Impact of line-of-sight structure on weak lensing observables of galaxy clusters

TL;DR

This work addresses how mass along the line of sight biases weak-lensing inferences of galaxy clusters. It forward-models 967 clusters from the FLAMINGO lightcone with both single-source-plane and Euclid-like source distributions, fitting spherical and elliptical NFW profiles (and a six-parameter eNFW$_6$ for BCG wobble) via Bayesian inference with Nautilus. Key results show a Euclid-like mass bias of $+5.3\pm1.4$% when using a spherical NFW model and $+6.1\pm1.3$% with an elliptical model, with a persistent axis-ratio bias of $-2.0\pm0.7$% and negligible LoS impact on BCG wobble, while concentration biases are more model-dependent and often smaller. The study also demonstrates that diagonal covariance assumptions underestimate the true LoS-driven scatter, highlighting the need to calibrate cluster-lensing pipelines on simulations with lightcone data, particularly for future deep surveys such as the Nancy Grace Roman Space Telescope. Overall, the results underscore the importance of accounting for line-of-sight structure to avoid biased mass and shape inferences and to accurately quantify uncertainties in cluster weak-lensing analyses.

Abstract

Weak gravitational lensing observations of galaxy clusters are sensitive to all mass along the line-of-sight, introducing systematic and additional statistical uncertainties due to intervening structures. We quantify their impact on the recovery of mass density profile parameters using 967 clusters from the highest-resolution FLAMINGO simulation. We construct mock weak lensing maps, including both single source plane mocks and Euclid-like mocks with a realistic source redshift distribution. Applying Bayesian inference with Nautilus, we fit spherical and elliptical Navarro-Frenk-White models to recover the cluster mass, concentration, axis ratio, and centre, which we use to measure the brightest cluster galaxy (BCG) offset from the potential centre, or `BCG wobble'. We find that the spherical model fits clusters along under-dense sight-lines better than those along over-dense ones. This introduces a positive skew in the relative error distributions for mass and concentration, which increases with source redshift. In Euclid-like mocks, this results in a mean mass bias of $+5.3\pm1.4$% (significant at $3.5σ$) when assuming a spherical NFW model. We also detect a mean axis ratio bias of $-2.0\pm0.7$% ($2.9σ$), with no significant bias in concentration. We measure a BCG wobble of ~14 kpc in our Euclid-like mocks, with negligible contribution from line-of-sight structure. Furthermore, we predict the scatter in mass estimates from future weak lensing surveys that have mean source redshifts $z_\text s \gtrsim 1.2$ (such as the Nancy Grace Roman Space Telescope), will be dominated by line-of-sight structure and hence assuming a diagonal covariance matrix will lead to overestimating the precision. We conclude that cluster weak lensing pipelines should be calibrated on simulations with lightcone data in order to properly account for the significant impact of line-of-sight structure.

Figures (10)

• Figure 1: High resolution convergence maps overlaid with reduced shear maps of an example cluster at $z=0.231$ with $M_{200}=9.9\times 10^{14} \text{ M}_\odot$. We show different lensing maps from left to right for source plane redshifts of $z_\text{s}$ = 0.8, 1.2, 2.0 and 3.0. For legibility, the reduced shear map has been down-sampled by a factor 30. At higher source redshifts, the gravitational lensing efficiency increases, but so does the amount of line-of-sight structure.
• Figure 2: The sample is subdivided into two subsamples having an over-dense (red) or under-dense (blue) line-of-sight for a given source redshift (shaded colours). Left: Median azimuthally averaged reduced tangential shear contribution from the line-of-sight, calculated as the difference between the reduced tangential shear from the CL+LoS mock and the CL mock, as a function of radius. Right: Median azimuthally averaged residuals, calculated as the difference between the reduced tangential shear from the best-fit model and the CL mock. On average, the residuals for clusters lying along over-dense and under-dense sight-lines are asymmetrically distributed around zero, potentially leading to a bias.
• Figure 3: Applying the sphNFW model we show the mean bias (top row) and scatter (bottom row) as a function of source redshift for the cluster's mass (left column) and concentration (right column), for our four mocks CL (black/dotted), CL+LoS (green/dashed), CL+$\sigma_\epsilon$ (blue/dot-dashed) and CL+LoS+$\sigma_\epsilon$ (red/solid). We estimate the bias of quantity "$\mathcal{Q}$" as the mean of the relative error distribution minus 1. We estimate the the upper bound scatter ($+$) and lower bound scatter ($-$) using the 84th- and 16th percentile of the relative error distribution, respectively.
• Figure 4: Same as Figure \ref{['fig:sph_mc_mean']}, but now employing the eNFW$_4$ model, which treats the axis ratio ($q$) as a free parameter (right column).
• Figure 5: Relative error distributions for the best-fit parameters in the Euclid+CL (purple) and Euclid+CL+LoS (orange) mocks. We show the relative error distribution for mass (left panel); concentration (right panel/top-left) under the assumption of the sphNFW model; and mass (right panel/bottom-left); concentration (right panel/top-right); and axis ratio (right panel/bottom-right) under the assumption of the eNFW$_4$ model. We report the difference of the means ($\Delta \mu$) and it's bootstrapped uncertainty on the top right of each panel. For Euclid-like data, line-of-sight structure positively biases mass estimates with the sphNFW model on the level of $+5.3\pm1.4,$%, which is significant at 3.5$\sigma$.