Euclid: Early Release Observations. Weak gravitational lensing analysis of Abell 2390

1. Problem and Objective

The primary objective of the Euclid space telescope is to constrain cosmological parameters via weak gravitational lensing (WL) and galaxy clustering. While Euclid is designed for wide-field cosmic shear surveys, its Early Release Observations (ERO) program targeted specific massive galaxy clusters to demonstrate its capabilities in high-shear regimes.

This paper addresses the challenge of performing a robust, tomographic weak lensing analysis on a single massive cluster (Abell 2390, $z=0.228$) using early Euclid data. The specific challenges tackled include:

• Shape Measurement: Validating new forward-modeling algorithms (LensMC) against established methods (KSB+, SourceXtractor++) in the high-shear environment of a cluster.
• Source Selection & Calibration: Accurately estimating photometric redshifts ($z_{ph}$) and calibrating their distributions ($n(z)$) using limited spectroscopic data and external reference catalogs (COSMOS).
• Contamination Correction: Quantifying and correcting for the dilution of the lensing signal caused by foreground cluster members, as well as biases introduced by source obscuration (bright cluster galaxies blocking background sources) and magnification.
• Mass Reconstruction: Deriving precise mass constraints ($M_{200c}$) and validating the consistency of results across different analysis pipelines and redshift bins.

2. Methodology

Data Sources

• Euclid ERO: Observations of Abell 2390 taken in November 2023 using the VIS (optical) and NISP (near-infrared) instruments. The VIS stack has a depth of $I_E \approx 27.0$ (5$\sigma$).
• Ground-Based Data: Archival multi-band imaging from Subaru/Suprime-Cam ($B, V, R_c, i, I_c, z'$) and CFHT/Megacam ($u$-band) to enable deep photometric redshift estimation.
• Preprocessing: Images were processed using the ERO pipeline, with "Flattened" stacks used for shape analysis. A deep-learning tool (DeNeb) was employed to subtract foreground Galactic cirrus emission, significantly improving background flatness.

Photometric Redshifts ($z_{ph}$)

• Code: Used Phosphoros, a Bayesian template-fitting code.
• Calibration: Due to limited spectroscopic data in the field (mostly cluster members), the team used a Self-Organizing Map (SOM) approach. They mapped the target galaxies to the COSMOS2020 reference catalog (rich in spectroscopic redshifts) in high-dimensional photometric space.
• Bins: Galaxies were split into magnitude bins ($22 < I_E < 24.5$ and $24.5 < I_E < 26.5$) and six tomographic redshift bins. The lowest ($0.2 < z < 0.3$) and highest ($z > 2.8$) bins were excluded from the final mass fit to avoid cluster member contamination and catastrophic outliers.

Shape Measurement Algorithms

Three independent algorithms were employed to measure galaxy ellipticities:

1. LensMC: A forward-modeling Markov Chain Monte Carlo (MCMC) method, designated for Euclid DR1. It models galaxies as bulge+disc profiles.
2. KSB+: A moment-based method (Kaiser-Squires-Broadhurst) widely used in previous ground-based cluster studies.
3. SourceXtractor++ (SE++): A model-fitting code using single Sérsic profiles, primarily used for photometry but also applied here for shape estimation.

• Calibration: Multiplicative shear biases were corrected. LensMC and KSB+ uncertainties were estimated at $\sim3.2\%$ (including PSF modeling and SED dependence).

Contamination and Bias Corrections

• Cluster Members: Identified via number density profiles. The excess of sources near the cluster center (low $z_{ph}$) was modeled and subtracted.
• Obscuration: Simulated galaxy injections (using GalSim) into real images were used to map the detection probability loss caused by bright cluster galaxies.
• Magnification: Modeled using a reference NFW halo to correct for the change in source number density and size due to lensing magnification.
• Boost Factor: A radial boost factor was derived to correct the shear signal for the remaining contamination.

