SourceREACH (Source REconstruction of Arcs behind Cluster Halos): A New Source Reconstruction Algorithm Optimized for Giant Arcs and Galaxy Cluster Lenses

TL;DR

SourceREACH tackles the challenge of extracting high-value information from extended giant arcs to constrain cluster mass distributions and background sources. It deconvolves the PSF, delenses image-plane pixels to the source plane, and applies adaptive smoothing via interpolation or regression before re-lensing to produce a model image, using a single $\chi^2$ constraint. Through tests on mock arcs and the Abell 370 giant arc from the HFF, the authors compare Radial Basis Function, KNN, Decision Tree, and Random Forest smoothing, concluding that the KNN Ball Tree with 6 neighbors provides the best balance between noise suppression and preservation of compact source features, with runtime of a few seconds per arc. This enables efficient integration of extended-arc information into cluster-model optimization and is poised to improve high-magnification region constraints in current and upcoming surveys like Euclid and LSST.

Abstract

We introduce a new algorithm designed for use with extended lensed images, specifically giant arcs lensed by galaxy clusters. These highly magnified images contain important information about both the mass distribution of the cluster and the properties of the background source, but modeling them requires significant computational effort. Our new source reconstruction methodology is designed to be accurate and efficient for high-resolution observations in which point spread function effects are not significant. The overall process deconvolves the observed image by the point spread function, de-lenses the image pixels, and uses interpolation or regression with smoothing to determine the model source. By working with de-lensed points, the method accounts for varying resolution across the source plane. We evaluate the speed and accuracy of different interpolation and regression methods using both mock data and real data for the giant arc in Abell 370. We find that utilizing K Nearest Neighbor Regression results in the best balance of noise smoothing and preservation of compact detail in the source.

Figures (11)

• Figure 1: Top left: Data image created from the HST F814W filter from the Hubble Frontier Fields program. Top right: Data arc with light from galaxies near the arc modeled and subtracted (except for two along the left portion of the arc, which were masked instead; see Paper 1 for more discussion). Bottom left: Masked and cleaned data arc, which was the input to pixsrc for our previous optimization runs. Bottom right: Cleaned and masked data arc after deconvolution with the Richardson-Lucy algorithm.
• Figure 2: Results from our de-lensing source reconstruction applied to the idealized mock arc with no noise and no PSF. Top Row: De-lensed source prior to smoothing and isolated mock arc. Remaining Rows: Smoothing method tests on the same set of pixels as above: Radial Basis Function Interpolation, K Nearest Neighbors Regression, Decision Tree Regression, and Random Forest Regression. First Column: Model source, with lensing caustics overlaid for reference. Second Column: Residuals between the model source and the de-lensed input points. Caustics overlaid for reference. Third Column: Model arc created from the smoothed source. Critical curves overlaid for reference. Fourth Column: Residuals between the model arc and the mock data; RMS is calculated within the data mask region. Critical curves overlaid for reference.
• Figure 3: Similar to Fig. \ref{['fig:NoNoiseNoPSF']} but for the noisy mock arc with no PSF.
• Figure 4: Results from our de-lensing source reconstruction applied to the cleaned data in the F814W filter for the observed arc in Abell 370. The structure of the figure is the same as in Fig. \ref{['fig:NoNoiseNoPSF']}; note that here we compare the PSF-convolved model arc to the cleaned data arc. Here we focus on Radial Basis Function Interpolation with different options.
• Figure 5: Similar to Fig. \ref{['fig:RBF']} but for different organization routine options for K Nearest Neighbors Regression.