CURLING - I. The Influence of Point-like Image Approximation on the Outcomes of Cluster Strong Lens Modeling

TL;DR

This paper investigates how approximating lensed images as point sources affects cluster strong lens modeling, revealing biases in magnification and cosmological constraints, and proposes a method to improve accuracy using extended surface brightness modeling.

Contribution

First to quantify biases from point-source approximation in JWST-like cluster lensing, and to demonstrate that modeling extended images significantly reduces these biases and enhances cosmological parameter constraints.

Findings

Point-source approximation biases magnification near critical curves.

Modeling extended surface brightness reduces magnification bias from 46.2% to 0.09%.

Improved modeling enhances the accuracy of cosmological parameter estimation.

Abstract

Cluster-scale strong lensing is a powerful tool for exploring the properties of dark matter and constraining cosmological models. However, due to the complex parameter space, pixelized strong lens modeling in galaxy clusters is computationally expensive, leading to the point-source approximation of strongly lensed extended images, potentially introducing systematic biases. Herein, as the first paper of the ClUsteR strong Lens modelIng for the Next-Generation observations (CURLING) program, we use lensing ray-tracing simulations to quantify the biases and uncertainties arising from the point-like image approximation for JWST-like observations. Our results indicate that the approximation works well for reconstructing the total cluster mass distribution, but can bias the magnification measurements near critical curves and the constraints on the cosmological parameters, the total matter density of the Universe $\Omega_{\rm m}$, and dark energy equation of state parameter $w$. To mitigate the biases, we propose incorporating the extended surface brightness distribution of lensed sources into the modeling. This approach reduces the bias in magnification from 46.2 per cent to 0.09 per cent for $\mu \sim 1000$. Furthermore, the median values of cosmological parameters align more closely with the fiducial model. In addition to the improved accuracy, we also demonstrate that the constraining power can be substantially enhanced. In conclusion, it is necessary to model cluster-scale strong lenses with pixelized multiple images, especially for estimating the intrinsic luminosity of highly magnified sources and accurate cosmography in the era of high-precision observations.