Mass Modeling

• Model: Spherical Navarro–Frenk–White (NFW) profile with a fixed concentration $c_{200c} = 4$ (consistent with previous studies).
• Fitting: Jointly fitted the tangential reduced shear profiles ($g_t$) of the four tomographic redshift bins and two magnitude bins over the radial range $0.5 \text{ Mpc} \le r \le 3.3 \text{ Mpc}$.
• Centering: The cluster center was fixed to the position derived from a companion strong-lensing analysis ($RA \approx 328.40494, Dec \approx 17.69460$), minimizing centering uncertainties.

3. Key Contributions

• First Detailed Euclid Cluster WL Analysis: This is the first comprehensive weak lensing analysis of a massive cluster using Euclid ERO data, demonstrating the telescope's capability for high-precision mass measurements.
• Algorithmic Validation: Provides an empirical cross-check of the new LensMC algorithm against established methods (KSB+, SE++) in a real cluster environment, confirming their consistency.
• Advanced Contamination Handling: Demonstrates a robust pipeline for correcting cluster member contamination that simultaneously accounts for source obscuration and magnification, showing that uncorrected number density profiles can misleadingly appear flat.
• Tomographic Strategy: Successfully implements a tomographic redshift binning strategy that mimics the future Euclid Wide Survey (EWS) workflow, validating the approach for future cosmological studies.
• Depth Extension: Shows that Euclid can effectively measure shapes down to $I_E \approx 26.5$, significantly deeper than the nominal EWS limit of $I_E = 24.5$, provided deep ground-based photometry is available for $z_{ph}$ estimation.

4. Results

Mass Constraints

The analysis yielded consistent mass estimates for Abell 2390 across all three shape catalogues (assuming $c_{200c}=4$):

• LensMC: $M_{200c} = 16.0 \pm 1.2 \text{ (stat)} \pm 1.7 \text{ (sys)} \times 10^{14} M_\odot$
• KSB+: $M_{200c} = 14.9 \pm 1.2 \text{ (stat)} \pm 1.6 \text{ (sys)} \times 10^{14} M_\odot$
• SE++: $M_{200c} = 14.5 \pm 1.1 \text{ (stat)} \pm 1.6 \text{ (sys)} \times 10^{14} M_\odot$

The results are in excellent agreement (within $1.2\sigma$ when including systematics) and align with previous ground-based measurements (e.g., Weighing the Giants, LoCuSS, CCCP).

Uncertainty Budget

• Statistical: Dominated by large-scale structure projections (11% relative uncertainty) and shape noise (8%).
• Systematic: The dominant systematic is shear calibration uncertainty ($\sim4.8\%$). Contamination correction and redshift calibration uncertainties contribute minimally ($<1.5\%$ combined).
• Total: The combined systematic uncertainty is approximately 5%.

Consistency Checks

• Tomographic Consistency: Mass constraints derived from individual redshift bins were consistent with the joint fit, indicating no strong redshift-dependent systematics.
• E-mode vs. B-mode: The convergence ($\kappa$) reconstruction showed a significant E-mode signal tracing the cluster galaxies, while the B-mode (rotated by $45^\circ$) was consistent with zero, confirming the removal of instrumental systematics.

5. Significance

This paper serves as a critical "proof of concept" for Euclid's weak lensing science. It demonstrates that:

1. Euclid's Resolution: The high spatial resolution ($0.1''$ pixel scale) allows for precise shape measurements even in the crowded, high-shear environment of a massive cluster.
2. Pipeline Robustness: The combination of new (LensMC) and established (KSB+, SE++) methods yields consistent results, building confidence in the Euclid data processing pipeline.
3. Future Cosmology: The successful application of tomographic binning and rigorous contamination correction validates the strategy for future Euclid cluster cosmology studies. These studies will rely on such techniques to break degeneracies between cosmological parameters and cluster mass-observable scaling relations.
4. Synergy: The analysis highlights the necessity of combining Euclid's deep space imaging with deep ground-based photometry (like Subaru or future LSST data) to maximize the utility of faint background sources for mass constraints.

In conclusion, the study confirms that Euclid is ready to deliver high-precision weak lensing mass measurements for galaxy clusters, paving the way for its primary mission of constraining dark energy and dark matter through large-scale structure.