Euclid: Early Release Observations. A combined strong and weak lensing solution for Abell 2390 beyond its virial radius

Technical Summary: Euclid Early Release Observations of Abell 2390

Problem and Context
Galaxy clusters serve as powerful gravitational lenses, allowing for the measurement of total mass distributions from their dense cores to regions well beyond their virial radii. While strong lensing (SL) provides high-resolution constraints on mass in the inner regions, it is limited by the mass-sheet degeneracy and restricted spatial coverage. Conversely, weak lensing (WL) extends to large radii but suffers from lower signal-to-noise ratios and atmospheric seeing limitations in ground-based observations. The challenge lies in combining these datasets to produce a unified, high-fidelity mass model that spans the entire cluster, from the central Brightest Cluster Galaxy (BCG) to the outskirts. This paper addresses this by presenting the first combined strong and weak lensing analysis of a galaxy cluster using data from the Euclid mission's Early Release Observations (ERO).

Methodology
The study focuses on the galaxy cluster Abell 2390 ($z = 0.228$). The analysis integrates two distinct datasets:

1. Weak Lensing Data: Derived from Euclid ERO VIS imaging, covering a field of view of $0.5 \text{ deg}^2$ with an angular resolution of $0.13''$ and a sampling of $0.1''$ per pixel. The authors constructed a "clean" catalogue of background galaxies by vetoing foreground and cluster member galaxies. Photometric redshifts were estimated using a combination of Euclid data and ancillary ground-based photometry from Subaru/Suprime-Cam and CFHT. Three independent shape measurement algorithms (SE++, KSB+, and LensMC) were merged to create the final shear catalogue.
2. Strong Lensing Data: The study utilizes pre-existing spectroscopic constraints from Hubble Space Telescope (HST) observations (Richard et al. 2008, 2021), including multiply imaged systems with redshifts ranging from $z \approx 0.53$ to $z \approx 4.88$.

The mass reconstruction was performed using WSLAP+, a hybrid lensing code. This method decomposes the deflection field into a superposition of 2D Gaussian functions (a free-form approach) and includes a parametric component for prominent member galaxies. The member galaxies act as a regularization factor, anchoring the solution and preventing spurious structures. The algorithm simultaneously fits the SL constraints (positions of multiple images) and WL constraints (binned shear measurements) by minimizing a residual function subject to physical constraints (positive masses). The grid resolution was adaptive, with higher density in the central region constrained by SL data.

Key Results

• Mass Profile: The combined SL+WL analysis successfully constrained the density profile over a wide radial range ($30 \text{ kpc} < r < 2000 \text{ kpc}$). The profile is well-described by a Navarro-Frenk-White (NFW) model with a concentration parameter $c = 6.5$ and a scale radius $r_s = 230 \text{ kpc}$.
• Virial Mass and Radius: The derived virial mass is $M_{200} = (1.48 \pm 0.29) \times 10^{15} M_\odot$, and the virial radius is $r_{200} = (2.05 \pm 0.13) \text{ Mpc}$.
• Consistency Checks:
  • The derived mass profile shows excellent agreement with previous X-ray results (Allen et al. 2001) that assumed hydrostatic equilibrium, indirectly confirming the cluster is in a nearly relaxed state.
  • The results are consistent with previous weak lensing studies based on ground-based data (Subaru/CFHT) and earlier strong lensing-only models.
  • The mass estimate aligns with the WL-only results derived from the same Euclid data in a companion paper (Schrabback et al. 2025).
• Morphology: The 2D mass map reveals an elongation in the Northwest-Southeast (NW-SE) direction, consistent with the distribution of X-ray emitting plasma and intracluster light. The absence of significant secondary peaks in the smooth mass distribution supports the conclusion of a relaxed dynamical state.
• Uncertainties: The authors note that uncertainties at large radii are partly driven by the mass-sheet degeneracy and the limited area of the ERO observations relative to the full field of view, as well as the reliance on ground-based data for photometric redshifts in the clean catalogue.

Significance and Claims
The paper claims that Abell 2390 represents the first example where Euclid data has been successfully combined with ancillary strong lensing data to constrain cluster masses out to and beyond the virial radius. The authors emphasize that Euclid's unique combination of wide field of view, high angular resolution, and depth allows for the detection of background galaxies down to $I_E \approx 27$ mag. This capability enables the production of similar high-quality mass models for hundreds of other clusters that possess existing strong lensing data from facilities like HST or JWST. The study demonstrates that Euclid's WL data can effectively complement existing SL constraints, overcoming the limitations of atmospheric seeing in ground-based WL and the small field of view in space-based SL-only studies. The authors conclude that while current results are limited by the specific ERO footprint and the lack of Euclid spectroscopic redshifts for the field, future full-survey data will significantly improve photometric redshift estimates and reduce mass-sheet degeneracy, further refining mass measurements for the cluster population.