残差包括关于弱透镜放大率 $\kappa$ 的信息，因此前景质量，因为对于一阶，非零 $\kappa$ 影响星系大小但不影响其他 FP 属性。我们还提供了一个模块化的，使用光度测量星系调查的模拟星系目录实现形式化的可扩展代码。我们发现，将 FP 信息与观测到的源星系数量计数相结合，可以比仅包含数量计数的估计器更好地约束质量和 photo-z 误差参数。特别是，如果包含 FP 残差，则质量约束的改进要好一个数量级。此外，我们发现质量估计器对选择效应具有鲁棒性。质量为 $M_H=10^{14}M_\odot$ 的前景透镜的有效尺寸噪声，在尺寸和表面亮度方面采用保守选择函数应用于源种群，为 $\sigma_{\kappa,\mathrm{效果}}=0.183$。