Precision Measurement of Large Shear Signals

TL;DR

The paper addresses the problem of measuring large gravitational-shear signals near massive clusters, where traditional weak-lensing estimators fail due to nonlinearities. It introduces a non-perturbative framework, Fourier_Quad_Nulling (FQN), which extends the Fourier_Quad approach by adding pseudo-shears to null quadrupole moments, yielding unbiased estimates of the reduced shear $g$ even for $g \gtrsim 0.5$. Through extensive simulations of regular and irregular galaxy morphologies with various PSFs and noise levels, FQN demonstrates robust performance for large shear, while the original Fourier_Quad method remains accurate only in the small-shear regime; at high SNR, per-galaxy measurements with ensemble averaging are effective, whereas at low SNR a joint analysis over multiple galaxies is required. This method enables more precise reconstruction of the shear distribution around clusters, improving constraints on foreground dark matter halos and cluster mass profiles.

Abstract

So far, estimators of galaxy shape distortions are only carefully studied perturbatively in the case of small shear signals, mainly for weak lensing science. However, in the neighborhood of massive foreground clusters, a large number of background galaxies can be significantly distorted. The measurement of such large shear signals could be quite nontrivial under general observing conditions, i.e., in the presence of the point spread function (PSF) and noise. In this work, we propose a non-perturbative method to exactly recover large shear signals ($\gtrsim 0.5$) under general conditions. We test the method on simulated galaxy images, and find that it is accurate down to the very faint end. This new method is particularly useful for more accurate recovery of the shear distribution in the neighborhood of massive foreground clusters, thereby improving the modeling of the underlying dark matter halo properties.

Figures (3)

• Figure 1: An example showing the behavior of the shear bias when the shear signals become large. The blue and red surfaces refer to the results of the FQ and FQN method respectively. The contours correspond to the values of 0.005, 0.035, 0.065, 0.095, 0.125 and 0.155 respectively.
• Figure 2: An example of the shear errors in regular galaxies at SNR = 40. Different colors in the plots represent different $g_2$ ($g_1$) input values. The dot-dashed curves correspond to the FQ results, while the solid lines correspond to the FQN results. The black dashed line indicates the zero baseline for comparison.
• Figure 3: An example of the shear errors using irregular galaxies with SNR = 10. The color scheme and line styles are the same as those in Fig.\ref{['fig:moffat-noise']}.